Showing 1–50 of 180 results for author: Jordan, A N

Caustics and Superenergy in the Quantum Bouncer

Authors: Marko. M. Ćosić, Andrew N. Jordan

Abstract: We investigate the quantum interference and energetic phenomena associated with classical caustics in the quantum bouncing ball problem, we refer to as quantum caustics. By considering an initial Gaussian wavepacket, we show that caustics associated with the underlying classical trajectory families are exhibited. We connect the associated phase singularity chains in the vicinity of the caustic wit… ▽ More We investigate the quantum interference and energetic phenomena associated with classical caustics in the quantum bouncing ball problem, we refer to as quantum caustics. By considering an initial Gaussian wavepacket, we show that caustics associated with the underlying classical trajectory families are exhibited. We connect the associated phase singularity chains in the vicinity of the caustic with the semiclassical Pearcey function built on the cusp catastrophe lines. We also quantify the amount of superenergy exhibited in these solutions - regions of space where the local energy exceeds the largest constituent energy eigenvalue. We give a complimentary description of the caustic and superenergy behavior using the Madelung/Bohm trajectories, which gives additional insight about the energy of the trajectories and how they traverse the phase singularity chains. △ Less

Submitted 3 August, 2026; originally announced August 2026.

Comments: 14 pages of text, 7 figures, 67 references, 4 appendices

MSC Class: 81V99; 81U15

Collective charge measurement in quantum dot chains: controlling barrier occupation and tunneling current

Authors: Alok Nath Singh, Rafael Sánchez, Andrew N. Jordan

Abstract: We investigate nonequilibrium transport in a triple-quantum-dot (TQD) system, where the central dot acts as a discrete tunnel barrier, subject to continuous monitoring by a quantum point contact (QPC) that is capacitively coupled to all three dots with independently tunable strengths. We show that this global measurement scheme affects transport in a qualitatively distinct manner from single-site… ▽ More We investigate nonequilibrium transport in a triple-quantum-dot (TQD) system, where the central dot acts as a discrete tunnel barrier, subject to continuous monitoring by a quantum point contact (QPC) that is capacitively coupled to all three dots with independently tunable strengths. We show that this global measurement scheme affects transport in a qualitatively distinct manner from single-site measurement. By engineering structured dephasing, measurement provides a significant improvement in the barrier occupation and tunneling current. In the strong-measurement limit, the steady state becomes independent of the underlying Hamiltonian parameters, and the barrier occupation can approach 1/2 for suitable measurement configurations. We identify an optimal measurement configuration that maximizes the steady-state current and show that near-optimal performance can be achieved with a simple central-dot readout scheme. △ Less

Submitted 18 May, 2026; originally announced May 2026.

Shot Noise Limited Triangulation

Authors: John C. Howell, Andrew N. Jordan

Abstract: We design a system-level architecture for approaching the shot noise limit for passive triangulation of a quasi-monochromatic point source. Our emphasis is not in the novelty of the basic physics, but that existing systems lose fundamental information in the measurement pipeline. We preserve that information through maintaining analog signals combined with common-mode noise rejection in the layers… ▽ More We design a system-level architecture for approaching the shot noise limit for passive triangulation of a quasi-monochromatic point source. Our emphasis is not in the novelty of the basic physics, but that existing systems lose fundamental information in the measurement pipeline. We preserve that information through maintaining analog signals combined with common-mode noise rejection in the layers of signal processing. We review the Cramer-Rao bound of angle sensing as applied to the field of triangulation. Using a monolithic camera/balanced detector system and a doubly-layered analog voltage differential system, we experimentally achieve nanometer-scale depth precision at 1.42 meter standoff with a baseline of only 10 centimeters. While still roughly two orders of magnitude above the shot noise limit, the results represent several orders of magnitude improvement over current camera-only or other position-sensitive detector systems. The system can be further improved with vibration and turbulence mitigation. △ Less

Submitted 5 May, 2026; originally announced May 2026.

Comments: 11 pages, 3 figures

Flux Pumped Kerr-Free Parametric Amplifier

Authors: Kagan Yanik, Irwin Huang, Bibek Bhandari, Bingcheng Qing, Ahmed Hajr, Ke Wang, David I. Santiago, Irfan Siddiqi, Justin Dressel, Andrew N. Jordan

Abstract: We propose a flux-pumped superconducting parametric amplifier based on symmetrically threaded superconducting quantum interference devices (SQUIDs) that achieves a Kerr-free operating point under suitable drive conditions. Eliminating the Kerr nonlinearity is advantageous for quantum-limited amplification, as it mitigates unwanted distortions in squeezing and prevents degradation of both gain and… ▽ More We propose a flux-pumped superconducting parametric amplifier based on symmetrically threaded superconducting quantum interference devices (SQUIDs) that achieves a Kerr-free operating point under suitable drive conditions. Eliminating the Kerr nonlinearity is advantageous for quantum-limited amplification, as it mitigates unwanted distortions in squeezing and prevents degradation of both gain and quantum efficiency in the high-gain strong drive regime. By replacing the central junction in the symmetrically threaded SQUIDs (STS) configuration with a linear inductor, we find that the Kerr-nonlinearity can be eliminated and the effective Hamiltonian reduces to that of a degenerate parametric amplifier (DPA), up to higher-order corrections in the zero-point fluctuations of the superconducting phase operator. We show that the deviations from ideal DPA behavior introduced by these higher-order terms are significantly weaker than those associated with a Kerr nonlinearity. Consequently, the STS design can be driven strongly while maintaining near-quantum-limited performance at the Kerr-free point. Our analysis predicts phase-preserving gain and efficiency approaching the quantum limit, with robust operation demonstrated up to 25 dB of gain. △ Less

Submitted 13 February, 2026; originally announced February 2026.

Comments: 17 pages, 10 figures

Theory of direct measurement of the quantum pseudo-distribution via its characteristic function

Authors: Andrew N. Jordan, David R. M. Arvidsson-Shukur, Aephraim M. Steinberg

Abstract: We propose a method for directly measuring the quantum mechanical pseudo-distribution of observable properties via its characteristic function. Vandermonde matrices of the eigenvalues play a central role in the theory. This proposal directly finds the pseudo-distribution using weak measurements of the generator of position moments (momentum translations). While the pseudo-distribution can be extra… ▽ More We propose a method for directly measuring the quantum mechanical pseudo-distribution of observable properties via its characteristic function. Vandermonde matrices of the eigenvalues play a central role in the theory. This proposal directly finds the pseudo-distribution using weak measurements of the generator of position moments (momentum translations). While the pseudo-distribution can be extracted from the data in a theory-agnostic way, it is shown that under quantum-mechanical formalism, the predicted pseudo-distribution is identified with the Kirkwood-Dirac pseudo-distribution. We discuss the construction of both the joint pseudo-distribution and a conditional pseudo-distribution, which is closely connected to weak-value physics. By permuting position and momentum measurements, we give a prescription to directly probe the canonical commutation relation and verify it for any quantum state. This work establishes the theory of a characteristic function approach to pseudo-distributions, as well as providing a constructive approach to measuring them directly. △ Less

Submitted 5 February, 2026; originally announced February 2026.

Comments: 9 pages, 1 figure

Universal Characterization of Quantum Vacuum Measurement Engines

Authors: Robert Czupryniak, Bibek Bhandari, Paolo Andrea Erdman, Andrew N Jordan

Abstract: Quantum measurements can inject energy into quantum systems, enabling engines whose operation is powered entirely by measurements. We develop a general theory of quantum vacuum measurement engines by introducing the quantum vacuum bending function (QVBF), a quantity that characterizes the lowering of the ground-state energy due to interactions. We show that all thermodynamic observables, including… ▽ More Quantum measurements can inject energy into quantum systems, enabling engines whose operation is powered entirely by measurements. We develop a general theory of quantum vacuum measurement engines by introducing the quantum vacuum bending function (QVBF), a quantity that characterizes the lowering of the ground-state energy due to interactions. We show that all thermodynamic observables, including work and efficiency, are governed solely by the shape of the ground-state energy landscape encoded in the QVBF, regardless of microscopic details. We further demonstrate that work fluctuations are defined by the curvature of QVBF modulated by a model-dependent quantity, and are constrained by a generalized quantum fluctuation relation that involves the interplay between quantum Fisher information and the ground-state energy landscape. Exactly solvable models and numerical simulations of single and many-body systems confirm the theory and illustrate how the QVBF alone determines the performance of quantum vacuum measurement engines. △ Less

Submitted 3 February, 2026; originally announced February 2026.

Comments: 26 pages: 6 pages - main body, 20 pages - supplementary material. 6 figures, 2 tables

Making the Virtual Real: Measurement-Powered Tunneling Engines

Authors: Rafael Sánchez, Alok Nath Singh, Andrew N. Jordan, Bibek Bhandari

Abstract: Quantum tunneling allows electrons to be transferred between two regions separated by an energetically forbidden barrier. Performing a position measurement that finds a particle in the barrier forces the tunneling electrons to transition from having a classically forbidden energy to an energy above the barrier height. We exploit this effect to define quantum tunneling engines that can use the unco… ▽ More Quantum tunneling allows electrons to be transferred between two regions separated by an energetically forbidden barrier. Performing a position measurement that finds a particle in the barrier forces the tunneling electrons to transition from having a classically forbidden energy to an energy above the barrier height. We exploit this effect to define quantum tunneling engines that can use the unconditioned detection of virtually occupied states as a resource for power generation and cooling. Leveraging energy exchange with the detector, we show that the device can operate in a hybrid regime, enabling simultaneous cooling and power generation. Furthermore, we demonstrate measurement-assisted autonomous refrigeration and "checkpoint" cooling driven purely by a thermal bias, without the need for an applied potential. We also find a "purification-by-noise" effect when the measurement drives the system into a stationary dark state. These results underscore the intriguing dual role of measurement as a thermodynamic resource and a dark state generator. △ Less

Submitted 25 October, 2025; originally announced October 2025.

