Showing 1–14 of 14 results for author: Crane, E

Observation of disorder-induced superfluidity

Authors: Nicole Ticea, Elias Portoles, Eliott Rosenberg, Alexander Schuckert, Aaron Szasz, Bryce Kobrin, Nicolas Pomata, Pranjal Praneel, Connie Miao, Shashwat Kumar, Ella Crane, Ilya Drozdov, Yuri Lensky, Sofia Gonzalez-Garcia, Thomas Kiely, Dmitry Abanin, Amira Abbas, Rajeev Acharya, Laleh Aghababaie Beni, Georg Aigeldinger, Ross Alcaraz, Sayra Alcaraz, Markus Ansmann, Frank Arute, Kunal Arya , et al. (277 additional authors not shown)

Abstract: The emergence of states with long-range correlations in a disordered landscape is rare, as disorder typically suppresses the particle mobility required for long-range coherence. But when more than two energy levels are available per site, disorder can induce resonances that locally enhance mobility. Here we explore phases arising from the interplay between disorder, kinetic energy, and interaction… ▽ More The emergence of states with long-range correlations in a disordered landscape is rare, as disorder typically suppresses the particle mobility required for long-range coherence. But when more than two energy levels are available per site, disorder can induce resonances that locally enhance mobility. Here we explore phases arising from the interplay between disorder, kinetic energy, and interactions on a superconducting processor with qutrit readout and control. Compressibility measurements distinguish an incompressible Mott insulator from surrounding compressible phases and reveal signatures of glassiness, reflected in non-ergodic behavior. Spatially-resolved two-point correlator measurements identify regions of the phase diagram with a non-vanishing condensate fraction. We also visualize the spectrum by measuring the dynamical structure factor. A linearly-dispersing phonon mode materializes in the superfluid, appearing even when disorder is introduced to the clean Mott insulator. Our results provide strong experimental evidence for disorder-induced superfluidity. △ Less

Submitted 3 February, 2026; v1 submitted 24 December, 2025; originally announced December 2025.

Comments: Supplement updated

Hybrid digital-analog protocols for simulating quantum multi-body interactions

Authors: Or Katz, Alexander Schuckert, Tianyi Wang, Eleanor Crane, Alexey V. Gorshkov, Marko Cetina

Abstract: While quantum simulators promise to explore quantum many-body physics beyond classical computation, their capabilities are limited by the available native interactions in the hardware. On many platforms, accessible Hamiltonians are largely restricted to one- and two-body interactions, limiting access to multi-body Hamiltonians and to systems governed by simultaneous, non-commuting interaction term… ▽ More While quantum simulators promise to explore quantum many-body physics beyond classical computation, their capabilities are limited by the available native interactions in the hardware. On many platforms, accessible Hamiltonians are largely restricted to one- and two-body interactions, limiting access to multi-body Hamiltonians and to systems governed by simultaneous, non-commuting interaction terms that are central to condensed matter, quantum chemistry, and high-energy physics. We introduce and experimentally demonstrate a hybrid digital-analog protocol that overcomes these limitations by embedding analog evolution between shallow entangling-gate layers. This method produces effective Hamiltonians with simultaneous non-commuting three- and four-body interactions that are generated non-perturbatively and without Trotter error -- capabilities not practically attainable on near-term hardware using purely digital or purely analog schemes. We implement our scheme on a trapped-ion quantum processor and use it to realize a topological spin chain exhibiting prethermal strong zero modes persisting at high temperature, as well as models featuring three- and four-body interactions. Our hardware-agnostic and scalable method opens new routes to realizing complex many-body physics across quantum platforms. △ Less

Submitted 24 December, 2025; originally announced December 2025.

