Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems

Abstract

Quantum computing is a promising approach to harnessing strong correlation in molecular systems; however, current devices only allow for hybrid quantum-classical algorithms with a shallow circuit depth, such as the variational quantum eigensolver (VQE). In this study, we report the importance of the Hamiltonian symmetry in constructing VQE circuits adaptively. This treatment often violates symmetry, thereby deteriorating the convergence of fidelity to the exact solution, and ultimately resulting in deeper circuits. We demonstrate that symmetry-projection can provide a simple yet effective solution to this problem, by keeping the quantum state in the correct symmetry space, to reduce the overall gate operations. The scheme also reveals the significance of preserving symmetry in computing molecular properties, as demonstrated in our illustrative calculations.

References in corpus (41)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Evaluating analytic gradients on quantum hardware
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Solving strongly correlated electron models on a quantum computer
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• Projected Hartree-Fock Theory
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Projected Quasiparticle Theory for Molecular Electronic Structure
• Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
• Variational Quantum Eigensolver with Fewer Qubits
• Quantum Orbital-Optimized Unitary Coupled Cluster Methods in the Strongly Correlated Regime: Can Quantum Algorithms Outperform their Classical Equivalents?
• Qubit-excitation-based adaptive variational quantum eigensolver
• Reducing qubit requirements for quantum simulation using molecular point group symmetries
• Orbital optimized unitary coupled cluster theory for quantum computer
• Efficient quantum circuits for quantum computational chemistry
• Calculating energy derivatives for quantum chemistry on a quantum computer
• Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation
• Symmetry-adapted variational quantum eigensolver
• Efficient step-merged quantum imaginary time evolution algorithm for quantum chemistry
• A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers
• ROHF Theory Made Simple
• Solving Nuclear Structure Problems with the Adaptive Variational Quantum Algorithm
• Theory of analytical energy derivatives for the variational quantum eigensolver
• Correlating AGP on a quantum computer
• Analytic gradients in variational quantum algorithms: Algebraic extensions of the parameter-shift rule to general unitary transformations
• Benchmarking adaptive variational quantum eigensolvers
• Variational quantum algorithm for molecular geometry optimization
• Spin-projection for quantum computation: A low-depth approach to strong correlation
• Configuration interaction combined with spin-projection for strongly correlated molecular electronic structures
• Shallow-circuit variational quantum eigensolver based on symmetry-inspired Hilbert space partitioning for quantum chemical calculations
• Filtering states with total spin on a quantum computer
• Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer
• General technique for analytical derivatives of post-projected Hartree-Fock

Cited by in corpus (6)

• Improved algorithms of quantum imaginary time evolution for ground and excited states of molecular systems
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• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
• Quantum computing of magnetic-skyrmion-like patterns in Heisenberg ferromagnets
• Mitigating the measurement overhead of ADAPT-VQE with optimised informationally complete generalised measurements