Comments: 10 pages, 7 figures

Journal ref: Phys. Rev. B 113, 125414 (2026)

Tunable Superconducting Quantum Interference Device Coupler for Fluxonium Qubits

Authors: Abhishek Chakraborty, Bibek Bhandari, D. Dominic Briseño-Colunga, Noah Stevenson, Zahra Pedramrazi, Chuan-Hong Liu, David I. Santiago, Irfan Siddiqi, Justin Dressel, Andrew N. Jordan

Abstract: Tunable couplers enable high-fidelity two-qubit gates leveraging high on/off coupling ratios and reduced crosstalk within a single design. We investigate a galvanically connected direct-current superconducting quantum interference device (dc SQUID) as a minimal tunable coupling element for fluxonium qubits. Comparing grounded and floating fluxonium designs, we find that the latter contains an extr… ▽ More Tunable couplers enable high-fidelity two-qubit gates leveraging high on/off coupling ratios and reduced crosstalk within a single design. We investigate a galvanically connected direct-current superconducting quantum interference device (dc SQUID) as a minimal tunable coupling element for fluxonium qubits. Comparing grounded and floating fluxonium designs, we find that the latter contains an extra sloshing mode that strongly hybridizes with the qubit modes, leading to significant static ZZ crosstalk. In contrast, the grounded design avoids this issue and allows suppression of static ZZ crosstalk using a shunting capacitor. Leveraging fast flux control, we present two schemes to implement two-qubit gates, predicting a $\sqrt{i\text{SWAP}}$-like gate with $99.9\%$ open-system fidelity in less than 6 nanoseconds assuming modest relaxation and dephasing rates. △ Less

Submitted 23 August, 2025; originally announced August 2025.

Comments: 16 pages, 10 figures

Development of a Chip-Scale Optical Gyroscope with Weak Measurement Amplification Readout

Authors: Kagan Yanik, Meiting Song, Yuhan Mei, Jaime Cardenas, Andrew N. Jordan

Abstract: The design of an integrated optical chip is proposed containing a rotation sensing ring resonator (optical gyroscope) coupled to an inverse weak value amplified Sagnac interferometer that amplifies the signal containing the phase information. We show that, for conservative parameter choices, our setup has a minimum detectable angular rotation rate of 0.1 deg/hr and an Allan deviation of 0.08 deg/h… ▽ More The design of an integrated optical chip is proposed containing a rotation sensing ring resonator (optical gyroscope) coupled to an inverse weak value amplified Sagnac interferometer that amplifies the signal containing the phase information. We show that, for conservative parameter choices, our setup has a minimum detectable angular rotation rate of 0.1 deg/hr and an Allan deviation of 0.08 deg/hr under expected ideal conditions. We also show that for an appropriate amount of input power, our design can improve the signal-to-noise ratio, the precision of angular rotation rate, and error in detection by more than ten times compared to a Sagnac interferometer coupled to a ring resonator. △ Less

Submitted 22 July, 2025; originally announced July 2025.

Comments: 11 pages, 6 figures

Demonstrating Superresolution in Radar Range Estimation Using a Denoising Autoencoder

Authors: Robert Czupryniak, Abhishek Chakraborty, Andrew N. Jordan, John C. Howell

Abstract: We apply machine learning methods to demonstrate range superresolution in remote sensing radar detection. Specifically, we implement a denoising autoencoder to estimate the distance between two equal intensity scatterers in the subwavelength regime. The machine learning models are trained on waveforms subject to a bandlimit constraint such that ranges much smaller than the inverse bandlimit are op… ▽ More We apply machine learning methods to demonstrate range superresolution in remote sensing radar detection. Specifically, we implement a denoising autoencoder to estimate the distance between two equal intensity scatterers in the subwavelength regime. The machine learning models are trained on waveforms subject to a bandlimit constraint such that ranges much smaller than the inverse bandlimit are optimized in their precision. The autoencoder achieves effective dimensionality reduction, with the bottleneck layer exhibiting a strong and consistent correlation with the true scatterer separation. We confirm reproducibility across different training sessions and network initializations by analyzing the scaled encoder outputs and their robustness to noise. We investigate the behavior of the bottleneck layer for the following types of pulses: a traditional sinc pulse, a bandlimited triangle-type pulse, and a theoretically near-optimal pulse created from a spherical Bessel function basis. The Bessel signal performs best, followed by the triangle wave, with the sinc signal performing worst, highlighting the crucial role of signal design in the success of machine-learning-based range resolution. △ Less

Submitted 17 June, 2025; originally announced June 2025.

Superoscillations and Physical Applications

Authors: Andrew N. Jordan, John C. Howell, Nicholas Vamivakas, Ebrahim Karimi

Abstract: This book chapter gives a selective review of physical implementations and applications of superoscillations and associated phenomena. We introduce the field by reviewing simple examples of superoscillations and showing how their existence naturally follows from the real part of the quantum mechanical weak value, which the parallel phenomena of supergrowth naturally follows from the imaginary part… ▽ More This book chapter gives a selective review of physical implementations and applications of superoscillations and associated phenomena. We introduce the field by reviewing simple examples of superoscillations and showing how their existence naturally follows from the real part of the quantum mechanical weak value, which the parallel phenomena of supergrowth naturally follows from the imaginary part. Focusing on electromagnetic applications, we review the topics of superoscillation and supergrowth in speckle, creating superoscillating hot spots with patterned filters, superspectroscopic discrimination of two molecules, noise mitigation and the engineering of super behavior in point spread functions for the purpose of optical superresolution. We also cover a variety of different methods for creating superoscillatory and supergrowing functions, reviewing both mathematical and physical ways to create this class of functions, and beyond. Promising directions for future research, including superoscillations in other wave phenomena, super radar, and generalized super-phenomena in quantum physics, are outlined. △ Less

Submitted 28 May, 2025; originally announced May 2025.

Comments: 31 pages, 14 figures

Journal ref: In: Alpay, D., Sabadini, I., Colombo, F. (eds) Operator Theory. Springer, Basel (2025)

Dynamical Sweet and Sour Regions in Bichromatically Driven Floquet Qubits

Authors: D. Dominic Briseño-Colunga, Bibek Bhandari, Debmalya Das, Long B. Nguyen, Yosep Kim, David I. Santiago, Irfan Siddiqi, Andrew N. Jordan, Justin Dressel

Abstract: Modern superconducting and semiconducting quantum hardware use external charge and microwave flux drives to both tune and operate devices. However, each external drive is susceptible to low-frequency (e.g., $1/f$) noise that can drastically reduce the decoherence lifetime of the device unless the drive is placed at specific operating points that minimize the sensitivity to fluctuations. We show th… ▽ More Modern superconducting and semiconducting quantum hardware use external charge and microwave flux drives to both tune and operate devices. However, each external drive is susceptible to low-frequency (e.g., $1/f$) noise that can drastically reduce the decoherence lifetime of the device unless the drive is placed at specific operating points that minimize the sensitivity to fluctuations. We show that operating a qubit in a driven frame using two periodic drives of distinct commensurate frequencies can have advantages over both monochromatically driven frames and static frames with constant offset drives. Employing Floquet theory, we analyze the spectral and lifetime characteristics of a two-level system under weak and strong bichromatic drives, identifying drive-parameter regions with high coherence (sweet spots) and highlighting regions where coherence is limited by additional sensitivity to noise at the drive frequencies (sour spots). We present analytical expressions for quasienergy gaps and dephasing rates, demonstrating that bichromatic driving can alleviate the trade-off between DC and AC noise robustness observed in monochromatic drives. This approach reveals continuous manifolds of doubly dynamical sweet spots, along which drive parameters can be varied without compromising coherence. Our results motivate further study of bichromatic Floquet engineering as a powerful strategy for maintaining tunability in high-coherence quantum systems. △ Less

Submitted 28 May, 2025; originally announced May 2025.

Comments: 16 pages, 5 figures

CDJ-Pontryagin Optimal Control for General Continuously Monitored Quantum Systems

Authors: Tathagata Karmakar, Andrew N. Jordan

Abstract: The Chantasri-Dressel-Jordan (CDJ) stochastic path integral formalism (Chantasri et al. 2013 and 2015) characterizes the statistics of the readouts and the most likely conditional evolution of continuously monitored quantum systems. In our work, we generalize the CDJ formalism to arbitrary continuously monitored systems by introducing a costate operator. We then prescribe a generalized Pontryagin'… ▽ More The Chantasri-Dressel-Jordan (CDJ) stochastic path integral formalism (Chantasri et al. 2013 and 2015) characterizes the statistics of the readouts and the most likely conditional evolution of continuously monitored quantum systems. In our work, we generalize the CDJ formalism to arbitrary continuously monitored systems by introducing a costate operator. We then prescribe a generalized Pontryagin's maximum principle for quantum systems undergoing arbitrary evolution and find conditions on optimal control protocols. We show that the CDJ formalism's most likely path can be cast as a quantum Pontryagin's maximum principle, where the cost function is the readout probabilities along a quantum trajectory. This insight allows us to derive general optimal control equations for arbitrary control parameters. We apply our results to a monitored oscillator in the presence of a parametric quadratic potential and variable quadrature measurements. We find the optimal potential strength and quadrature angle for fixed-end point problems. The optimal parametric potential is analytically shown to have a "bang-bang" form. We apply our protocol to three quantum oscillator examples relevant to Bosonic quantum computing. The first example considers a binomial codeword preparation from an error word, the second example looks into cooling to the ground state from an even cat state, and the third example investigates a cat state to cat state evolution. We compare the statistics of the fidelities of the final state with respect to the target state for trajectories generated under the optimal control with those generated under a sample control. Compared to the latter case, we see a 40-196% increase in the number of trajectories reaching more than 95% fidelities under the optimal control. Our work provides a systematic prescription for finding quantum optimal control for continuously monitored systems. △ Less

Submitted 14 March, 2026; v1 submitted 10 April, 2025; originally announced April 2025.

