Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits

• URL: http://arxiv.org/abs/2012.02795v2
• Date: Tue, 8 Jun 2021 15:19:16 GMT
• Title: Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits
• Authors: Jonas Richter, Arijeet Pal
• Abstract summary: We show that random circuits provide tailor-made building blocks for simulating quantum many-body systems. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution. We numerically demonstrate the algorithm by simulating the buildup of correlation functions in one- and two-dimensional quantum spin systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

Related papers

• Dynamical simulations of many-body quantum chaos on a quantum computer [3.731709137507907]
  We study a class of maximally chaotic circuits known as dual unitary circuits. We show that a superconducting quantum processor with 91 qubits is able to accurately simulate these correlators. We then probe dynamics beyond exact verification, by perturbing the circuits away from the dual unitary point.
  arXiv  Detail & Related papers  (2024-11-01T17:57:13Z)
• Randomized term grouping over physical law on digital quantum simulation [0.0]
  We introduce a randomized algorithm based on qDrift to compute Hamiltonian dynamics on digital quantum computers. We frame it as physDrift because conservation laws in physics are obeyed during evolution of arbitrary quantum states.
  arXiv  Detail & Related papers  (2023-09-24T13:15:39Z)
• Overhead-constrained circuit knitting for variational quantum dynamics [0.0]
  We use circuit knitting to partition a large quantum system into smaller subsystems that can each be simulated on a separate device. We show that the same method can be used to reduce the circuit depth by cutting long-ranged gates.
  arXiv  Detail & Related papers  (2023-09-14T17:01:06Z)
• Stabilization of Discrete Time-Crystaline Response on a Superconducting Quantum Computer by increasing the Interaction Range [0.0]
  We present the outcomes of a digital quantum simulation where we overcome the limitations of the qubit connectivity in NISQ devices. We demonstrate how to implement couplings among physically disconnected qubits at the cost of increasing the circuit depth.
  arXiv  Detail & Related papers  (2023-05-23T18:00:12Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation [55.41644538483948]
  Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates. We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
  arXiv  Detail & Related papers  (2021-08-06T19:38:03Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Low-depth Hamiltonian Simulation by Adaptive Product Formula [3.050399782773013]
  Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. Here, we propose an adaptive approach to construct a low-depth time evolution circuit. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.
  arXiv  Detail & Related papers  (2020-11-10T18:00:42Z)
• 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.