Symbolic Hamiltonian Compiler for Hybrid Qubit-Boson Processors

Authors: Ethan Decker, Erik Gustafson, Evan McKinney, Alex K. Jones, Lucas Goetz, Ang Li, Alexander Schuckert, Samuel Stein, Gushu Li, Eleanor Crane

Abstract: Quantum simulation of the interactions of fermions and bosons -- the fundamental particles of nature -- is essential for modeling complex quantum systems in material science, chemistry and high-energy physics and has been proposed as a promising application of fermion-boson quantum computers, which overcome the overhead encountered in mapping fermions and bosons to qubits. However, compiling the s… ▽ More Quantum simulation of the interactions of fermions and bosons -- the fundamental particles of nature -- is essential for modeling complex quantum systems in material science, chemistry and high-energy physics and has been proposed as a promising application of fermion-boson quantum computers, which overcome the overhead encountered in mapping fermions and bosons to qubits. However, compiling the simulation of specific fermion-boson Hamiltonians into the natively available fermion-boson gate set is challenging. In particular, the large local dimension of bosons renders matrix-based compilation methods, as used for qubits and in existing tools such as Bosonic Qiskit or OpenFermion, challenging. We overcome this issue by introducing a novel symbolic compiler based on matrix-free symbolic manipulation of second quantised Hamiltonians, which automates the decomposition of fermion-boson second quantized problems into qubit-boson instruction set architectures. This integration establishes a comprehensive pipeline for simulating quantum systems on emerging qubit-boson and fermion-boson hardware, paving the way for their large-scale usage. △ Less

Submitted 30 May, 2025; originally announced June 2025.

Constrained many-body phases in a $\mathbb{Z}_2$-Higgs lattice gauge theory

Authors: Alexander Schuckert, Stefan Kühn, Kevin C. Smith, Eleanor Crane, Steven M. Girvin

Abstract: We study the ground-state phase diagram of a one-dimensional $\mathbb{Z}_2$ lattice gauge theory coupled to soft-core bosonic matter at unit filling, inspired by the Higgs sector of the standard model. Through a combination of analytical perturbative approaches, exact diagonalization, and density-matrix-renormalization-group simulations, we uncover a rich phase diagram driven by gauge-field-mediat… ▽ More We study the ground-state phase diagram of a one-dimensional $\mathbb{Z}_2$ lattice gauge theory coupled to soft-core bosonic matter at unit filling, inspired by the Higgs sector of the standard model. Through a combination of analytical perturbative approaches, exact diagonalization, and density-matrix-renormalization-group simulations, we uncover a rich phase diagram driven by gauge-field-mediated resonant pair hopping and the confinement of single particles. The pair hopping results in a bunching state with superextensive energy and macroscopic particle number fluctuations at strong electric field strengths and weak on-site interactions. The bunching state crosses over into a pair superfluid phase as the on-site interaction increases, characterized by a finite superfluid density and powerlaw-decaying pair correlations. At large on-site interaction strengths and driven by effective interactions induced by the gauge constraint, the superfluid transitions into an incompressible pair Mott insulator phase. At weak field strengths and on-site interactions, we find a plasma-like region, where single bosons exhibit large short-range correlations and the ground state is composed almost equally of states with even and odd local boson occupation. The presence of a bunching state with large number fluctuations, which is difficult to study using classical numerics, motivates experimental realizations in hybrid boson-qubit quantum simulation platforms such as circuit QED, neutral atoms, and trapped ions. Our findings highlight the rich interplay between gauge fields and soft-core bosonic matter. △ Less

Submitted 5 March, 2025; originally announced March 2025.

Comments: 4+2 pages, 5+1 figures

Fault-tolerant fermionic quantum computing

Authors: Alexander Schuckert, Eleanor Crane, Alexey V. Gorshkov, Mohammad Hafezi, Michael J. Gullans

Abstract: Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in mapping time evolution under fermionic Hamiltonians to qubit gates renders this endeavor challenging. We introduce fermionic fault-tolerant quantum computing, a fra… ▽ More Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in mapping time evolution under fermionic Hamiltonians to qubit gates renders this endeavor challenging. We introduce fermionic fault-tolerant quantum computing, a framework which removes this overhead altogether. Using native fermionic operations we first construct a repetition code which corrects phase errors only. Within a fermionic color code, which corrects for both phase and loss errors, we then realize a universal fermionic gate set, including transversal fermionic Clifford gates. Interfacing with qubit color codes we introduce qubit-fermion fault-tolerant computation, which allows for qubit-controlled fermionic time evolution, a crucial subroutine in state-of-the-art quantum algorithms. As an application, we consider simulating crystalline materials, finding an exponential improvement in circuit depth for a single time step from $\mathcal{O}(N)$ to $\mathcal{O}(\log(N))$ with respect to lattice site number $N$ while retaining a site count of $\tilde{\mathcal{O}}(N)$, implying a linear-in-$N$ end-to-end gate depth for simulating materials, as opposed to quadratic in previous approaches. We also introduce a fermion-inspired qubit algorithm with $O(\mathrm{log}(N)$ depth, but a prohibitive number of additional ancilla qubits. We show how our framework can be implemented in neutral atoms, overcoming the apparent inability of neutral atoms to implement non-number-conserving gates. Our work opens the door to fermion-qubit fault-tolerant quantum computation in platforms with native fermions such as neutral atoms, quantum dots and donors in silicon, with applications in quantum chemistry, material science, and high-energy physics. △ Less