Comments: 42 pages, 9 figures

Journal ref: Quantum 10, 2043 (2026)

Capturing an Electron in the Virtual State

Authors: Alok Nath Singh, Bibek Bhandari, Rafael Sánchez, Andrew N. Jordan

Abstract: We address a foundational question in quantum mechanics: Can a particle be directly found in a classically forbidden virtual state? We instantiate this conceptual question by investigating the traversal of electrons through a tunnel barrier, which we define in a triple quantum dot (TQD) system where the occupation of the central dot is energetically avoided. The motivation behind this setup is to… ▽ More We address a foundational question in quantum mechanics: Can a particle be directly found in a classically forbidden virtual state? We instantiate this conceptual question by investigating the traversal of electrons through a tunnel barrier, which we define in a triple quantum dot (TQD) system where the occupation of the central dot is energetically avoided. The motivation behind this setup is to answer whether the central dot is occupied or not during a virtual transition when it is being explicitly monitored. We investigate this problem in two different limits of continuous measurements: the stochastic quantum diffusion and the quantum jump. We find that, even though individual trajectories differ considerably across these limits, measuring leads to a higher occupation in the central dot on average. Our results demonstrate that the act of observation fundamentally reshapes tunneling dynamics, resolving the seeming paradox of detecting a particle in a classically forbidden region: weak measurements partially localize the particle, while strong measurements enforce a discontinuous either/or detection or no detection outcome. △ Less

Submitted 20 July, 2026; v1 submitted 13 March, 2025; originally announced March 2025.

Comments: v3: Updated to match the published version in New Journal of Physics

Journal ref: New J. Phys. 28 074503 (2026)

Revealing the fuel of a quantum continuous measurement-based refrigerator

Authors: Cyril Elouard, Sreenath K. Manikandan, Andrew N. Jordan, Geraldine Haack

Abstract: While quantum measurements have been shown to constitute a resource for operating quantum thermal machines, the nature of the energy exchanges involved in the interaction between system and measurement apparatus is still under debate. In this work, we show that a microscopic model of the apparatus is necessary to unambiguously determine whether quantum measurements provide energy in the form of he… ▽ More While quantum measurements have been shown to constitute a resource for operating quantum thermal machines, the nature of the energy exchanges involved in the interaction between system and measurement apparatus is still under debate. In this work, we show that a microscopic model of the apparatus is necessary to unambiguously determine whether quantum measurements provide energy in the form of heat or work. We illustrate this result by considering a measurement-based refrigerator, made of a double quantum dot embedded in a two-terminal device, with the charge of one of the dots being continuously monitored. Tuning the parameters of the measurement device interpolates between a heat- and a work-fueled regimes with very different thermodynamic efficiency. Notably, we demonstrate a trade-off between a maximal thermodynamic efficiency when the measurement-based refrigerator is fueled by heat and a maximal measurement efficiency quantified by the signal-to-noise ratio in the work-fueled regime. Our analysis offers a new perspective on the nature of the energy exchanges occurring during a quantum measurement, paving the way for energy optimization in quantum protocols and quantum machines. △ Less

Submitted 2 February, 2026; v1 submitted 14 February, 2025; originally announced February 2025.

Comments: Published version

Journal ref: Phys. Rev. E 113, 014134 (2026)

Entanglement dynamics in collision models and entanglement quilts

Authors: Le Hu, Andrew N. Jordan

Abstract: We study the entanglement dynamics of a family of quantum collision models by analytically solving the pairwise concurrence for all qubit pairs. We introduce a diagrammatic method that offers an intuitive, frame-by-frame understanding of these dynamics. This allows us to monitor how a single collision affects the entanglement of the whole many-body system in some special cases. We focus on a class… ▽ More We study the entanglement dynamics of a family of quantum collision models by analytically solving the pairwise concurrence for all qubit pairs. We introduce a diagrammatic method that offers an intuitive, frame-by-frame understanding of these dynamics. This allows us to monitor how a single collision affects the entanglement of the whole many-body system in some special cases. We focus on a class of models where the square of concurrence is a conserved quantity in the qubit collisions, aiding us to formulate general rules of entanglement propagation. In particular, among the multiple examples we will be showing, we identify a type of genuine multipartite entanglement, which we refer to as \textit{entanglement quilt}, where every qubit is entangled with every other qubit. We find that in some models, an entanglement quilt is hypersensitive to local excitation fluctuations: The presence of even a single excited qubit can destroy the entanglement quilts. We offer a detailed mathematical treatment on the phenomena, which can help us understand the disappearance of long-range entanglement in condensed matter systems above zero temperature. We also speculate about a possible property of the entanglement quilt: Every subsystem of it is entangled with every other subsystem. △ Less

Submitted 21 January, 2025; originally announced January 2025.

Comments: 14+7 pages, 10 figures

GPU-accelerated Effective Hamiltonian Calculator

Authors: Abhishek Chakraborty, Taylor L. Patti, Brucek Khailany, Andrew N. Jordan, Anima Anandkumar

Abstract: Effective Hamiltonian calculations for large quantum systems can be both analytically intractable and numerically expensive using standard techniques. In this manuscript, we present numerical techniques inspired by Nonperturbative Analytical Diagonalization (NPAD) and the Magnus expansion for the efficient calculation of effective Hamiltonians. While these tools are appropriate for a wide array of… ▽ More Effective Hamiltonian calculations for large quantum systems can be both analytically intractable and numerically expensive using standard techniques. In this manuscript, we present numerical techniques inspired by Nonperturbative Analytical Diagonalization (NPAD) and the Magnus expansion for the efficient calculation of effective Hamiltonians. While these tools are appropriate for a wide array of applications, we here demonstrate their utility for models that can be realized in circuit-QED settings. Our numerical techniques are available as an open-source Python package, ${\rm qCH_{eff}}$, which is available on GitHub (https://github.com/NVlabs/qCHeff) and PyPI (https://pypi.org/project/qcheff/). We use the CuPy library for GPU-acceleration and report up to 15x speedup on GPU over CPU for NPAD, and up to 42x speedup for the Magnus expansion (compared to QuTiP), for large system sizes. △ Less

Submitted 1 December, 2025; v1 submitted 15 November, 2024; originally announced November 2024.

Comments: 20 pages, 8 figures. The source code is available at https://github.com/NVlabs/qCHeff

Journal ref: Quantum 9, 1946 (2025)

Quantum Benchmarking of High-Fidelity Noise-Biased Operations on a Detuned-Kerr-Cat Qubit

Authors: Bingcheng Qing, Ahmed Hajr, Ke Wang, Gerwin Koolstra, Long B. Nguyen, Jordan Hines, Irwin Huang, Bibek Bhandari, Larry Chen, Ziqi Kang, Christian Jünger, Noah Goss, Nikitha Jain, Hyunseong Kim, Kan-Heng Lee, Akel Hashim, Nicholas E. Frattini, Zahra Pedramrazi, Justin Dressel, Andrew N. Jordan, David I. Santiago, Irfan Siddiqi

Abstract: Ubiquitous noises in quantum systems remain a key obstacle to building quantum computers, necessitating the use of quantum error correction codes. Recently, error-correcting codes tailored for noise-biased systems have been shown to offer high fault-tolerance thresholds and reduced hardware overhead, positioning noise-biased qubits as promising candidates for building universal quantum computers.… ▽ More Ubiquitous noises in quantum systems remain a key obstacle to building quantum computers, necessitating the use of quantum error correction codes. Recently, error-correcting codes tailored for noise-biased systems have been shown to offer high fault-tolerance thresholds and reduced hardware overhead, positioning noise-biased qubits as promising candidates for building universal quantum computers. However, quantum operations on these platforms remain challenging, and their noise structures have not yet been rigorously benchmarked to the same extent as those of conventional quantum hardware. In this work, we develop a comprehensive quantum control toolbox for a scalable noise-biased qubit, detuned Kerr-cat qubit, including initialization, universal single-qubit gates and quantum non-demolition readout. We systematically characterize the noise structure of these operations using gate set tomography and dihedral randomized benchmarking, achieving high local gate fidelities, with $\mathcal{F}[Z(π/2)]=99.2\%$ and $\mathcal{F}[X(π/2)]=92.5\%$. Notably, the noise bias of the detuned Kerr-cat qubit approaches 250, which outperforms its resonant-Kerr-cat qubit counterparts as reported previously, representing a new state-of-the-art performance benchmark for noise-biased qubits. Moreover, our results reveal a critical overestimation of operational noise bias inferred from bit-flip and phase-flip times alone, highlighting the necessity of a precise and direct benchmarking for noise-biased qubit operations. Our work thus establishes a framework for systematically characterizing and validating the performance of quantum operations in structured-noise architectures, which lays the groundwork for implementing efficient quantum error correction in next-generation architectures. △ Less

Submitted 7 August, 2025; v1 submitted 7 November, 2024; originally announced November 2024.

Comments: 16 pages, 13 figures

Measurement time of weak measurements on large entangled systems

Authors: Truong-Son P. Van, Andrew N. Jordan, David W. Snoke

Abstract: It is well established that starting only with strong, projective quantum measurements, experiments can be designed to allow weak measurements, which lead to random walk between the possible final measurement outcomes. However, one can ask the reverse question: starting with only weak measurements, can all the results of standard strong measurements be recovered? Prior work has shown that some res… ▽ More It is well established that starting only with strong, projective quantum measurements, experiments can be designed to allow weak measurements, which lead to random walk between the possible final measurement outcomes. However, one can ask the reverse question: starting with only weak measurements, can all the results of standard strong measurements be recovered? Prior work has shown that some results can be, such as the Born rule for the probability of measurement outcomes as a function of wave intensity. In this paper we show that another crucial result can be reproduced by purely weak measurements, namely the collapse of a many-body, nonlocally entangled wave function on a time scale comparable to the characteristic time of a single, local measurement; for an entangled state of a single excitation among $N$ qubits, we find the collapse time scales as a double logarithm of $N$. This result affirms the self-consistency of the hypothesis that spontaneous weak measurements lie at the base of all physical measurements, independent of human observers. △ Less

Submitted 5 February, 2025; v1 submitted 10 October, 2024; originally announced October 2024.

