arXiv subjects

Robert M. Parrish

Publications and source records attributed to Robert M. Parrish.

24 records · Page 2Linked to original sources

arXiv2020

Low Rank Density Matrix Evolution for Noisy Quantum Circuits

In this work, we present an efficient rank-compression approach for the classical simulation of Kraus decoherence channels in noisy quantum circuits. The approximation is achieved through iterative compression of the density matrix based on its leading eigenbasis during each simulation step without the need to store, manipulate, or diagonalize the full matrix. We implement this algorithm in an in-house simulator, and show that the low rank algorithm speeds up simulations by more than two orders of magnitude over an existing implementation of full rank simulator, and with negligible error in the target noise and final observables. Finally, we demonstrate the utility of the low rank method as applied to representative problems of interest by using the algorithm to speed-up noisy simulations of Grover's search algorithm and quantum chemistry solvers.

quant-ph↗

arXiv2019

Quantum Filter Diagonalization: Quantum Eigendecomposition without Full Quantum Phase Estimation

We develop a quantum filter diagonalization method (QFD) that lies somewhere between the variational quantum eigensolver (VQE) and the phase estimation algorithm (PEA) in terms of required quantum circuit resources and conceptual simplicity. QFD uses a set of of time-propagated guess states as a variational basis for approximate diagonalization of a sparse Pauli Hamiltonian. The variational coefficients of the basis functions are determined by the Rayleigh-Ritz procedure by classically solving a generalized eigenvalue problem in the space of time-propagated guess states. The matrix elements of the subspace Hamiltonian and subspace metric matrix are each determined in quantum circuits by a one-ancilla extended swap test, i.e., statistical convergence of a one-ancilla PEA circuit. These matrix elements can be determined by many parallel quantum circuit evaluations, and the final Ritz estimates for the eigenvectors can conceptually be prepared as a linear combination over separate quantum state preparation circuits. The QFD method naturally provides for the computation of ground-state, excited-state, and transition expectation values. We numerically demonstrate the potential of the method by classical simulations of the QFD algorithm for an N=8 octamer of BChl-a chromophores represented by an 8-qubit ab initio exciton model (AIEM) Hamiltonian. Using only a handful of time-displacement points and a coarse, variational Trotter expansion of the time propagation operators, the QFD method recovers an accurate prediction of the absorption spectrum.

quant-ph↗

arXiv2019

Hybrid Quantum/Classical Derivative Theory: Analytical Gradients and Excited-State Dynamics for the Multistate Contracted Variational Quantum Eigensolver

The maturation of analytical derivative theory over the past few decades has enabled classical electronic structure theory to provide accurate and efficient predictions of a wide variety of observable properties. However, classical implementations of analytical derivative theory take advantage of explicit computational access to the approximate electronic wavefunctions in question, which is not possible for the emerging case of hybrid quantum/classical methods. Here, we develop an efficient Lagrangian-based approach for analytical first derivatives of hybrid quantum/classical methods using only observable quantities from the quantum portion of the algorithm. Specifically, we construct the key first-derivative property of the nuclear energy gradient for the recently-developed multistate, contracted variant of the variational quantum eigensolver (MC-VQE) within the context of the ab initio exciton model (AIEM). We show that a clean separation between the quantum and classical parts of the problem is enabled by the definition of an appropriate set of relaxed density matrices, and show how the wavefunction response equations in the quantum part of the algorithm (coupled-perturbed MC-VQE or CP-MC-VQE equations) are decoupled from the wavefunction response equations and and gradient perturbations in the classical part of the algorithm. We explore the magnitudes of the Hellmann-Feynman and response contributions to the gradients in quantum circuit simulations of MC-VQE+AIEM and demonstrate a quantum circuit simulator implementation of adiabatic excited state dynamics with MC-VQE+AIEM.

quant-ph↗

arXiv2019

Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver

We develop an extension of the variational quantum eigensolver (VQE) algorithm - multistate, contracted VQE (MC-VQE) - that allows for the efficient computation of the transition energies between the ground state and several low-lying excited states of a molecule, as well as the oscillator strengths associated with these transitions. We numerically simulate MC-VQE by computing the absorption spectrum of an ab initio exciton model of an 18-chromophore light-harvesting complex from purple photosynthetic bacteria.

quant-ph↗

arXiv2019

A Jacobi Diagonalization and Anderson Acceleration Algorithm For Variational Quantum Algorithm Parameter Optimization

The optimization of circuit parameters of variational quantum algorithms such as the variational quantum eigensolver (VQE) or the quantum approximate optimization algorithm (QAOA) is a key challenge for the practical deployment of near-term quantum computing algorithms. Here, we develop a hybrid quantum/classical optimization procedure inspired by the Jacobi diagonalization algorithm for classical eigendecomposition, and combined with Anderson acceleration. In the first stage, analytical tomography fittings are performed for a local cluster of circuit parameters via sampling of the observable objective function at quadrature points in the circuit angles. Classical optimization is used to determine the optimal circuit parameters within the cluster, with the other circuit parameters frozen. Different clusters of circuit parameters are then optimized in "sweeps,'' leading to a monotonically-convergent fixed-point procedure. In the second stage, the iterative history of the fixed-point Jacobi procedure is used to accelerate the convergence by applying Anderson acceleration/Pulay's direct inversion of the iterative subspace (DIIS). This Jacobi+Anderson method is numerically tested using a quantum circuit simulator (without noise) for a representative test case from the multistate, contracted variant of the variational quantum eigensolver (MC-VQE), and is found to be competitive with and often faster than Powell's method and L-BFGS.

quant-ph↗

arXiv2013

Tensor hypercontraction: A universal technique for the resolution of matrix elements of local, finite-range $N$-body potentials in many-body quantum problems

Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the eXact Tensor HyperContraction (X-THC) method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchange-like" contractions.

nucl-th↗