Submitted 16 July, 2025; v1 submitted 13 November, 2024; originally announced November 2024.

Comments: 8+9 pages, 5+2 figures

Hybrid Oscillator-Qubit Quantum Processors: Simulating Fermions, Bosons, and Gauge Fields

Authors: Eleanor Crane, Kevin C. Smith, Teague Tomesh, Alec Eickbusch, John M. Martyn, Stefan Kühn, Lena Funcke, Michael Austin DeMarco, Isaac L. Chuang, Nathan Wiebe, Alexander Schuckert, Steven M. Girvin

Abstract: We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact decompositions of particle interactions such as density-density terms and gauge-invariant hopping, as well as approximate methods based on the Baker-Campbell Hausdorff for… ▽ More We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact decompositions of particle interactions such as density-density terms and gauge-invariant hopping, as well as approximate methods based on the Baker-Campbell Hausdorff formulas including the magnetic field term for the $U(1)$ quantum link model in $(2+1)$D. We use this framework to show how to simulate dynamics using Trotterisation, perform ancilla-free partial error detection using Gauss's law, measure non-local observables, estimate ground state energies using a oscillator-qubit variational quantum eigensolver as well as quantum signal processing, and we numerically study the influence of hardware errors in circuit QED experiments. To show the advantages over all-qubit hardware, we perform an end-to-end comparison of the gate complexity for the gauge-invariant hopping term and find an improvement of the asymptotic scaling with the boson number cutoff $S$ from $\mathcal{O}(\log(S)^2)$ to $\mathcal{O}(1)$ in our framework as well as, for bosonic matter, a constant factor improvement of better than $10^4$. We also find an improvement from $\mathcal{O}(\log(S))$ to $\mathcal{O}(1)$ for the $U(1)$ magnetic field term. While our work focusses on an implementation in superconducting hardware, our framework can also be used in trapped ion, and neutral atom hardware. This work establishes digital quantum simulation with hybrid oscillator-qubit hardware as a viable and advantageous method for the study of qubit-boson models in materials science, chemistry, and high-energy physics. △ Less

Submitted 5 September, 2024; originally announced September 2024.

Comments: 48+8 pages, 24+3 figures

Analog Quantum Simulator of a Quantum Field Theory with Fermion-Spin Systems in Silicon

Authors: Ali Rad, Alexander Schuckert, Eleanor Crane, Gautam Nambiar, Fan Fei, Jonathan Wyrick, Richard M. Silver, Mohammad Hafezi, Zohreh Davoudi, Michael J. Gullans

Abstract: Simulating fermions coupled to spin degrees of freedom, relevant for a range of quantum field theories, represents a promising application for quantum simulators. Mapping fermions to qubits is challenging in $2+1$ and higher spacetime dimensions, and mapping bosons demands substantial quantum-computational overhead. These features complicate the realization of mixed fermion-boson quantum systems i… ▽ More Simulating fermions coupled to spin degrees of freedom, relevant for a range of quantum field theories, represents a promising application for quantum simulators. Mapping fermions to qubits is challenging in $2+1$ and higher spacetime dimensions, and mapping bosons demands substantial quantum-computational overhead. These features complicate the realization of mixed fermion-boson quantum systems in digital quantum computers. We propose a native fermion-(large-)spin analog quantum simulator by utilizing dopant arrays in silicon. Specifically, we show how to use a dynamical lattice of coupled nuclear spins and conduction-band electrons to realize a quantum field theory: an extended Jackiw-Rebbi model involving coupled fermions and quantum rotors. We demonstrate the feasibility of observing dynamical mass generation and a confinement-deconfinement quantum phase transition in 1+1 dimensions on this platform, even in the presence of strong long-range Coulomb interactions. Furthermore, we employ finite-temperature Hartree-Fock-Bogoliubov simulations to investigate the dynamics of mass generation in two-dimensional square and honeycomb arrays, showing that this phenomenon can be simulated with realistic experimental parameters. Our findings reveal two distinct phases, and demonstrate robustness against the addition of Coulomb interactions. Finally, we discuss experimental signatures of the phases through transport and local charge sensing in dopant arrays. This study lays the foundation for quantum simulations of quantum field theories exhibiting fermions coupled to spin degrees of freedom using donors in silicon. △ Less