Comments: Update title

Reconstructing Superoscillations Buried Deeply in Noise

Authors: Derek D. White, Shunxing Zhang, Barbara Soda, Achim Kempf, Daniele C. Struppa, Andrew N. Jordan, John C. Howell

Abstract: We utilize a method using frequency combs to construct waves that feature superoscillations - local regions of the wave that exhibit a change in phase that the bandlimits of the wave should not otherwise allow. This method has been shown to create superoscillating regions that mimic any analytic function - even ones well outside the bandlimits - to an arbitrary degree of accuracy. We experimentall… ▽ More We utilize a method using frequency combs to construct waves that feature superoscillations - local regions of the wave that exhibit a change in phase that the bandlimits of the wave should not otherwise allow. This method has been shown to create superoscillating regions that mimic any analytic function - even ones well outside the bandlimits - to an arbitrary degree of accuracy. We experimentally demonstrate that these waves are extremely robust against noise, allowing for accurate reconstruction of a superoscillating target function thoroughly buried in noise. We additionally show that such a construction can be easily used to range-resolve a signal well below the commonly accepted fundamental limit. △ Less

Submitted 10 October, 2024; v1 submitted 7 October, 2024; originally announced October 2024.

Artificially intelligent Maxwell's demon for optimal control of open quantum systems

Authors: Paolo Andrea Erdman, Robert Czupryniak, Bibek Bhandari, Andrew N. Jordan, Frank Noé, Jens Eisert, Giacomo Guarnieri

Abstract: Feedback control of open quantum systems is of fundamental importance for practical applications in various contexts, ranging from quantum computation to quantum error correction and quantum metrology. Its use in the context of thermodynamics further enables the study of the interplay between information and energy. However, deriving optimal feedback control strategies is highly challenging, as it… ▽ More Feedback control of open quantum systems is of fundamental importance for practical applications in various contexts, ranging from quantum computation to quantum error correction and quantum metrology. Its use in the context of thermodynamics further enables the study of the interplay between information and energy. However, deriving optimal feedback control strategies is highly challenging, as it involves the optimal control of open quantum systems, the stochastic nature of quantum measurement, and the inclusion of policies that maximize a long-term time- and trajectory-averaged goal. In this work, we employ a reinforcement learning approach to automate and capture the role of a quantum Maxwell's demon: the agent takes the literal role of discovering optimal feedback control strategies in qubit-based systems that maximize a trade-off between measurement-powered cooling and measurement efficiency. Considering weak or projective quantum measurements, we explore different regimes based on the ordering between the thermalization, the measurement, and the unitary feedback timescales, finding different and highly non-intuitive, yet interpretable, strategies. In the thermalization-dominated regime, we find strategies with elaborate finite-time thermalization protocols conditioned on measurement outcomes. In the measurement-dominated regime, we find that optimal strategies involve adaptively measuring different qubit observables reflecting the acquired information, and repeating multiple weak measurements until the quantum state is "sufficiently pure", leading to random walks in state space. Finally, we study the case when all timescales are comparable, finding new feedback control strategies that considerably outperform more intuitive ones. We discuss a two-qubit example where we explore the role of entanglement and conclude discussing the scaling of our results to quantum many-body systems. △ Less

Submitted 27 August, 2024; originally announced August 2024.

Comments: 16+10 pages, 21 figures

Journal ref: Quantum Science and Technology 10, 025047 (2025)

Symmetrically Threaded Superconducting Quantum Interference Devices As Next Generation Kerr-cat Qubits

Authors: Bibek Bhandari, Irwin Huang, Ahmed Hajr, Kagan Yanik, Bingcheng Qing, Ke Wang, David I Santiago, Justin Dressel, Irfan Siddiqi, Andrew N Jordan

Abstract: We theoretically explore an alternative circuit for Kerr-cat qubits based on symmetrically threaded Superconducting Quantum Interference Devices (SQUID). The Symmetrically Threaded SQUIDs (STS) architecture employs a simplified flux-pumped design that suppresses two-photon dissipation, a dominant loss mechanism in high-Kerr regimes, by engineering the drive Hamiltonian's flux operator to generate… ▽ More We theoretically explore an alternative circuit for Kerr-cat qubits based on symmetrically threaded Superconducting Quantum Interference Devices (SQUID). The Symmetrically Threaded SQUIDs (STS) architecture employs a simplified flux-pumped design that suppresses two-photon dissipation, a dominant loss mechanism in high-Kerr regimes, by engineering the drive Hamiltonian's flux operator to generate only even-order harmonics. By fulfilling two critical criteria for practical Kerr-cat qubit operation, the STS emerges as an ideal platform: (1) a static Hamiltonian with diluted Kerr nonlinearity (achieved via the STS's middle branch) and (2) a drive Hamiltonian restricted to even harmonics, which ensures robust two-photon driving with reduced dissipation. For weak Kerr nonlinearity, we find that the coherent state lifetime ($T_α$) is similar between STS and SNAIL circuits. However, STS Kerr-cat qubits exhibit enhanced resistance to higher-order photon dissipation, enabling significantly extended $T_α$ even with stronger Kerr nonlinearities ($\sim$10 MHz). In contrast to SNAIL, STS Kerr-cat qubits display a $T_α$ dip under weak two-photon driving for high Kerr coefficient. We demonstrate that this dip can be suppressed by applying drive-dependent detuning, enabling Kerr-cat qubit operation with only eight Josephson junctions (of energies 80 GHz); fewer junctions suffice for higher junction energies. We further validate the robustness of the STS design by studying the impact of strong flux driving and asymmetric Josephson junctions on $T_α$. With the proposed design and considering a cat size of 10 photons, we predict $T_α$ of the order of tens of milliseconds, even in the presence of multi-photon heating and dephasing effects. △ Less

Submitted 30 July, 2025; v1 submitted 18 May, 2024; originally announced May 2024.

Comments: 29 pages, 14 figures

Journal ref: PRX Quantum 6, 030338 (2025)

The Best Radar Ranging Pulse to Resolve Two Reflectors

Authors: Andrew N. Jordan, John C. Howell, Achim Kempf, Shunxing Zhang, Derek White

Abstract: Previous work established fundamental bounds on subwavelength resolution for the radar range resolution problem, called superradar [Phys. Rev. Appl. 20, 064046 (2023)]. In this work, we identify the optimal waveforms for distinguishing the range resolution between two reflectors of identical strength. We discuss both the unnormalized optimal waveform as well as the best square-integrable pulse, an… ▽ More Previous work established fundamental bounds on subwavelength resolution for the radar range resolution problem, called superradar [Phys. Rev. Appl. 20, 064046 (2023)]. In this work, we identify the optimal waveforms for distinguishing the range resolution between two reflectors of identical strength. We discuss both the unnormalized optimal waveform as well as the best square-integrable pulse, and their variants. Using orthogonal function theory, we give an explicit algorithm to optimize the wave pulse in finite time to have the best performance. We also explore range resolution estimation with unnormalized waveforms with multi-parameter methods to also independently estimate loss and time of arrival. These results are consistent with the earlier single parameter approach of range resolution only and give deeper insight into the ranging estimation problem. Experimental results are presented using radio pulse reflections inside coaxial cables, showing robust range resolution smaller than a tenth of the inverse bandedge, with uncertainties close to the derived Cramér-Rao bound. △ Less

Submitted 11 May, 2024; originally announced May 2024.

Comments: 8 pages, 8 figures

Journal ref: Phys. Rev. Research 6, 033341 - Published 27 September, 2024

Giant Thermoelectric Response of Fluxons in Superconductors

Authors: Alok Nath Singh, Bibek Bhandari, Alessandro Braggio, Francesco Giazotto, Andrew N. Jordan

Abstract: Thermoelectric devices that operate on quantum principles have been under extensive investigation in the past decades. These devices are at the fundamental limits of miniaturized heat engines and refrigerators, advancing the field of quantum thermodynamics. Most research in this area concerns the use of conduction electrons and holes as charge and heat carriers, and only very recently have superco… ▽ More Thermoelectric devices that operate on quantum principles have been under extensive investigation in the past decades. These devices are at the fundamental limits of miniaturized heat engines and refrigerators, advancing the field of quantum thermodynamics. Most research in this area concerns the use of conduction electrons and holes as charge and heat carriers, and only very recently have superconductors been considered as thermal engines and thermoelectric devices. Here, we investigate the thermoelectric response of an Abrikosov vortex in type-II superconductors in the deep quantum limit. We consider two thermoelectric geometries, a type-II SIN junction and a local Scanning Tunneling Microscope (STM)-tip normal metal probe over the superconductor. We exploit the strong breaking of particle-hole symmetry in bound states at sub-gap energies within the superconducting vortex to realize a giant thermoelectric response in the presence of fluxons. We predict a thermovoltage of a few mV/K at sub-Kelvin temperatures using both semi-analytic and numerical self-consistent solutions of the Bogoliubov-de Gennes equations. Relevant thermoelectric coefficients and figures of merit are found within our model, both in linear and nonlinear regimes. The ZT of the SIN junction is around 1, rising to above 3 for the STM junction centered at the vortex core. We also discuss how this system can be used as a sensitive thermocouple, diode, or localized bolometer to detect low-energy single photons. △ Less

Submitted 8 May, 2024; originally announced May 2024.

