Non-unitary operations for ground-state calculations in near term quantum computers

Abstract

We introduce a quantum Monte Carlo inspired reweighting scheme to accurately compute energies from optimally short quantum circuits. This effectively hybrid quantum-classical approach features both entanglement provided by a short quantum circuit, and the presence of an effective non-unitary operator at the same time. The functional form of this projector is borrowed from classical computation and is able to filter-out high-energy components generated by a sub-optimal variational quantum heuristic ansatz. The accuracy of this approach is demonstrated numerically in finding energies of entangled ground-states of many-body lattice models. We demonstrate a practical implementation on IBM quantum hardwares up to an 8 qubits circuit.

arXiv comment5 pages + supplementary materials

References in corpus (38)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Correlated Electrons in High Temperature Superconductors
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Complexity in Strongly Correlated Electronic Systems
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Scalable Quantum Simulation of Molecular Energies
• Towards Quantum Chemistry on a Quantum Computer
• Towards Practical Quantum Variational Algorithms
• Validating quantum computers using randomized model circuits
• Quantum optimization using variational algorithms on near-term quantum devices
• Identifying Topological Order by Entanglement Entropy
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• Gate count estimates for performing quantum chemistry on small quantum computers
• Solving strongly correlated electron models on a quantum computer
• Error-mitigated digital quantum simulation
• Correlated geminal wave function for molecules: an efficient resonating valence bond approach
• Resonating Valence Bond Wave Functions for Strongly Frustrated Spin Systems
• Superconductivity in the two-dimensional t-J model
• Mapping local Hamiltonians of fermions to local Hamiltonians of spins
• Variational description of Mott insulators
• Gate-efficient simulation of molecular eigenstates on a quantum computer
• Phase diagram of hydrogen and a hydrogen-helium mixture at planetary conditions by Quantum Monte Carlo simulations
• The Jastrow antisymmetric geminal power in Hilbert space: theory, benchmarking, and application to a novel transition state
• Static and dynamical correlation in diradical molecules by Quantum Monte Carlo using the Jastrow Antisymmetrized Geminal Power ansatz
• Magnetism and superconductivity in the $t-t^{\prime }-J$ model
• A Jastrow factor coupled cluster theory for weak and strong electron correlation
• Preparing projected entangled pair states on a quantum computer
• Absence of static stripes in the two-dimensional $t-J$ model by an accurate and systematic quantum Monte Carlo approach
• Emulating the one-dimensional Fermi-Hubbard model by a double chain of qubits
• Assessing the Accuracy of the Jastrow Antisymmetrized Geminal Power in the H4 Model System

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