• Corpus ID: 248887392

# Exponential challenges in unbiasing quantum Monte Carlo algorithms with quantum computers

@inproceedings{Mazzola2022ExponentialCI,
title={Exponential challenges in unbiasing quantum Monte Carlo algorithms with quantum computers},
author={Guglielmo Mazzola and Giuseppe Carleo},
year={2022}
}
• Published 18 May 2022
• Physics
Recently, Huggins et. al. [1] devised a general projective Quantum Monte Carlo method suitable for implementation on quantum computers. This hybrid approach, however, relies on a subroutine –the computation of the local energy estimator on the quantum computer– that is intrinsically aﬀected by an exponential scaling of the computational time with the number of qubits. By means of numerical experiments, we show that this exponential scaling manifests prominently already on systems below the…

## References

SHOWING 1-10 OF 10 REFERENCES
Unbiasing fermionic quantum Monte Carlo with a quantum computer
• Physics
Nature
• 2022
The results demonstrate a new paradigm of hybrid quantum-classical algorithm, surpassing the popular variational quantum eigensolver in terms of potential towards the first practical quantum advantage in ground state many-electron calculations.
Progress towards practical quantum variational algorithms
• Physics
• 2015
The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the
Simulating Quantum Circuits with Sparse Output Distributions
• Computer Science
Electron. Colloquium Comput. Complex.
• 2013
We show that several quantum circuit families can be simulated efficiently classically if it is promised that their output distribution is approximately sparse i.e. the distribution is close to one
Low overhead quantum computation using lattice surgery
• Computer Science
• 2018
It is shown that lattice surgery reduces the storage overhead, and the distillation overhead by nearly a factor of 5, making it possible to run algorithms with $10^8$ T gates using only $3.7\times 10^5$ physical qubits capable of executing gates with error.
Ground-state correlations of quantum antiferromagnets: A Green-function Monte Carlo study.
• Physics
Physical review. B, Condensed matter
• 1990
A well-known transformation is used to map the spin problem onto a system of hard-core bosons that allows us to exploit interesting analogies between magnetism and superfluidity.
Finite-size study of the ground-state energy, susceptibility, and spin-wave velocity for the Heisenberg antiferromagnet.
• Runge
• Physics
Physical review. B, Condensed matter
• 1992
The Green's-function Monte Carlo method is used to calculate very accurate ground-state energies of the two-dimensional, spin-1/2 Heisenberg antiferromagnet, and the value of {ital Z}{sub {chi}} computed here is in agreement with the series-expansion results of Singh and of Zheng, Oitmaa, and Hamer, thereby clearing up a previous inconsistency.
Quantum Monte Carlo Approaches for Correlated Systems
Over the past several decades, computational approaches to studying strongly-interacting systems have become increasingly varied and sophisticated. This book provides a comprehensive introduction to
THE GROUND STATE OF THE ELECTRON GAS BY A STOCHASTIC METHOD
., • ' % . ^ : K ~* B J£L~i0813_ 4JC-4 J NATIONAL RESOURCE FOR COMPUTATION IN CHEMISTRY^ '• • ' THE 81R0UND STATED 6|/THE ELECTION A - - .A r >'--H .1 ,4- v c ' M \>~ r tAWRfctftE BERKELEY LABORATORY
Quantum Monte Carlo simulations of solids
• Physics
• 2001
This article describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems. These stochastic
Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Physics
Physical review letters
• 2005
It is proved that the sign problem is nondeterministic polynomial (NP) hard, implying that a generic solution of the sign problems would also solve all problems in the complexity class NP inPolynomial time.