Comments: 11 pages, 4 figures

Journal ref: Phys. Rev. Lett. 133, 256002 (2024)

High-Coherence Kerr-cat qubit in 2D architecture

Authors: Ahmed Hajr, Bingcheng Qing, Ke Wang, Gerwin Koolstra, Zahra Pedramrazi, Ziqi Kang, Larry Chen, Long B. Nguyen, Christian Junger, Noah Goss, Irwin Huang, Bibek Bhandari, Nicholas E. Frattini, Shruti Puri, Justin Dressel, Andrew N. Jordan, David Santiago, Irfan Siddiqi

Abstract: The Kerr-cat qubit is a bosonic qubit in which multi-photon Schrodinger cat states are stabilized by applying a two-photon drive to an oscillator with a Kerr nonlinearity. The suppressed bit-flip rate with increasing cat size makes this qubit a promising candidate to implement quantum error correction codes tailored for noise-biased qubits. However, achieving strong light-matter interactions neces… ▽ More The Kerr-cat qubit is a bosonic qubit in which multi-photon Schrodinger cat states are stabilized by applying a two-photon drive to an oscillator with a Kerr nonlinearity. The suppressed bit-flip rate with increasing cat size makes this qubit a promising candidate to implement quantum error correction codes tailored for noise-biased qubits. However, achieving strong light-matter interactions necessary for stabilizing and controlling this qubit has traditionally required strong microwave drives that heat the qubit and degrade its performance. In contrast, increasing the coupling to the drive port removes the need for strong drives at the expense of large Purcell decay. By integrating an effective band-block filter on-chip, we overcome this trade-off and realize a Kerr-cat qubit in a scalable 2D superconducting circuit with high coherence. This filter provides 30 dB of isolation at the qubit frequency with negligible attenuation at the frequencies required for stabilization and readout. We experimentally demonstrate quantum non-demolition readout fidelity of 99.6% for a cat with 8 photons. Also, to have high-fidelity universal control over this qubit, we combine fast Rabi oscillations with a new demonstration of the X(90) gate through phase modulation of the stabilization drive. Finally, the lifetime in this architecture is examined as a function of the cat size of up to 10 photons in the oscillator achieving a bit-flip time higher than 1 ms and only a linear decrease in the phase-flip time, in good agreement with the theoretical analysis of the circuit. Our qubit shows promise as a building block for fault-tolerant quantum processors with a small footprint. △ Less

Submitted 19 May, 2024; v1 submitted 25 April, 2024; originally announced April 2024.

Exploring the Accuracy of Interferometric Quantum Measurements under Conservation Laws

Authors: Nicolò Piccione, Maria Maffei, Andrew N. Jordan, Kater W. Murch, Alexia Auffèves

Abstract: A (target) quantum system is often measured through observations performed on a second (meter) system to which the target is coupled. In the presence of global conservation laws holding on the joint meter-target system, the Wigner-Araki-Yanase theorem and its generalizations predict a lower-bound on the measurement's error (Ozawa's bound). While practically negligible for macroscopic meters, it be… ▽ More A (target) quantum system is often measured through observations performed on a second (meter) system to which the target is coupled. In the presence of global conservation laws holding on the joint meter-target system, the Wigner-Araki-Yanase theorem and its generalizations predict a lower-bound on the measurement's error (Ozawa's bound). While practically negligible for macroscopic meters, it becomes relevant for microscopic ones. Here, we propose a simple interferometric setup, arguably within reach of present technology, in which a flying particle (a microscopic quantum meter) is used to measure a qubit by interacting with it in one arm of the interferometer. In this scenario, the globally conserved quantity is the total energy of particle and qubit. We show how the measurement error, $\varepsilon$, is linked to the non-stationary nature of the measured observable and the finite duration of the target-meter interaction while Ozawa's bound, $\varepsilon_{\mathrm B}$, only depends on the momentum uncertainty of the meter's wavepacket. When considering short wavepackets with respect to the evolution time of the qubit, we show that $\varepsilon/\varepsilon_{\mathrm B}$ is strictly tied to the position-momentum uncertainty of the meter's wavepacket and $\varepsilon/\varepsilon_{\mathrm B} \rightarrow 1$ only when employing Gaussian wavepackets. On the contrary, long wavepackets of any shape lead to $\varepsilon/\varepsilon_{\mathrm B} \rightarrow \sqrt{2}$. In addition to their fundamental relevance, our findings have important practical consequences for optimal resource management in quantum technologies. △ Less

Submitted 19 December, 2024; v1 submitted 19 April, 2024; originally announced April 2024.

Comments: 5 pages plus appendices. 2 Figures

Journal ref: Phys. Rev. Lett. 133, 240202 (2024)

Properties and Applications of the Kirkwood-Dirac Distribution

Authors: David R. M. Arvidsson-Shukur, William F. Braasch Jr., Stephan De Bievre, Justin Dressel, Andrew N. Jordan, Christopher Langrenez, Matteo Lostaglio, Jeff S. Lundeen, Nicole Yunger Halpern

Abstract: Recent years have seen the Kirkwood-Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be applied to problems in quantum-information processing. A notable difference to the Wigner function is that the KD distribution can represent a quantum state in te… ▽ More Recent years have seen the Kirkwood-Dirac (KD) distribution come to the forefront as a powerful quasi-probability distribution for analysing quantum mechanics. The KD distribution allows tools from statistics and probability theory to be applied to problems in quantum-information processing. A notable difference to the Wigner function is that the KD distribution can represent a quantum state in terms of arbitrary observables. This paper reviews the KD distribution, in three parts. First, we present definitions and basic properties of the KD distribution and its generalisations. Second, we summarise the KD distribution's extensive usage in the study or development of measurement disturbance; quantum metrology; weak values; direct measurements of quantum states; quantum thermodynamics; quantum scrambling and out-of-time-ordered correlators; and the foundations of quantum mechanics, including Leggett-Garg inequalities, the consistent-histories interpretation and contextuality. We emphasise connections between operational quantum advantages and negative or non-real KD quasi-probabilities. Third, we delve into the KD distribution's mathematical structure. We summarise the current knowledge regarding the geometry of KD-positive states (the states for which the KD distribution is a classical probability distribution), describe how to witness and quantify KD non-positivity, and outline relationships between KD non-positivity, coherence and observables' incompatibility. △ Less

Submitted 3 January, 2025; v1 submitted 27 March, 2024; originally announced March 2024.

Comments: 42 pages, 14 figures; as published in NJP

Journal ref: New J. Phys., 26, 121201, (2024)

Quantum energetics of a non-commuting measurement

Authors: Xiayu Linpeng, Nicolò Piccione, Maria Maffei, Léa Bresque, Samyak P. Prasad, Andrew N. Jordan, Alexia Auffèves, Kater W. Murch

Abstract: When a measurement observable does not commute with a quantum system's Hamiltonian, the energy of the measured system is typically not conserved during the measurement. Instead, energy can be transferred between the measured system and the meter. In this work, we experimentally investigate the energetics of non-commuting measurements in a circuit quantum electrodynamics system containing a transmo… ▽ More When a measurement observable does not commute with a quantum system's Hamiltonian, the energy of the measured system is typically not conserved during the measurement. Instead, energy can be transferred between the measured system and the meter. In this work, we experimentally investigate the energetics of non-commuting measurements in a circuit quantum electrodynamics system containing a transmon qubit embedded in a 3D microwave cavity. We show through spectral analysis of the cavity photons that a frequency shift is imparted on the probe, in balance with the associated energy changes of the qubit. Our experiment provides new insights into foundations of quantum measurement, as well as a better understanding of the key mechanisms at play in quantum energetics. △ Less

Submitted 27 November, 2023; v1 submitted 22 November, 2023; originally announced November 2023.

Comments: 9 pages, 4 figures

Fundamental mechanisms of energy exchanges in autonomous measurements based on dispersive qubit-light interaction

Authors: Nicolò Piccione, Maria Maffei, Xiayu Linpeng, Andrew N. Jordan, Kater W. Murch, Alexia Auffèves

Abstract: Measuring an observable which does not commute with the Hamiltonian of a quantum system usually modifies the mean energy of this system. In an autonomous measurement scheme, coupling the system to a quantum meter, the system's energy change must be compensated by the meter's energy change. Here, we theoretically study such an autonomous meter-system dynamics: a qubit interacting dispersively with… ▽ More Measuring an observable which does not commute with the Hamiltonian of a quantum system usually modifies the mean energy of this system. In an autonomous measurement scheme, coupling the system to a quantum meter, the system's energy change must be compensated by the meter's energy change. Here, we theoretically study such an autonomous meter-system dynamics: a qubit interacting dispersively with a light pulse propagating in a one-dimensional waveguide. The phase of the light pulse is shifted, conditioned to the qubit's state along the $z$-direction, while the orientation of the qubit Hamiltonian is arbitrary. As the interaction is dispersive, photon number is conserved so that energy balance has to be attained by spectral deformations of the light pulse. Building on analytical and numerical solutions, we reveal the mechanism underlying this spectral deformation and display how it compensates for the qubit's energy change. We explain the formation of a three-peak structure of the output spectrum and we provide the conditions under which this is observable. △ Less

Submitted 3 July, 2024; v1 submitted 20 November, 2023; originally announced November 2023.

Comments: 9 pages plus appendices, 9 figures

Journal ref: Phys. Rev. A 109, 063707 (2024)

Signs of the rates in the Lindblad master equations can always be arbitrarily determined

Authors: Le Hu, Andrew N. Jordan

Abstract: Determining the Markovianity and non-Markovianity of a quantum process is a critical problem in the theory of open quantum systems, as their behaviors differ significantly in terms of complexity. It is well recognized that a quantum process is Markovian if and only if the quantum master equation can be written in the standard Lindblad form with all rates nonnegative for all time. However, here we… ▽ More Determining the Markovianity and non-Markovianity of a quantum process is a critical problem in the theory of open quantum systems, as their behaviors differ significantly in terms of complexity. It is well recognized that a quantum process is Markovian if and only if the quantum master equation can be written in the standard Lindblad form with all rates nonnegative for all time. However, here we present a striking result that \textit{any} finite-dimensional open quantum system dynamics can be described by a quantum master equation in the Lindblad form with all rates nonnegative for all time. In fact, it can be shown that one can arbitrarily decide the sign of the rates in any case at any time interval. Note that here we take an unconventional approach where the quantum master equation we construct will in general be state-dependent, which means that the Hamiltonian, jump operators and rates will all depend on the current state of the density matrix $ρ(t)$. Our findings raise serious questions on the current criterion in determining Markovianity and non-Markovianity in open quantum system dynamics. △ Less

Submitted 27 October, 2023; originally announced October 2023.

