Year: 2022
Type: article
Abstract: Stoquastic Hamiltonians play a role in the computational complexity of the local Hamiltonian problem as well as the study of classical simulability. In particular, stoquastic Hamiltonians can be straightforwardly simulated using Monte Carlo techniques. We address the question of whether two or more Hamiltonians may be made simultaneously stoquastic via a unitary transformation. This question has important implications for the complexity of simulating quantum annealing where quantum advantage is related to the stoquasticity of the Hamiltonians involved in the anneal. We find that for almost all problems no such unitary exists and show that the problem of determining the existence of such a unitary is equivalent to identifying if there is a solution to a system of polynomial (in)equalities in the matrix elements of the initial and transformed Hamiltonians. Solving such a system of equations is NP-hard. We highlight a geometric understanding of this problem in terms of a collection of generalized Bloch vectors.
Source: Physical Review A
Authors: Jacob Bringewatt, Lucas T. Brady
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, U.S. Department of Energy, National Aeronautics and Space Administration, National Institute of Standards and Technology, Defense Advanced Research Projects Agency, Office of Science, Ames Research Center, Multidisciplinary University Research Initiative, Advanced Scientific Computing Research, Air Force Office of Scientific Research, Army Research Office
Awards: G1543527024, G1938338418, G1965873410, G2127201742, G2277900919, QLCI-CI: NSF Quantum Leap Challenge Institute for Robust Quantum Simulation, G3138666703, FUNDAMENTAL ALGORITHMIC RESEARCH FOR QUANTUM COMPUTING, FUNDAMENTAL ALGORITHMIC RESEARCH FOR QUANTUM COMPUTING, G4010038600, DOE COMPUTATIONAL SCIENCE GRADUATE FELLOWSHIP (CSGF) GRANT 2019 COHORT, G4782275651, EFFICIENT AND RELIABLE MAPPING OF QUANTUM COMPUTATIONS ONTO REALISTIC ARCHITECTURES, G4850096730, QUANTUM COMPUTING IN CHEMICAL AND MATERIAL SCIENCES, G5372923749, QUANTUM COMPUTING IN CHEMICAL AND MATERIAL SCIENCES, DOE COMPUTATIONAL SCIENCE GRADUATE FELLOWSHIP (CSGF) GRANT 2019 COHORT, G7436220671, EFFICIENT AND RELIABLE MAPPING OF QUANTUM COMPUTATIONS ONTO REALISTIC ARCHITECTURES, G8532239345, G8729776176
OpenAlex ID: W4226026944