Fault-tolerant quantum computation of molecular observables

Abstract

Over the past three decades significant reductions have been made to the cost of estimating ground-state energies of molecular Hamiltonians with quantum computers. However, comparatively little attention has been paid to estimating the expectation values of other observables with respect to said ground states, which is important for many industrial applications. In this work we present a novel expectation value estimation (EVE) quantum algorithm which can be applied to estimate the expectation values of arbitrary observables with respect to any of the system's eigenstates. In particular, we consider two variants of EVE: std-EVE, based on standard quantum phase estimation, and QSP-EVE, which utilizes quantum signal processing (QSP) techniques. We provide rigorous error analysis for both both variants and minimize the number of individual phase factors for QSPEVE. These error analyses enable us to produce constant-factor quantum resource estimates for both std-EVE and QSP-EVE across a variety of molecular systems and observables. For the systems considered, we show that QSP-EVE reduces (Toffoli) gate counts by up to three orders of magnitude and reduces qubit width by up to 25% compared to std-EVE. While estimated resource counts remain far too high for the first generations of fault-tolerant quantum computers, our estimates mark a first of their kind for both the application of expectation value estimation and modern QSP-based techniques.

arXiv comment36 pages, 9 figures

References in corpus (33)

• Quantum Amplitude Amplification and Estimation
• Quantum Algorithms Revisited
• Recent developments in the PySCF program package
• Hamiltonian Simulation by Qubitization
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Elucidating Reaction Mechanisms on Quantum Computers
• Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• How accurate is density functional theory at predicting dipole moments? An assessment using a new database of 200 benchmark values
• Even more efficient quantum computations of chemistry through tensor hypercontraction
• Halving the cost of quantum addition
• Quantum computing enhanced computational catalysis
• Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
• Optimal Quantum Measurements of Expectation Values of Observables
• Near-optimal ground state preparation
• Efficient phase-factor evaluation in quantum signal processing
• Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices
• Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians
• Reliably assessing the electronic structure of cytochrome P450 on today's classical computers and tomorrow's quantum computers
• Preparing ground states of quantum many-body systems on a quantum computer
• Quantum Algorithm for Spectral Measurement with Lower Gate Count
• Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules
• Low communication high performance ab initio density matrix renormalization group algorithms
• Optimal quantum circuits for general phase estimation
• Quantum Filter Diagonalization with Double-Factorized Hamiltonians
• Quantum Algorithms for Estimating Physical Quantities using Block-Encodings
• On the energy landscape of symmetric quantum signal processing
• Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer
• Efficient quantum computation of molecular forces and other energy gradients
• Computing Ground State Properties with Early Fault-Tolerant Quantum Computers
• Perturbation theory with quantum signal processing
• Near-Optimal Quantum Algorithms for Multivariate Mean Estimation
• Effects of Cosine Tapering Window on Quantum Phase Estimation

Cited by in corpus (7)

• Drug design on quantum computers
• Benchmarking quantum computers
• Faster quantum chemistry simulations on a quantum computer with improved tensor factorization and active volume compilation
• Estimation of electrostatic interaction energies on a trapped-ion quantum computer
• Resource-optimized fault-tolerant simulation of the Fermi-Hubbard model and high-temperature superconductor models
• Simulating optically-active spin defects with a quantum computer
• Measuring Correlation and Entanglement between Molecular Orbitals on a Trapped-Ion Quantum Computer