Simulating ManyBody Systems with a Projective Quantum Eigensolver
Abstract
We present a new hybrid quantumclassical algorithm for optimizing unitary coupledcluster (UCC) wave functions deemed the projective quantum eigensolver (PQE), amenable to nearterm noisy quantum hardware. Contrary to variational quantum algorithms, PQE optimizes a trial state using residuals (projections of the Schrödinger equation) rather than energy gradients. We show that the residuals may be evaluated by simply measuring two energy expectation values per element. We also introduce a selected variant of PQE (SPQE) that uses an adaptive ansatz built from arbitraryorder particlehole operators, offering an alternative to gradientbased selection procedures. PQE and SPQE are tested on a set of molecular systems covering both the weak and strong correlation regimes, including hydrogen clusters with four to ten atoms and the Be_{H 2} molecule. When employing a fixed ansatz, we find that PQE can converge disentangled (factorized) UCC wave functions to essentially identical energies as variational optimization while requiring fewer computational resources. A comparison of SPQE and adaptive variational quantum algorithms shows that—for ansätze containing the same number of parameters—the two methods yield results of comparable accuracy. Finally, we show that for a target energy accuracy, SPQE provides a parameterization of similar size or more concise than the one obtained via selected configuration interaction and the density matrix renormalization group on one to threedimensional strongly correlated H_{10} systems in terms of number of variational parameters.
 Publication:

PRX Quantum
 Pub Date:
 July 2021
 DOI:
 10.1103/PRXQuantum.2.030301
 arXiv:
 arXiv:2102.00345
 Bibcode:
 2021PRXQ....2c0301S
 Keywords:

 Quantum Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Physics  Chemical Physics
 EPrint:
 PRX Quantum 2, 030301 (2021)