Comments: 5 pages

Experimental realization of supergrowing fields

Authors: Sethuraj K. R., Tathagata Karmakar, S. A. Wadood, Andrew N. Jordan, A. Nick Vamivakas

Abstract: Supergrowth refers to the local amplitude growth rate of a signal being faster than its fastest Fourier mode. In contrast, superoscillation pertains to the variation of the phase. Compared to the latter, supergrowth can have exponentially higher intensities and promises improvement over superoscillation-based superresolution imaging. Here, we demonstrate the experimental synthesis of controlled su… ▽ More Supergrowth refers to the local amplitude growth rate of a signal being faster than its fastest Fourier mode. In contrast, superoscillation pertains to the variation of the phase. Compared to the latter, supergrowth can have exponentially higher intensities and promises improvement over superoscillation-based superresolution imaging. Here, we demonstrate the experimental synthesis of controlled supergrowing fields with a maximum growth rate of ~19.1 times the system-bandlimit. Our work is an essential step toward realizing supergrowth-based far-field superresolution imaging. △ Less

Submitted 30 August, 2023; originally announced September 2023.

Fundamental Limits on Subwavelength Range Resolution

Authors: Andrew N. Jordan, John C. Howell

Abstract: We establish fundamental bounds on subwavelength resolution for the radar ranging problem, ``super radar''. Information theoretical metrics are applied to probe the resolution limits for the case of both direct electric field measurement and photon-counting measurements. To establish fundamental limits, we begin with the simplest case of range resolution of two point targets from a metrology persp… ▽ More We establish fundamental bounds on subwavelength resolution for the radar ranging problem, ``super radar''. Information theoretical metrics are applied to probe the resolution limits for the case of both direct electric field measurement and photon-counting measurements. To establish fundamental limits, we begin with the simplest case of range resolution of two point targets from a metrology perspective. These information-based metrics establish fundamental bounds on both the minimal discrimination distance of two targets as well as the precision on the separation of two subwavelength resolved targets. For the minimal separation distance, both the direct field method and photon counting method show that the discriminability vanishes quadratically as the target separation goes to zero, and is proportional to the variance of the second derivative of the electromagnetic field profile. Nevertheless, robust subwavelength estimation is possible. Several different band-limited function classes are introduced to optimize discrimination. We discuss the application of maximum likelihood estimation to improve the range precision with optimal performance. The general theory of multi-parameter estimation is analyzed, and a simple example of estimating both the separation and relative strength of the two point reflectors is presented. △ Less

Submitted 11 August, 2023; originally announced August 2023.

Comments: 11 pages, 3 figures

Journal ref: Phys. Rev. Applied 20, 064046 (2023)

A quantum Stirling heat engine operating in finite time

Authors: Debmalya Das, George Thomas, Andrew N. Jordan

Abstract: In a quantum Stirling heat engine, the heat exchanged with two thermal baths is partly utilized for performing work by redistributing the energy levels of the working substance. We analyze the thermodynamics of a quantum Stirling engine operating in finite time. We develop a model in which a time-dependent potential barrier changes the energy-level structure of the working substance. The process t… ▽ More In a quantum Stirling heat engine, the heat exchanged with two thermal baths is partly utilized for performing work by redistributing the energy levels of the working substance. We analyze the thermodynamics of a quantum Stirling engine operating in finite time. We develop a model in which a time-dependent potential barrier changes the energy-level structure of the working substance. The process takes place under a constant interaction with the thermal bath. We further show that in the limit of slow operation of the cycle and low temperature, the efficiency of such an engine approaches Carnot efficiency. We also show that the maximum output power , for the strokes that affect the energy levels, is obtained at an intermediate operating speed, demonstrating the importance of a finite-time analysis. △ Less

Submitted 24 July, 2023; originally announced July 2023.

Comments: 11 pages, 8 figures

Journal ref: Phys. Rev. A 108, 012220 (2023)

Probabilistic Unitary Formulation of Open Quantum System Dynamics

Authors: Le Hu, Andrew N. Jordan

Abstract: We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous dynamics can always be described by the Lindblad master equation with all jump operators being unitary. We call this formalism the probabilistic unitary formulation o… ▽ More We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous dynamics can always be described by the Lindblad master equation with all jump operators being unitary. We call this formalism the probabilistic unitary formulation of open quantum system dynamics. This formalism is shown to be exact under all cases, and does not rely on any assumptions other than the continuity and differentiability of the density matrix. Moreover, it requires as few as $d-1$ jump operators, instead of $d^2-1$, to describe the open dynamics in the most general case, where $d$ is the dimension of Hilbert space of the system. Importantly, different from the conventional Lindblad master equation, this formalism is state-dependent, meaning that the Hamiltonian, jump operators, and rates, in general all depend on the current state of the density matrix. Hence one needs to know the explicit expression of the density matrix in order to write down the probabilistic unitary master equation explicitly. Experimentally, the formalism provides a scheme to control a quantum state to evolve along designed non-unitary quantum trajectories, and can be potentially useful in quantum computing and quantum control scenes since only unitary resources are needed for implementation. △ Less

Submitted 12 December, 2024; v1 submitted 11 July, 2023; originally announced July 2023.

Comments: 10 pages, 2 figures

Journal ref: Phys. Rev. A 110, 062205 (2024)

Supergrowth and sub-wavelength object imaging

Authors: Tathagata Karmakar, Abhishek Chakraborty, A. Nick Vamivakas, Andrew N. Jordan

Abstract: We further develop the concept of supergrowth [Jordan, Quantum Stud.: Math. Found. $\textbf{7}$, 285-292 (2020)], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function being higher than its largest wavenumber. We identify the superoscillating and supergrowing regions of a canonical oscillatory function and find the maximum values of local growth r… ▽ More We further develop the concept of supergrowth [Jordan, Quantum Stud.: Math. Found. $\textbf{7}$, 285-292 (2020)], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function being higher than its largest wavenumber. We identify the superoscillating and supergrowing regions of a canonical oscillatory function and find the maximum values of local growth rate and wavenumber. Next, we provide a quantitative comparison of lengths and relevant intensities between the superoscillating and the supergrowing regions of a canonical oscillatory function. Our analysis shows that the supergrowing regions contain intensities that are exponentially larger in terms of the highest local wavenumber compared to the superoscillating regions. Finally, we prescribe methods to reconstruct a sub-wavelength object from the imaging data using both superoscillatory and supergrowing point spread functions. Our investigation provides an experimentally preferable alternative to the superoscillation based superresolution schemes and is relevant to cutting-edge research in far-field sub-wavelength imaging. △ Less

Submitted 6 July, 2023; originally announced July 2023.

Comments: 9 pages, 3 figures

Beyond Superoscillation: General Theory of Approximation with Bandlimited Functions

Authors: Tathagata Karmakar, Andrew N. Jordan

Abstract: We give a general strategy to construct superoscillating/growing functions using an orthogonal polynomial expansion of a bandlimited function. The degree of superoscillation/growth is controlled by an anomalous expectation value of a pseudodistribution that exceeds the band limit. The function is specified via the rest of its cumulants of the pseudodistribution. We give an explicit construction us… ▽ More We give a general strategy to construct superoscillating/growing functions using an orthogonal polynomial expansion of a bandlimited function. The degree of superoscillation/growth is controlled by an anomalous expectation value of a pseudodistribution that exceeds the band limit. The function is specified via the rest of its cumulants of the pseudodistribution. We give an explicit construction using Legendre polynomials in the Fourier space, which leads to an expansion in terms of spherical Bessel functions in the real space. The other expansion coefficients may be chosen to optimize other desirable features, such as the range of super behavior. We provide a prescription to generate bandlimited functions that mimic an arbitrary behavior in a finite interval. As target behaviors, we give examples of a superoscillating function, a supergrowing function, and even a discontinuous step function. We also look at the energy content in a superoscillating/supergrowing region and provide a bound that depends on the minimum value of the logarithmic derivative in that interval. Our work offers a new approach to analyzing superoscillations/supergrowth and is relevant to the optical field spot generation endeavors for far-field superresolution imaging. △ Less

Submitted 6 June, 2023; originally announced June 2023.

Comments: 10 pages, 4 figures

Reservoir-Free Decoherence in Flying Qubits

Authors: Nicolò Piccione, Léa Bresque, Andrew N. Jordan, Robert S. Whitney, Alexia Auffèves

Abstract: An effective time-dependent Hamiltonian can be implemented by making a quantum system fly through an inhomogeneous potential, realizing, for example, a quantum gate on its internal degrees of freedom. However, flying systems have a spatial spread that will generically entangle the internal and spatial degrees of freedom, leading to decoherence in the internal state dynamics, even in the absence of… ▽ More An effective time-dependent Hamiltonian can be implemented by making a quantum system fly through an inhomogeneous potential, realizing, for example, a quantum gate on its internal degrees of freedom. However, flying systems have a spatial spread that will generically entangle the internal and spatial degrees of freedom, leading to decoherence in the internal state dynamics, even in the absence of any external reservoir. We provide formulas valid at all times for the dynamics, fidelity, and change of entropy for ballistic particles with small spatial spreads, quantified by $Δx$. This non-Markovian decoherence can be significant for ballistic flying qubits (scaling as $Δx^2$) but usually not for flying qubits carried by a moving potential well (scaling as $Δx^6$). We also discuss a method to completely counteract this decoherence for a ballistic qubit later measured. △ Less

Submitted 12 June, 2024; v1 submitted 4 May, 2023; originally announced May 2023.

Comments: 4 pages, 3 figures, plus supplemental material

Journal ref: Phys. Rev. Lett. 132, 220403 (2024)

Describing the Wave Function Collapse Process with a State-dependent Hamiltonian

Authors: Le Hu, Andrew N. Jordan

Abstract: It is well-known that quantum mechanics admits two distinct evolutions: the unitary evolution, which is deterministic and well described by the Schrödinger equation, and the collapse of the wave function, which is probablistic, generally non-unitary, and cannot be described by the Schrödinger equation. In this paper, starting with pure states, we show how the continuous collapse of the wave functi… ▽ More It is well-known that quantum mechanics admits two distinct evolutions: the unitary evolution, which is deterministic and well described by the Schrödinger equation, and the collapse of the wave function, which is probablistic, generally non-unitary, and cannot be described by the Schrödinger equation. In this paper, starting with pure states, we show how the continuous collapse of the wave function can be described by the Schrödinger equation with a stochastic, time-dependent Hamiltonian. We analytically solve for the Hamiltonian responsible for projective measurements on an arbitrary $n$-level system and the position measurement on an harmonic oscillator in the ground state, and propose several experimental schemes to verify and utilize the conclusions. A critical feature is that the Hamiltonian must be state-dependent. We then discuss how the above formalism can also be applied to describe the collapse of the wave function of mixed quantum states. The formalism we proposed may unify the two distinct evolutions in quantum mechanics. △ Less

Submitted 6 April, 2026; v1 submitted 23 January, 2023; originally announced January 2023.