Submitted 3 July, 2024; originally announced July 2024.

Observation of a finite-energy phase transition in a one-dimensional quantum simulator

Authors: Alexander Schuckert, Or Katz, Lei Feng, Eleanor Crane, Arinjoy De, Mohammad Hafezi, Alexey V. Gorshkov, Christopher Monroe

Abstract: One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out that a phase transition… ▽ More One of the most striking many-body phenomena in nature is the sudden change of macroscopic properties as the temperature or energy reaches a critical value. Such equilibrium transitions have been predicted and observed in two and three spatial dimensions, but have long been thought not to exist in one-dimensional (1D) systems. Fifty years ago, Dyson and Thouless pointed out that a phase transition in 1D can occur in the presence of long-range interactions, but an experimental realization has so far not been achieved due to the requirement to both prepare equilibrium states and realize sufficiently long-range interactions. Here we report on the first experimental demonstration of a finite-energy phase transition in 1D. We use the simple observation that finite-energy states can be prepared by time-evolving product initial states and letting them thermalize under the dynamics of a many-body Hamiltonian. By preparing initial states with different energies in a 1D trapped-ion quantum simulator, we study the finite-energy phase diagram of a long-range interacting quantum system. We observe a ferromagnetic equilibrium phase transition as well as a crossover from a low-energy polarized paramagnet to a high-energy unpolarized paramagnet in a system of up to $23$ spins, in excellent agreement with numerical simulations. Our work demonstrates the ability of quantum simulators to realize and study previously inaccessible phases at finite energy density. △ Less

Submitted 30 October, 2023; originally announced October 2023.

Comments: 5+9 pages, 4+14 figures

Journal ref: Nature Physics 21, 374-379 (2025)

Momentum-space imaging of ultra-thin electron liquids in delta-doped silicon

Authors: Procopios Constantinou, Taylor J. Z. Stock, Eleanor Crane, Alexander Kölker, Marcel van Loon, Juerong Li, Sarah Fearn, Henric Bornemann, Nicolò D'Anna, Andrew J. Fisher, Vladimir N. Strocov, Gabriel Aeppli, Neil J. Curson, Steven R. Schofield

Abstract: Two-dimensional dopant layers ($δ$-layers) in semiconductors provide the high-mobility electron liquids (2DELs) needed for nanoscale quantum-electronic devices. Key parameters such as carrier densities, effective masses, and confinement thicknesses for 2DELs have traditionally been extracted from quantum magnetotransport. In principle, the parameters are immediately readable from the one-electron… ▽ More Two-dimensional dopant layers ($δ$-layers) in semiconductors provide the high-mobility electron liquids (2DELs) needed for nanoscale quantum-electronic devices. Key parameters such as carrier densities, effective masses, and confinement thicknesses for 2DELs have traditionally been extracted from quantum magnetotransport. In principle, the parameters are immediately readable from the one-electron spectral function that can be measured by angle-resolved photoemission spectroscopy (ARPES). Here, buried 2DEL $δ$-layers in silicon are measured with soft X-ray (SX) ARPES to obtain detailed information about their filled conduction bands and extract device-relevant properties. This study takes advantage of the larger probing depth and photon energy range of SX-ARPES relative to vacuum ultraviolet (VUV) ARPES to accurately measure the $δ$-layer electronic confinement. The measurements are made on ambient-exposed samples and yield extremely thin ($\approx 1$ $nm$) and dense ($\approx$ $10^{14}$ $cm^2$) 2DELs. Critically, this method is used to show that $δ$-layers of arsenic exhibit better electronic confinement than $δ$-layers of phosphorus fabricated under identical conditions. △ Less

Submitted 29 September, 2023; originally announced September 2023.

