Quantum Speed-Up at Zero Temperature via Coherent Catalysis

Abstract

It is known that secondary non-stoquastic drivers may offer speed-ups or catalysis in some models of adiabatic quantum computation accompanying the more typical transverse field driver. Their combined intent is to raze potential barriers to zero during adiabatic evolution from a false vacuum to a true minimum; first order phase transitions are softened into second order transitions. We move beyond mean-field analysis to a fully quantum model of a spin ensemble undergoing adiabatic evolution in which the spins are mapped to a variable mass particle in a continuous one-dimensional potential. We demonstrate the necessary criteria for enhanced mobility or `speed-up' across potential barriers is actually a quantum form of the Rayleigh criterion. Quantum catalysis is exhibited in models where previously thought not possible, when barriers cannot be eliminated. For the $3$-spin model with secondary anti-ferromagnetic driver, catalysed time complexity scales between linear and quadratically with the number of qubits. As a corollary, we identify a useful resonance criterion for quantum phase transition that differs from the classical one, but converges on it, in the thermodynamic limit.

Notes associated with a talk given at UC Berkeley, October 2017 (v3 is Phys. Rev. A accepted version)

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Cited by in corpus (15)

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• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
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• Variationally Scheduled Quantum Simulation
• De-Signing Hamiltonians for Quantum Adiabatic Optimization
• Circumventing superexponential runtimes for hard instances of quantum adiabatic optimization
• Permutation Matrix Representation Quantum Monte Carlo
• Deep learning optimal quantum annealing schedules for random Ising models
• Diagonal Catalysts in Quantum Adiabatic Optimization
• Symmetry-Protected Quantum Adiabatic Evolution in Spontaneous Symmetry-Breaking Transitions
• Improving nonstoquastic quantum annealing with spin-reversal transformations
• Exponential speedup of incoherent tunneling via dissipation
• Boosting quantum annealing performance through direct polynomial unconstrained binary optimization
• Reduction of the energy-gap scaling by coherent catalysis in models of quantum annealing