Comments: 12 pages, 1 figure

Journal ref: Quantum Stud.: Math. Found. 13, 22 (2026)

Measurement-based quantum thermal machines with feedback control

Authors: Bibek Bhandari, Robert Czupryniak, Paolo Andrea Erdman, Andrew N. Jordan

Abstract: We investigate coupled-qubit-based thermal machines powered by quantum measurements and feedback. We consider two different versions of the machine: 1) a quantum Maxwell's demon where the coupled-qubit system is connected to a detachable single shared bath, and 2) a measurement-assisted refrigerator where the coupled-qubit system is in contant with a hot and cold bath. In the quantum Maxwell's dem… ▽ More We investigate coupled-qubit-based thermal machines powered by quantum measurements and feedback. We consider two different versions of the machine: 1) a quantum Maxwell's demon where the coupled-qubit system is connected to a detachable single shared bath, and 2) a measurement-assisted refrigerator where the coupled-qubit system is in contant with a hot and cold bath. In the quantum Maxwell's demon case we discuss both discrete and continuous measurements. We find that the power output from a single qubit-based device can be improved by coupling it to the second qubit. We further find that the simultaneous measurement of both qubits can produce higher net heat extraction compared to two setups operated in parallel where only single-qubit measurements are performed. In the refrigerator case, we use continuous measurement and unitary operations to power the coupled-qubit-based refrigerator. We find that the cooling power of a refrigerator operated with swap operations can be enhanced by performing suitable measurements. △ Less

Submitted 2 May, 2023; v1 submitted 2 December, 2022; originally announced December 2022.

Comments: 12 pages, 9 figures

Journal ref: Entropy 2023, 25(2), 204

Cyclic Superconducting Quantum Refrigerators Using Guided Fluxon Propagation

Authors: Tathagata Karmakar, Étienne Jussiau, Sreenath K. Manikandan, Andrew N. Jordan

Abstract: We propose cyclic quantum refrigeration in solid-state, employing a gas of magnetic field vortices in a type-II superconductor -- also known as fluxons -- as the cooling agent. Refrigeration cycles are realized by envisioning a racetrack geometry consisting of both adiabatic and isothermal arms, etched into a type-II superconductor. The guided propagation of fluxons in the racetrack is achieved by… ▽ More We propose cyclic quantum refrigeration in solid-state, employing a gas of magnetic field vortices in a type-II superconductor -- also known as fluxons -- as the cooling agent. Refrigeration cycles are realized by envisioning a racetrack geometry consisting of both adiabatic and isothermal arms, etched into a type-II superconductor. The guided propagation of fluxons in the racetrack is achieved by applying an external electrical current, in a Corbino geometry, through the sample. A gradient of magnetic field is set across the racetrack allowing one to adiabatically cool down and heat up the fluxons, which subsequently exchange heat with the cold, and hot reservoirs, respectively. We characterize the steady state of refrigeration cycles thermodynamically for both $s-$wave and $d-$wave pairing symmetries, and present their figures of merit such as the cooling power delivered, and the coefficient of performance. Our cooling principle can offer significant cooling for on-chip micro-refrigeration purposes, by locally cooling below the base temperatures achievable in a conventional dilution refrigerator. We estimate $10\mathrm{nW}/\mathrm{mm}^2$ of cooling power per unit area under typical operating conditions. Integrating the fluxon fridge to quantum circuits can enhance their coherence time by locally suppressing thermal fluctuations, and improve the efficiency of single photon detectors and charge sensors. △ Less

Submitted 30 November, 2022; originally announced December 2022.

Comments: 13 pages, 6 figures

Programmable Heisenberg interactions between Floquet qubits

Authors: Long B. Nguyen, Yosep Kim, Akel Hashim, Noah Goss, Brian Marinelli, Bibek Bhandari, Debmalya Das, Ravi K. Naik, John Mark Kreikebaum, Andrew N. Jordan, David I. Santiago, Irfan Siddiqi

Abstract: The fundamental trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, many emerging quantum architectures are designed to achieve high coherence at the expense of having fixed spectra and consequently limited types of controllable interactions. Here, by adiabatically transforming fixed-frequenc… ▽ More The fundamental trade-off between robustness and tunability is a central challenge in the pursuit of quantum simulation and fault-tolerant quantum computation. In particular, many emerging quantum architectures are designed to achieve high coherence at the expense of having fixed spectra and consequently limited types of controllable interactions. Here, by adiabatically transforming fixed-frequency superconducting circuits into modifiable Floquet qubits, we demonstrate an XXZ Heisenberg interaction with fully adjustable anisotropy. This interaction model is on one hand the basis for many-body quantum simulation of spin systems, and on the other hand the primitive for an expressive quantum gate set. To illustrate the robustness and versatility of our Floquet protocol, we tailor the Heisenberg Hamiltonian and implement two-qubit iSWAP, CZ, and SWAP gates with estimated fidelities of 99.32(3)%, 99.72(2)%, and 98.93(5)%, respectively. In addition, we implement a Heisenberg interaction between higher energy levels and employ it to construct a three-qubit CCZ gate with a fidelity of 96.18(5)%. Importantly, the protocol is applicable to various fixed-frequency high-coherence platforms, thereby unlocking a suite of essential interactions for high-performance quantum information processing. From a broader perspective, our work provides compelling avenues for future exploration of quantum electrodynamics and optimal control using the Floquet framework. △ Less

Submitted 18 November, 2022; originally announced November 2022.

Time-Dependent Hamiltonian Reconstruction using Continuous Weak Measurements

Authors: Karthik Siva, Gerwin Koolstra, John Steinmetz, William P. Livingston, Debmalya Das, Larry Chen, John Mark Kreikebaum, Noah Stevenson, Christian Jünger, David I. Santiago, Irfan Siddiqi, Andrew N. Jordan

Abstract: Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent time evolution and do not explicitly reconstruct the full time-dependent Hamiltonian or interrupt evolution for tomography. Here, we experimentally demonstrate… ▽ More Reconstructing the Hamiltonian of a quantum system is an essential task for characterizing and certifying quantum processors and simulators. Existing techniques either rely on projective measurements of the system before and after coherent time evolution and do not explicitly reconstruct the full time-dependent Hamiltonian or interrupt evolution for tomography. Here, we experimentally demonstrate that an a priori unknown, time-dependent Hamiltonian can be reconstructed from continuous weak measurements concurrent with coherent time evolution in a system of two superconducting transmons coupled by a flux-tunable coupler. In contrast to previous work, our technique does not require interruptions, which would distort the recovered Hamiltonian. We introduce an algorithm which recovers the Hamiltonian and density matrix from an incomplete set of continuous measurements and demonstrate that it reliably extracts amplitudes of a variety of single qubit and entangling two qubit Hamiltonians. We further demonstrate how this technique reveals deviations from a theoretical control Hamiltonian which would otherwise be missed by conventional techniques. Our work opens up novel applications for continuous weak measurements, such as studying non-idealities in gates, certifying analog quantum simulators, and performing quantum metrology. △ Less

Submitted 14 November, 2022; originally announced November 2022.

Comments: Main text: 12 pages, 4 figures. Appendix: 10 pages, 4 figures

Quantum State Driving along Arbitrary Trajectories

Authors: Le Hu, Andrew N. Jordan

Abstract: Starting with the quantum brachistochrone problem of the infinitesimal form, we solve the minimal time and corresponding time-dependent Hamiltonian to drive a pure quantum state with limited resources along arbitrary pre-assigned trajectories. It is also shown that out of all possible trajectories, with limited resources, which are physically accessible and which are not. The solution is then gene… ▽ More Starting with the quantum brachistochrone problem of the infinitesimal form, we solve the minimal time and corresponding time-dependent Hamiltonian to drive a pure quantum state with limited resources along arbitrary pre-assigned trajectories. It is also shown that out of all possible trajectories, with limited resources, which are physically accessible and which are not. The solution is then generalized to the mixed quantum state cases, and applied to trajectories parameterized by single or multiple parameters with discrete or continuous spectrum. We then compare the solution to that of the counterdiabatic driving, and show how the Berry phase is directly involved in both driving processes. △ Less

Submitted 17 July, 2023; v1 submitted 4 November, 2022; originally announced November 2022.

Comments: 7 pages, 3 figures

Journal ref: Phys. Rev. Research 5, 033045 (2023)

Anomalous energy exchanges and Wigner function negativities in a single qubit gate

Authors: Maria Maffei, Cyril Elouard, Bruno O. Goes, Benjamin Huard, Andrew N. Jordan, Alexia Auffèves

Abstract: Anomalous weak values and Wigner function's negativity are well known witnesses of quantum contextuality. We show that these effects occur when analyzing the energetics of a single qubit gate generated by a resonant coherent field traveling in a waveguide. The buildup of correlations between the qubit and the field is responsible for bounds on the gate fidelity, but also for a nontrivial energy ba… ▽ More Anomalous weak values and Wigner function's negativity are well known witnesses of quantum contextuality. We show that these effects occur when analyzing the energetics of a single qubit gate generated by a resonant coherent field traveling in a waveguide. The buildup of correlations between the qubit and the field is responsible for bounds on the gate fidelity, but also for a nontrivial energy balance recently observed in a superconducting setup. In the experimental scheme, the field is continuously monitored through heterodyne detection and then post-selected over the outcomes of a final qubit's measurement. The post-selected data can be interpreted as field's weak values and can show anomalous values in the variation of the field's energy. We model the joint system dynamics with a collision model, gaining access to the qubit-field entangled state at any time. We find an analytical expression of the quasi-probability distribution of the post-selected heterodyne signal, i.e. the conditional Husimi-Q function. The latter grants access to all the field's weak values: we use it to obtain that of the field's energy change and display its anomalous behaviour. Finally, we derive the field's conditional Wigner function and show that anomalous weak values and Wigner function's negativities arise for the same values of the gate's angle. △ Less

Submitted 11 October, 2022; originally announced October 2022.

