A quantum computing approach to fixed-node Monte Carlo using classical shadows

Abstract

Quantum Monte Carlo (QMC) methods are powerful approaches for solving electronic structure problems. Although they often provide high-accuracy solutions, the precision of most QMC methods is ultimately limited by a trial wave function that must be used. Recently, an approach has been demonstrated to allow the use of trial wave functions prepared on a quantum computer [Nature 603, 416 (2022)] in the auxiliary-field QMC (AFQMC) method, using classical shadows to estimate the required overlaps. However, this approach has an exponential post-processing step to construct these overlaps, when performing classical shadows obtained using random Clifford circuits. Here, we study an approach to avoid this exponentially scaling step by using a fixed-node Monte Carlo method, based on full configuration interaction quantum Monte Carlo (FCIQMC). This method is applied to the local unitary cluster Jastrow (LUCJ) ansatz. We consider H${}_4$, ferrocene and benzene molecules using up to 12 qubits as examples. Circuits are compiled to native gates for typical near-term architectures, and we assess the impact of circuit-level depolarizing noise on the method. We also provide a comparison of AFQMC and fixed-node approaches, demonstrating that AFQMC is more robust to errors, although extrapolations of the fixed-node energy reduce this discrepancy. Although the method can be used to reach chemical accuracy, the sampling cost to achieve this is high even for small active spaces, suggesting caution for the prospect of outperforming conventional QMC approaches.

16 pages, 8 figures

References in corpus (39)

• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Improved Simulation of Stabilizer Circuits
• Recent developments in the PySCF program package
• Predicting Many Properties of a Quantum System from Very Few Measurements
• The Variational Quantum Eigensolver: a review of methods and best practices
• Efficient Z-Gates for Quantum Computing
• Noise tailoring for scalable quantum computation via randomized compiling
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Quantum Monte Carlo method using phase-free random walks with Slater determinants
• Automated construction of molecular active spaces from atomic valence orbitals
• Concrete Categorical Model of a Quantum Circuit Description Language with Measurement
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• Semistochastic Projector Monte Carlo Method
• A perspective on the current state-of-the-art of quantum computing for drug discovery applications
• Quantum algorithms to simulate many-body physics of correlated fermions
• Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
• Hadamard-free circuits expose the structure of the Clifford group
• The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method
• A Jastrow-type decomposition in quantum chemistry for low-depth quantum circuits
• Semi-stochastic full configuration interaction quantum Monte Carlo: developments and application
• Matchgate Shadows for Fermionic Quantum Simulation
• The Jastrow antisymmetric geminal power in Hilbert space: theory, benchmarking, and application to a novel transition state
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
• Shorter stabilizer circuits via Bruhat decomposition and quantum circuit transformations
• A Jastrow factor coupled cluster theory for weak and strong electron correlation
• Efficient multireference perturbation theory without high-order reduced density matrices
• Multireference configuration interaction and perturbation theory without reduced density matrices
• Systematic Comparison and Cross-validation of Fixed-Node Diffusion Monte Carlo and Phaseless Auxiliary-Field Quantum Monte Carlo in Solids
• FCI-QMC approach to the Fermi polaron
• Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations
• Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows
• Unbiasing Fermionic Auxiliary-Field Quantum Monte Carlo with Matrix Product State Trial Wavefunctions
• Quantum-assisted Monte Carlo algorithms for fermions
• Exponential challenges in unbiasing quantum Monte Carlo algorithms with quantum computers
• Identification of topological phases using classically-optimized variational quantum eigensolver
• An Improved Upper Bound for the Ground State Energy of Fermion Lattice Models
• Beyond CCSD(T) accuracy at lower scaling with auxiliary field quantum Monte Carlo

Cited by in corpus (1)

• Enhancing quantum computations with the synergy of auxiliary field quantum Monte Carlo and computational basis tomography