Digital quantum magnetism on a trapped-ion quantum computer
Authors:
Reza Haghshenas,
Eli Chertkov,
Michael Mills,
Wilhelm Kadow,
Sheng-Hsuan Lin,
Yi-Hsiang Chen,
Chris Cade,
Ido Niesen,
Tomislav Begušić,
Manuel S. Rudolph,
Cristina Cirstoiu,
Kevin Hemery,
Conor Mc Keever,
Michael Lubasch,
Etienne Granet,
Charles H. Baldwin,
John P. Bartolotta,
Matthew Bohn,
Justin J. Burau,
Julia Cline,
Matthew DeCross,
Joan M. Dreiling,
Cameron Foltz,
David Francois,
John P. Gaebler
, et al. (34 additional authors not shown)
Abstract:
Digital quantum matter -- realized when discrete quantum gates approximate continuous time evolution -- is susceptible to heating into chaotic, structureless states. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a…
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Digital quantum matter -- realized when discrete quantum gates approximate continuous time evolution -- is susceptible to heating into chaotic, structureless states. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviors observed in equilibrium systems, ranging from the nontrivial microscopic origins of thermalization itself to the stabilization of effective models hosting exotic emergent properties. Here, we use Quantinuum's system model H2 quantum computer to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics due to approximate energy conservation, and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration. Our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of $99.94(1)\%$), and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.
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Submitted 21 April, 2026; v1 submitted 26 March, 2025;
originally announced March 2025.
Complexity of Supersymmetric Systems and the Cohomology Problem
Authors:
Chris Cade,
P. Marcos Crichigno
Abstract:
We consider the complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with $\mathcal N=2 $ supersymmetry and show that the problem remains $\mathsf{QMA}$-complete. Our main motivation for studying this is the well-known fact that the ground state energy of a supersymmetric system is exactly zero if and only if a certain cohomology group is nontrivial. This opens the…
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We consider the complexity of the local Hamiltonian problem in the context of fermionic Hamiltonians with $\mathcal N=2 $ supersymmetry and show that the problem remains $\mathsf{QMA}$-complete. Our main motivation for studying this is the well-known fact that the ground state energy of a supersymmetric system is exactly zero if and only if a certain cohomology group is nontrivial. This opens the door to bringing the tools of Hamiltonian complexity to study the computational complexity of a large number of algorithmic problems that arise in homological algebra, including problems in algebraic topology, algebraic geometry, and group theory. We take the first steps in this direction by introducing the $k$-local Cohomology problem and showing that it is $\mathsf{QMA}_1$-hard and, for a large class of instances, is contained in $\mathsf{QMA}$. We then consider the complexity of estimating normalized Betti numbers and show that this problem is hard for the quantum complexity class $\mathsf{DQC}1$, and for a large class of instances is contained in $\mathsf{BQP}$. In light of these results, we argue that it is natural to frame many of these homological problems in terms of finding ground states of supersymmetric fermionic systems. As an illustration of this perspective we discuss in some detail the model of Fendley, Schoutens, and de Boer consisting of hard-core fermions on a graph, whose ground state structure encodes $l$-dimensional holes in the independence complex of the graph. This offers a new perspective on existing quantum algorithms for topological data analysis and suggests new ones.
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Submitted 18 April, 2024; v1 submitted 30 June, 2021;
originally announced July 2021.