Molecular Properties from Quantum Krylov Subspace Diagonalization
arXiv:2501.05286 · doi:10.1021/acs.jctc.5c00194
Abstract
Quantum Krylov subspace diagonalization is a prominent candidate for early fault tolerant quantum simulation of many-body and molecular systems, but so far the focus has been mainly on computing ground-state energies. We go beyond this by deriving analytical first-order derivatives for quantum Krylov methods and show how to obtain relaxed one and two particle reduced density matrices of the Krylov eigenstates. The direct approach to measuring these matrices requires a number of distinct measurement that scales quadratically with the Krylov dimension . Here, we show how to reduce this scaling to a constant. This is done by leveraging quantum signal processing to prepare Krylov eigenstates, including exited states, in depth linear in . We also compare several measurement schemes for efficiently obtaining the expectation value of an operator with states prepared using quantum signal processing. We validate our approach by computing the nuclear gradient of a small molecule and estimating its variance.
References in corpus (39)
- A variational eigenvalue solver on a quantum processor
- Barren plateaus in quantum neural network training landscapes
- Noisy intermediate-scale quantum (NISQ) algorithms
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Hamiltonian Simulation by Qubitization
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- Elucidating Reaction Mechanisms on Quantum Computers
- Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
- Entanglement-free Heisenberg-limited phase estimation
- Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
- Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
- Hamiltonian simulation with nearly optimal dependence on all parameters
- Even more efficient quantum computations of chemistry through tensor hypercontraction
- Quantum computing enhanced computational catalysis
- Is there evidence for exponential quantum advantage in quantum chemistry?
- Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
- Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
- Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers
- Fermionic partial tomography via classical shadows
- Efficient phase-factor evaluation in quantum signal processing
- Reliably assessing the electronic structure of cytochrome P450 on today's classical computers and tomorrow's quantum computers
- Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules
- Quantum Power Method by a Superposition of Time-Evolved States
- Calculating energy derivatives for quantum chemistry on a quantum computer
- Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation
- Matchgate Shadows for Fermionic Quantum Simulation
- Quantum Algorithm for Molecular Properties and Geometry Optimization
- Exact and efficient Lanczos method on a quantum computer
- A theory of quantum subspace diagonalization
- Theory of analytical energy derivatives for the variational quantum eigensolver
- Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer
- Efficient quantum computation of molecular forces and other energy gradients
- Reducing the runtime of fault-tolerant quantum simulations in chemistry through symmetry-compressed double factorization
- Accelerating Quantum Computations of Chemistry Through Regularized Compressed Double Factorization
- Efficient Quantum Analytic Nuclear Gradients with Double Factorization
- Analysis of quantum Krylov algorithms with errors
- Tailored and Externally Corrected Coupled Cluster with Quantum Inputs
- Sampling Error Analysis in Quantum Krylov Subspace Diagonalization
- Measurement-efficient quantum Krylov subspace diagonalisation