Comments: Published in Advanced Science as a Research Article

Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements

Authors: Kevin C. Smith, Eleanor Crane, Nathan Wiebe, S. M. Girvin

Abstract: The ground state of the spin-1 Affleck, Kennedy, Lieb and Tasaki (AKLT) model is a paradigmatic example of both a matrix product state and a symmetry-protected topological phase, and additionally holds promise as a resource state for measurement-based quantum computation. Having a nonzero correlation length, the AKLT state cannot be exactly prepared by a constant-depth unitary circuit composed of… ▽ More The ground state of the spin-1 Affleck, Kennedy, Lieb and Tasaki (AKLT) model is a paradigmatic example of both a matrix product state and a symmetry-protected topological phase, and additionally holds promise as a resource state for measurement-based quantum computation. Having a nonzero correlation length, the AKLT state cannot be exactly prepared by a constant-depth unitary circuit composed of local gates. In this work, we demonstrate that this no-go limit can be evaded by augmenting a constant-depth circuit with fusion measurements, such that the total preparation time is independent of system size and entirely deterministic. We elucidate our preparation scheme using the language of tensor networks, and furthermore show that the $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry of the AKLT state directly affords this speed-up over previously known preparation methods. To demonstrate the practical advantage of measurement-assisted preparation on noisy intermediate-scale quantum (NISQ) devices, we carry out our protocol on an IBM Quantum processor. We measure both the string order and entanglement spectrum of prepared AKLT chains and, employing these as metrics, find improved results over the known (purely unitary) sequential preparation approach. We conclude with a demonstration of quantum teleportation using the AKLT state prepared by our measurement-assisted scheme. This work thus serves to provide an efficient strategy to prepare a specific resource in the form of the AKLT state and, more broadly, experimentally demonstrates the possibility for realizable improvement in state preparation afforded by measurement-based circuit depth reduction strategies on NISQ-era devices. △ Less

Submitted 10 April, 2023; v1 submitted 31 October, 2022; originally announced October 2022.

Comments: 17 pages, 8 figures. Supplemental Material: 13 pages, 11 figures

Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics

Authors: Alexander Schuckert, Annabelle Bohrdt, Eleanor Crane, Michael Knap

Abstract: Preparing finite temperature states in quantum simulators of spin systems, such as trapped ions or Rydberg atoms in optical tweezers, is challenging due to their almost perfect isolation from the environment. Here, we show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality and equivalent to the one in Lu, Banuls and Cirac, PRX Quantum 2, 0203… ▽ More Preparing finite temperature states in quantum simulators of spin systems, such as trapped ions or Rydberg atoms in optical tweezers, is challenging due to their almost perfect isolation from the environment. Here, we show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality and equivalent to the one in Lu, Banuls and Cirac, PRX Quantum 2, 020321 (2021). It consists of classical importance sampling of initial states and a measurement of the Loschmidt echo with a quantum simulator. We use the method as a quantum-inspired classical algorithm and simulate the protocol with matrix product states to analyze the requirements on a quantum simulator. This way, we show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators. We propose a concrete measurement protocol for the Loschmidt echo and discuss the influence of measurement noise, dephasing, as well as state preparation and measurement errors. We argue that the algorithm is robust against those imperfections under realistic conditions. △ Less

Submitted 4 May, 2023; v1 submitted 3 June, 2022; originally announced June 2022.

Comments: 4+3 pages, 4+1 figures

Journal ref: Phys. Rev. B 107, L140410 (2023)

