Variational quantum state diagonalization
Abstract Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost evaluation), and a classical computer uses this information to adjust the parameters of the gate sequence. Here we present such an algorithm for quantum state diagonalization. State diagonalization has applications in condensed matter physics (e.g., entanglement spectroscopy) as well as in machine learning (e.g., principal component analysis). For a quantum state ρ and gate sequence U , our cost function quantifies how far $$$$U\rho U^\dagger$$$$ is from being diagonal. We introduce short-depth quantum circuits to quantify our cost. Minimizing this cost returns a gate sequence that approximately diagonalizes ρ . One can then read out approximations of the largest eigenvalues, and the associated eigenvectors, of ρ . As a proof-of-principle, we implement our algorithm on Rigetti’s quantum computer to diagonalize one-qubit states and on a simulator to find the entanglement spectrum of the Heisenberg model ground state.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Quantum Information Science (QIS)
- Sponsoring Organization:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1619716
- Alternate ID(s):
- OSTI ID: 1544727
- Report Number(s):
- LA-UR-18-29266; 57; PII: 167
- Journal Information:
- npj Quantum Information, Journal Name: npj Quantum Information Vol. 5 Journal Issue: 1; ISSN 2056-6387
- Publisher:
- Nature Publishing GroupCopyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English
Web of Science
Similar Records
Quantum-assisted quantum compiling
Estimation of biquadratic and bicubic Heisenberg effective couplings from multiorbital Hubbard models