Faster Digital Quantum Simulation by Symmetry Protection

• URL: http://arxiv.org/abs/2006.16248v2
• Date: Sun, 14 Feb 2021 16:33:03 GMT
• Title: Faster Digital Quantum Simulation by Symmetry Protection
• Authors: Minh C. Tran, Yuan Su, Daniel Carney, Jacob M. Taylor
• Abstract summary: We show that by introducing quantum gates implementing unitary transformations one can induce destructive interference between the errors from different steps of the simulation. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We apply the symmetry protection technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory.
• Score: 0.6554326244334866
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We prove a bound on this approximation error, exponentially improving a recent result of Burgarth, Facchi, Gramegna, and Pascazio. We apply the symmetry protection technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory. For both systems, the technique can reduce the simulation error by several orders of magnitude over the unprotected simulation. Finally, we provide numerical evidence suggesting that the technique can also protect simulation against other types of coherent, temporally correlated errors, such as the $1/f$ noise commonly found in solid-state experiments.

Related papers

• Trapped-ion quantum simulation of the Fermi-Hubbard model as a lattice gauge theory using hardware-aware native gates [0.3370543514515051]
  Trotterization-based quantum simulations have shown promise, but implementations on current hardware are limited by noise. A mapping of the Fermi-Hubbard model to a Z2 LGT was recently proposed that restricts the dynamics to a subspace protected by additional symmetries, and its ability for post-selection error mitigation was verified through noisy classical simulations. In particular, a novel combination of iteratively preconditioned gradient descent (IPG) and subsystem von Neumann Entropy compression reduces the 2-qubit gate count of FHM quantum simulation by 35%.
  arXiv  Detail & Related papers  (2024-11-12T13:21:12Z)
• Symmetry-protection Zeno phase transition in monitored lattice gauge theories [0.0]
  We show the existence of a sharp transition, triggered by the measurement rate, between a protected gauge-theory regime and an irregular regime. Our results shed light on the dissipative criticality of strongly-interacting, highly-constrained quantum systems.
  arXiv  Detail & Related papers  (2024-05-28T18:18:06Z)
• Efficient quantum algorithms for testing symmetries of open quantum systems [17.55887357254701]
  In quantum mechanics, it is possible to eliminate degrees of freedom by leveraging symmetry to identify the possible physical transitions. Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures. We develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers.
  arXiv  Detail & Related papers  (2023-09-05T18:05:26Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions [0.5277756703318045]
  We simulate the dynamics of a lattice gauge theory in 1+1 dimensions using a trapped-ion system with up to six qubits. We demonstrate non-perturbative effects such as pair creation for times much longer than previously accessible. This work demonstrates the integrated theoretical, algorithmic, and experimental approach that is essential for efficient simulation of lattice gauge theories.
  arXiv  Detail & Related papers  (2021-12-28T19:00:01Z)
• Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
  We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state. In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
  arXiv  Detail & Related papers  (2021-12-27T21:15:35Z)
• Hybridized Methods for Quantum Simulation in the Interaction Picture [69.02115180674885]
  We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations. Physical applications of these hybridized methods yield a gate complexity scaling as $log2 Lambda$ in the electric cutoff. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost.
  arXiv  Detail & Related papers  (2021-09-07T20:01:22Z)
• Realizing a dynamical topological phase in a trapped-ion quantum simulator [0.0]
  Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics. We show how to create, protect, and manipulate quantum entanglement that self-correct against large classes of errors. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient techniques to manipulate quantum information.
  arXiv  Detail & Related papers  (2021-07-20T18:00:00Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.