Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware

• URL: http://arxiv.org/abs/2003.06886v3
• Date: Thu, 26 Aug 2021 12:49:22 GMT
• Title: Hamiltonian Simulation Algorithms for Near-Term Quantum Hardware
• Authors: Laura Clinton, Johannes Bausch, Toby Cubitt
• Abstract summary: We develop quantum algorithms for Hamiltonian simulation "one level below" the circuit model. We analyse the impact of these techniques under the standard error model. We derive analytic circuit identities for efficiently synthesising multi-qubit evolutions from two-qubit interactions.
• Score: 6.445605125467574
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with severely restricted resources, this overhead may be unjustifiable. In this work, we develop quantum algorithms for Hamiltonian simulation "one level below" the circuit model, exploiting the underlying control over qubit interactions available in principle in most quantum hardware implementations. We then analyse the impact of these techniques under the standard error model where errors occur per gate, and an error model with a constant error rate per unit time. To quantify the benefits of this approach, we apply it to a canonical example: time-dynamics simulation of the 2D spin Fermi-Hubbard model. We derive analytic circuit identities for efficiently synthesising multi-qubit evolutions from two-qubit interactions. Combined with new error bounds for Trotter product formulas tailored to the non-asymptotic regime and a careful analysis of error propagation under the aforementioned per-gate and per-time error models, we improve upon the previous best methods for Hamiltonian simulation by multiple orders of magnitude. By our calculations, for a 5$\mathbf\times$5 Fermi-Hubbard lattice we reduce the circuit depth from 800,160 to 1460 in the per-gate error model, or the circuit-depth-equivalent to 440 in the per-time error model. This brings Hamiltonian simulation, previously beyond reach of current hardware for non-trivial examples, significantly closer to being feasible in the NISQ era.

Related papers

• Improved Digital Quantum Simulation by Non-Unitary Channels [0.5999777817331317]
  We study the performance of non-unitary simulation channels and consider the error structure of channels constructed from a weighted average of unitary circuits. We show that averaging over just a few simulation circuits can significantly reduce the Trotterization error for both single-step short-time and multi-step long-time simulations.
  arXiv  Detail & Related papers  (2023-07-24T18:00:02Z)
• Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation [0.5729426778193399]
  We show how errors due to Trotterized time evolution can be mitigated through the use of algorithmic techniques. Our approach is to extrapolate to zero Trotter step size, akin to zero-noise extrapolation techniques for mitigating hardware errors.
  arXiv  Detail & Related papers  (2022-12-29T01:21:26Z)
• Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation [1.433758865948252]
  We show how to design MPFs that do not amplify the hardware and sampling errors, and demonstrate their performance. We observe an error reduction of up to an order of magnitude when compared to a product formula approach by suppressing hardware noise with Pauli Twirling, pulse efficient transpilation, and a novel zero-noise extrapolation based on scaled cross-resonance pulses.
  arXiv  Detail & Related papers  (2022-07-22T18:00:05Z)
• 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)
• Hamiltonian simulation with random inputs [74.82351543483588]
  Theory of average-case performance of Hamiltonian simulation with random initial states. Numerical evidence suggests that this theory accurately characterizes the average error for concrete models.
  arXiv  Detail & Related papers  (2021-11-08T19:08:42Z)
• 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)
• 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)
• 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)
• 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)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)
• 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.