Visualizing spinon Fermi surfaces with time-dependent spectroscopy

Authors: Alexander Schuckert, Annabelle Bohrdt, Eleanor Crane, Fabian Grusdt

Abstract: Quantum simulation experiments have started to explore regimes that are not accessible with exact numerical methods. In order to probe these systems and enable new physical insights, the need for measurement protocols arises that can bridge the gap to solid state experiments, and at the same time make optimal use of the capabilities of quantum simulation experiments. Here we propose applying time-… ▽ More Quantum simulation experiments have started to explore regimes that are not accessible with exact numerical methods. In order to probe these systems and enable new physical insights, the need for measurement protocols arises that can bridge the gap to solid state experiments, and at the same time make optimal use of the capabilities of quantum simulation experiments. Here we propose applying time-dependent photo-emission spectroscopy, an established tool in solid state systems, in cold atom quantum simulators. Concretely, we suggest combining the method with large magnetic field gradients, unattainable in experiments on real materials, to drive Bloch oscillations of spinons, the emergent quasiparticles of spin liquids. We show in exact diagonalization simulations of the one-dimensional $t-J$ model that the spinons start to populate previously unoccupied states in an effective band structure, thus allowing to visualize states invisible in the equilibrium spectrum. The dependence of the spectral function on the time after the pump pulse reveals collective interactions among spinons. In numerical simulations of small two-dimensional systems, spectral weight appears at the ground state energy at momentum $\mathbf{q} = (π,π)$, where the equilibrium spectral response is strongly suppressed up to higher energies, indicating a possible route towards solving the mystery of the Fermi arcs in the cuprate materials. △ Less

Submitted 27 May, 2021; originally announced May 2021.

Comments: 4+10 pages, 4+4 figures

Journal ref: Phys. Rev. B 104, 235107 (2021)

Rydberg Entangling Gates in Silicon

Authors: Eleanor Crane, Alexander Schuckert, Nguyen H. Le, Andrew J. Fisher

Abstract: In this paper, we propose a new Rydberg entangling gate scheme which we demonstrate theoretically to have an order of magnitude improvement in fidelities and speed over existing protocols. We find that applying this gate to donors in silicon would help overcome the strenuous requirements on atomic precision donor placement and substantial gate tuning, which so far has hampered scaling. We calculat… ▽ More In this paper, we propose a new Rydberg entangling gate scheme which we demonstrate theoretically to have an order of magnitude improvement in fidelities and speed over existing protocols. We find that applying this gate to donors in silicon would help overcome the strenuous requirements on atomic precision donor placement and substantial gate tuning, which so far has hampered scaling. We calculate multivalley Rydberg interactions for several donor species using the Finite Element Method, and show that induced electric dipole and Van der Waals interactions, calculated here for the first time, are important even for low-lying excited states. We show that Rydberg gate operation is possible within the lifetime of donor excited states with 99.9% fidelity for the creation of a Bell state in the presence of decoherence. △ Less

Submitted 24 November, 2020; v1 submitted 26 August, 2020; originally announced August 2020.

Comments: 14 pages, 12 figures

Journal ref: Phys. Rev. Research 3, 033086 (2021)

Optically Controlled Entangling Gates in Randomly Doped Silicon

Authors: Eleanor Crane, Thomas Crane, Nguyen H. Le, Alexander Schuckert, Andrew J. Fisher

Abstract: Randomly-doped silicon has many competitive advantages for quantum computation; not only is it fast to fabricate but it could naturally contain high numbers of qubits and logic gates as a function of doping densities. We determine the densities of entangling gates in randomly doped silicon comprising two different dopant species. First, we define conditions and plot maps of the relative locations… ▽ More Randomly-doped silicon has many competitive advantages for quantum computation; not only is it fast to fabricate but it could naturally contain high numbers of qubits and logic gates as a function of doping densities. We determine the densities of entangling gates in randomly doped silicon comprising two different dopant species. First, we define conditions and plot maps of the relative locations of the dopants necessary for them to form exchange interaction mediated entangling gates. Second, using nearest neighbour Poisson point process theory, we calculate the doping densities necessary for maximal densities of single and dual-species gates. We find agreement of our results with a Monte Carlo simulation, for which we present the algorithms, which handles multiple donor structures and scales optimally with the number of dopants and use it to extract donor structures not captured by our Poisson point process theory. Third, using the moving average cluster expansion technique, we make predictions for a proof of principle experiment demonstrating the control of one species by the orbital excitation of another. These combined approaches to density optimization in random distributions may be useful for other condensed matter systems as well as applications outside physics. △ Less

Submitted 1 February, 2019; originally announced February 2019.

Comments: 14 pages, 10 figures

Journal ref: Phys. Rev. B 100, 064201 (2019)