Randomized term grouping over physical law on digital quantum simulation

• URL: http://arxiv.org/abs/2309.14378v2
• Date: Thu, 28 Sep 2023 13:06:20 GMT
• Title: Randomized term grouping over physical law on digital quantum simulation
• Authors: Songqinghao Yang
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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. Empirically we achieved better spectral error reduction with hydrogen chain model compared to previous protocols. Noisy model are investigated as well and we characterised them in the circuit with different schemes, i.e. an attenuation of the measured expectation value is fixed by keeping the circuit depth the same and depolarising error is simulated with randomly applied Pauli gates. This makes it our proposal particularly feasible for implementing and testing on present-day noisy hardware.

Related papers

• Classical simulations of noisy variational quantum circuits [0.0]
  Noisely affects quantum computations so that they not only become less accurate but also easier to simulate classically as systems scale up. We construct a classical simulation algorithm, LOWESA, for estimating expectation values of noisy parameterised quantum circuits.
  arXiv  Detail & Related papers  (2023-06-08T17:52:30Z)
• Simulating prethermalization using near-term quantum computers [1.2189422792863451]
  We propose an experimental protocol for probing dynamics and equilibrium properties on near-term digital quantum computers. We show that it is possible to study thermalization even with a relatively coarse Trotter decomposition of the Hamiltonian evolution of interest.
  arXiv  Detail & Related papers  (2023-03-15T09:04:57Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• 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)
• 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)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• 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)
• Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits [0.0]
  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.
  arXiv  Detail & Related papers  (2020-12-04T19:00:00Z)
• 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)
• Term Grouping and Travelling Salesperson for Digital Quantum Simulation [6.945601123742983]
  Digital simulation of quantum dynamics by evaluating the time evolution of a Hamiltonian is the initially proposed application of quantum computing. The large number of quantum gates required for emulating the complete second quantization form of the Hamiltonian makes such an approach unsuitable for near-term devices. We propose a new term ordering strategy, max-commute-tsp, that simultaneously mitigates both algorithmic and physical errors.
  arXiv  Detail & Related papers  (2020-01-16T18:33:24Z)

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.