Comments: 8 pages, 3 figures

Super-phenomena in arbitrary quantum observables

Authors: Andrew N. Jordan, Yakir Aharonov, Daniele C. Struppa, Fabrizio Colombo, Irene Sabadini, Tomer Shushi, Jeff Tollaksen, John C. Howell, A. Nick Vamivakas

Abstract: Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier coefficient. We generalize this effect to arbitrary quantum mechanical operators as a weak value, where the preselected state is a superposition of eigenstates of the operator with eigenvalues bounded to a range, and the postselection state is a local position. Superbehavior of this ope… ▽ More Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier coefficient. We generalize this effect to arbitrary quantum mechanical operators as a weak value, where the preselected state is a superposition of eigenstates of the operator with eigenvalues bounded to a range, and the postselection state is a local position. Superbehavior of this operator occurs whenever the operator's weak value exceeds its eigenvalue bound. We give illustrative examples of this effect for total angular momentum and energy. In the later case, we demonstrate a sequence of harmonic oscillator potentials where a finite energy state converges everywhere on the real line, using only bounded superpositions of states whose asymptotic energy vanishes - "energy out of nothing". This limit requires postselecting the particle in a region whose size diverges in the considered limit. We further show that superenergy behavior implies that the state superoscillates in time with a rate given by the superenergy divided by the reduced Planck's constant. This example demonstrates the possibility of mimicking a high-energy state with coherent superpositions of nearly zero-energy states for as wide a spatial region as desired. We provide numerical evidence of these features to further bolster and elucidate our claims. △ Less

Submitted 7 February, 2024; v1 submitted 12 September, 2022; originally announced September 2022.

Comments: 9 pages, 5 figures, expanded treatment of time

Journal ref: Phys. Rev. A 110, 012206 - Published 8 July, 2024

Many-body quantum vacuum fluctuation engines

Authors: Étienne Jussiau, Léa Bresque, Alexia Auffèves, Kater W. Murch, Andrew N. Jordan

Abstract: We propose a many-body quantum engine powered by the energy difference between the entangled ground state of the interacting system and local separable states. Performing local energy measurements on an interacting many-body system can produce excited states from which work can be extracted via local feedback operations. These measurements reveal the quantum vacuum fluctuations of the global groun… ▽ More We propose a many-body quantum engine powered by the energy difference between the entangled ground state of the interacting system and local separable states. Performing local energy measurements on an interacting many-body system can produce excited states from which work can be extracted via local feedback operations. These measurements reveal the quantum vacuum fluctuations of the global ground state in the local basis and provide the energy required to run the engine. The reset part of the engine cycle is particularly simple: The interacting many-body system is coupled to a cold bath and allowed to relax to its entangled ground state. We illustrate our proposal on two types of many-body systems: a chain of coupled qubits and coupled harmonic oscillator networks. These models faithfully represent fermionic and bosonic excitations, respectively. In both cases, analytical results for the work output and efficiency of the engine can be obtained. Generically, the work output scales as the number of quantum systems involved, while the efficiency limits to a constant. We prove the efficiency is controlled by the "local entanglement gap" -- the energy difference between the global ground state and the lowest energy eigenstate of the local Hamiltonian. In the qubit chain case, we highlight the impact of a quantum phase transition on the engine's performance as work and efficiency sharply increase at the critical point. In the case of a one-dimensional oscillator chain, we show the efficiency approaches unity as the number of coupled oscillators increases, even at finite work output. △ Less

Submitted 22 August, 2023; v1 submitted 15 August, 2022; originally announced August 2022.

Comments: 19 pages, 9 figures

Post-selection and quantum energetics

Authors: Spencer Rogers, Andrew N. Jordan

Abstract: We investigate the anomalous energy change of the measurement apparatus when a qubit is measured in bases that do not commute with energy. We model two possible measurement implementations: one is a quantum clock model with a completely time-independent Hamiltonian, while the other is a Jaynes-Cummings model which is time-dependent but conserves the total excitation number. We look at the mean ene… ▽ More We investigate the anomalous energy change of the measurement apparatus when a qubit is measured in bases that do not commute with energy. We model two possible measurement implementations: one is a quantum clock model with a completely time-independent Hamiltonian, while the other is a Jaynes-Cummings model which is time-dependent but conserves the total excitation number. We look at the mean energy change of the measurement apparatus in both models, conditioned on the qubit post-selection, and find that this change can be much greater than the level spacing of the qubit, like an anomalous weak value. In the clock model, the expression for the apparatus energy shift explicitly contains the weak value of the qubit Hamiltonian. However, in our case, no explicit weak measurements are carried out. Our two models give different results, which we explain to be a consequence of the non-degenerate spectrum of the Jaynes-Cummings model. We compare our calculations in the Jaynes-Cummings model with the experimental data of [J. Stevens, et al, arXiv:2109.09648 (2021)] and find good agreement when the conditions of our derivation are valid. △ Less

Submitted 28 July, 2022; originally announced July 2022.

Comments: 23 pages, 6 figures

Journal ref: Phys. Rev. A 106, 052214 (2022)

Energy-efficient quantum non-demolition measurement with a spin-photon interface

Authors: Maria Maffei, Bruno O. Goes, Stephen C. Wein, Andrew N. Jordan, Loïc Lanco, Alexia Auffèves

Abstract: Spin-photon interfaces (SPIs) are key devices of quantum technologies, aimed at coherently transferring quantum information between spin qubits and propagating pulses of polarized light. We study the potential of a SPI for quantum non demolition (QND) measurements of a spin state. After being initialized and scattered by the SPI, the state of a light pulse depends on the spin state. It thus plays… ▽ More Spin-photon interfaces (SPIs) are key devices of quantum technologies, aimed at coherently transferring quantum information between spin qubits and propagating pulses of polarized light. We study the potential of a SPI for quantum non demolition (QND) measurements of a spin state. After being initialized and scattered by the SPI, the state of a light pulse depends on the spin state. It thus plays the role of a pointer state, information being encoded in the light's temporal and polarization degrees of freedom. Building on the fully Hamiltonian resolution of the spin-light dynamics, we show that quantum superpositions of zero and single photon states outperform coherent pulses of light, producing pointer states which are more distinguishable with the same photon budget. The energetic advantage provided by quantum pulses over coherent ones is maintained when information on the spin state is extracted at the classical level by performing projective measurements on the light pulses. The proposed schemes are robust against imperfections in state of the art semi-conducting devices. △ Less

Submitted 30 August, 2023; v1 submitted 19 May, 2022; originally announced May 2022.

Comments: Accepted for publication in Quantum

Journal ref: Quantum 7, 1099 (2023)

Thermodynamics of Quantum Measurement and the Demon's Arrow of Time

Authors: Kagan Yanik, Bibek Bhandari, Sreenath K. Manikandan, Andrew N. Jordan

Abstract: We discuss the thermodynamic aspects of a single qubit based device, powered by weak quantum measurements, and feedback controlled by a quantum Maxwell's demon. We discuss both discrete and time-continuous operation of the measurement based device at finite temperature of the reservoir. In the discrete example where a demon acquires information via discrete weak measurements, we find that the ther… ▽ More We discuss the thermodynamic aspects of a single qubit based device, powered by weak quantum measurements, and feedback controlled by a quantum Maxwell's demon. We discuss both discrete and time-continuous operation of the measurement based device at finite temperature of the reservoir. In the discrete example where a demon acquires information via discrete weak measurements, we find that the thermodynamic variables including the heat exchanged, extractable work, and the entropy produced are completely determined by an information theoretic measure of the demon's perceived arrow of time. We also discuss a realistic time-continuous operation of the device where the feedback is applied after a sequence of weak measurements. In the time-continuous limit, we derive the exact finite-time statistics of work, heat and entropy changes along individual quantum trajectories of the quantum measurement process, and relate them to the demon's arrow of time. △ Less

Submitted 30 September, 2022; v1 submitted 16 May, 2022; originally announced May 2022.

Comments: 9 pages, 7 figures

Analog Quantum Simulation of the Dynamics of Open Quantum Systems with Quantum Dots and Microelectronic Circuits

Authors: Chang Woo Kim, John M. Nichol, Andrew N. Jordan, Ignacio Franco

Abstract: We introduce a general setup for the analog quantum simulation of the dynamics of open quantum systems based on semiconductor quantum dots electrically connected to a chain of quantum $RLC$ electronic circuits. The dots are chosen to be in the regime of spin-charge hybridization to enhance their sensitivity to the $RLC$ circuits while mitigating the detrimental effects of unwanted noise. In this c… ▽ More We introduce a general setup for the analog quantum simulation of the dynamics of open quantum systems based on semiconductor quantum dots electrically connected to a chain of quantum $RLC$ electronic circuits. The dots are chosen to be in the regime of spin-charge hybridization to enhance their sensitivity to the $RLC$ circuits while mitigating the detrimental effects of unwanted noise. In this context, we establish an experimentally realizable map between the hybrid system and a qubit coupled to thermal harmonic environments of arbitrary complexity that enables the analog quantum simulation of open quantum systems. We assess the utility of the simulator by numerically exact emulations that indicate that the experimental setup can faithfully mimic the intended target even in the presence of its natural inherent noise. We further provide a detailed analysis of the physical requirements on the quantum dots and the $RLC$ circuits needed to experimentally realize this proposal that indicates that the simulator can be created with existing technology. The approach can exactly capture the effects of highly structured non-Markovian quantum environments typical of photosynthesis and chemical dynamics, and offer clear potential advantages over conventional and even quantum computation. The proposal opens a general path for effective quantum dynamics simulations based on semiconductor quantum dots. △ Less

Submitted 5 October, 2022; v1 submitted 22 March, 2022; originally announced March 2022.