Accelerating Quantum Computations of Chemistry Through Regularized Compressed Double Factorization

Abstract

We propose the regularized compressed double factorization (RC-DF) method to classically compute compressed representations of molecular Hamiltonians that enable efficient simulation with noisy intermediate scale (NISQ) and error corrected quantum algorithms. We find that already for small systems with 12 to 20 qubits, the resulting NISQ measurement scheme reduces the number of measurement bases by roughly a factor of three and the shot count to reach chemical accuracy by a factor of three to six compared to truncated double factorization (DF) and we see order of magnitude improvements over Pauli grouping schemes. We demonstrate the scalability of our approach by performing RC-DF on the CpdI species of cytochrome P450 with 58 orbitals and find that using the resulting compressed Hamiltonian cuts the run time of qubitization and truncated DF based error corrected algorithms almost in half and even outperforms the lambda parameters achievable with tensor hypercontraction (THC) while at the same time reducing the CCSD(T) energy error heuristic by an order of magnitude.

References in corpus (23)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Recent developments in the PySCF program package
• Quantum Error Mitigation
• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• Even more efficient quantum computations of chemistry through tensor hypercontraction
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Quantum computing enhanced computational catalysis
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Automated construction of molecular active spaces from atomic valence orbitals
• Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
• Low rank representations for quantum simulation of electronic structure
• Reliably assessing the electronic structure of cytochrome P450 on today's classical computers and tomorrow's quantum computers
• Matchgate Shadows for Fermionic Quantum Simulation
• Quantum Filter Diagonalization with Double-Factorized Hamiltonians
• Error mitigation via verified phase estimation
• Purification-based quantum error mitigation of pair-correlated electron simulations
• Cartan sub-algebra approach to efficient measurements of quantum observables
• Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
• Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space
• Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver
• Efficient Quantum Analytic Nuclear Gradients with Double Factorization

Cited by in corpus (7)

• Faster quantum chemistry simulations on a quantum computer with improved tensor factorization and active volume compilation
• Quantum Simulation of Realistic Materials in First Quantization Using Non-local Pseudopotentials
• Fast quantum simulation of electronic structure by spectrum amplification
• Molecular Properties from Quantum Krylov Subspace Diagonalization
• Simulating Chemistry with Fermionic Optical Superlattices
• Phase estimation with partially randomized time evolution
• Moments-based quantum computation of the electric dipole moment of molecular systems