Accelerated Quantum Monte Carlo with Mitigated Error on Noisy Quantum Computer

Yang, Yongdan; Lü, Bin; Liu, Ying

doi:10.1103/prxquantum.2.040361

Cited by 23 publications

(16 citation statements)

References 63 publications

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“…Note added in proof: After this work was nearly complete, a theory paper by Yang et al appeared on arXiv 42 , describing a quantum algorithm for assisting real-time dynamics with unconstrained QMC.…”

Section: Articlementioning

confidence: 99%

Unbiasing fermionic quantum Monte Carlo with a quantum computer

Huggins

O’Gorman

Rubin

et al. 2022

Nature

135

157

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Interacting many-electron problems pose some of the greatest computational challenges in science, with essential applications across many fields. The solutions to these problems will offer accurate predictions of chemical reactivity and kinetics, and other properties of quantum systems1–4. Fermionic quantum Monte Carlo (QMC) methods5,6, which use a statistical sampling of the ground state, are among the most powerful approaches to these problems. Controlling the fermionic sign problem with constraints ensures the efficiency of QMC at the expense of potentially significant biases owing to the limited flexibility of classical computation. Here we propose an approach that combines constrained QMC with quantum computation to reduce such biases. We implement our scheme experimentally using up to 16 qubits to unbias constrained QMC calculations performed on chemical systems with as many as 120 orbitals. These experiments represent the largest chemistry simulations performed with the help of quantum computers, while achieving accuracy that is competitive with state-of-the-art classical methods without burdensome error mitigation. Compared with the popular variational quantum eigensolver7,8, our hybrid quantum-classical computational model offers an alternative path towards achieving a practical quantum advantage for the electronic structure problem without demanding exceedingly accurate preparation and measurement of the ground-state wavefunction.

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Section: Articlementioning

confidence: 99%

Unbiasing fermionic quantum Monte Carlo with a quantum computer

Huggins

O’Gorman

Rubin

et al. 2022

Nature

135

157

View full text Add to dashboard Cite

show abstract

“…Gate reductions may be possible using other approximations of U(t) [47][48][49][50][51][52]. At the cost of classical signal-tonoise problems, stochastic state preparation yields shallower circuits [53][54][55][56]. Furthermore, performing scale setting classically can reduce quantum resources [57][58][59].…”

Section: Kks =mentioning

confidence: 99%

Improved Hamiltonians for Quantum Simulations

Carena,

Lamm,

et al. 2022

Preprint

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The quantum simulation of lattice gauge theories for the foreseeable future will be hampered by limited resources. The historical success of Symanzik-improved lattice actions in classical simulations strongly suggests that improved Hamiltonians will reduce quantum resources for fixed discretization errors. In this work, we consider Symanzik-improved lattice Hamiltonians for pure gauge theories and design quantum circuits for O(a 2 )-improved Hamiltonians in terms of primitive group gates. An explicit demonstration for Z2 is presented including exploratory tests using the ibm perth device.

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“…circuit depth) increases polynomially with the system size and imaginary time and polylogarithmically with the desired accuracy. This polylogarithmic scaling behaviour is obtained by cancelling Trotterisation errors according to the leading-order rotation (LOR) formula [26]. Given the imaginary-time evolution, we solve the groundstate problem following the projector QMC approach [27,28].…”

Section: Introductionmentioning

confidence: 99%

Error-resilient Monte Carlo quantum simulation of imaginary time

Huo

Liu

2023

Quantum

Self Cite

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Computing the ground-state properties of quantum many-body systems is a promising application of near-term quantum hardware with a potential impact in many fields. The conventional algorithm quantum phase estimation uses deep circuits and requires fault-tolerant technologies. Many quantum simulation algorithms developed recently work in an inexact and variational manner to exploit shallow circuits. In this work, we combine quantum Monte Carlo with quantum computing and propose an algorithm for simulating the imaginary-time evolution and solving the ground-state problem. By sampling the real-time evolution operator with a random evolution time according to a modified Cauchy-Lorentz distribution, we can compute the expected value of an observable in imaginary-time evolution. Our algorithm approaches the exact solution given a circuit depth increasing polylogarithmically with the desired accuracy. Compared with quantum phase estimation, the Trotter step number, i.e. the circuit depth, can be thousands of times smaller to achieve the same accuracy in the ground-state energy. We verify the resilience to Trotterisation errors caused by the finite circuit depth in the numerical simulation of various models. The results show that Monte Carlo quantum simulation is promising even without a fully fault-tolerant quantum computer.

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Accelerated Quantum Monte Carlo with Mitigated Error on Noisy Quantum Computer

Cited by 23 publications

References 63 publications

Unbiasing fermionic quantum Monte Carlo with a quantum computer

Unbiasing fermionic quantum Monte Carlo with a quantum computer

Improved Hamiltonians for Quantum Simulations

Error-resilient Monte Carlo quantum simulation of imaginary time

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