Quantum and Classical in Adiabatic Computation

Abstract

Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialised state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose groundstate encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimisation algorithms and quantum adiabatic optimisation. This new perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing - though inconclusive - results.

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Cited by in corpus (20)

• Quantum information processing with superconducting circuits: a review
• What is the Computational Value of Finite Range Tunneling?
• Probing for quantum speedup in spin glass problems with planted solutions
• Decoherence in adiabatic quantum computation
• Reexamining classical and quantum models for the D-Wave One processor
• Quantum Annealing Correction with Minor Embedding
• Quantum annealing of the $p$-spin model under inhomogeneous transverse field driving
• Nested Quantum Annealing Correction
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Scalable effective temperature reduction for quantum annealers via nested quantum annealing correction
• Benchmarking quantum annealing dynamics: the spin-vector Langevin model
• Error suppression in adiabatic quantum computing with qubit ensembles
• An Anisotropic Landau-Lifschitz-Gilbert model of dissipation in qubits
• Retrieving the ground state of spin glasses using thermal noise: Performance of quantum annealing at finite temperatures
• On the quantum spin glass transition on the Bethe lattice
• Dissipative failure of adiabatic quantum transport as a dynamical phase transition
• Recursive simulation of quantum annealing
• A Generalised Haldane Map from the Matrix Product State Path Integral to the Critical Theory of the $J_1$-$J_2$ Chain
• The Perturbed Ferromagnetic Chain: A Tuneable Test of Quantum Hardness in the Transverse-Field Ising Model
• Phase Transitions in the Classical Simulability of Open Quantum Systems