Performance Evaluation of Adiabatic Quantum Computation via Quantum Speed Limits and Possible Applications to Many-Body Systems

Abstract

The quantum speed limit specifies a universal bound of the fidelity between the initial state and the time-evolved state. We apply this method to find a bound of the fidelity between the adiabatic state and the time-evolved state. The bound is characterized by the counterdiabatic Hamiltonian and can be used to evaluate the worst case performance of the adiabatic quantum computation. The result is improved by imposing additional conditions and we examine several models to find a tight bound. We also derive a different type of quantum speed limits that is meaningful even when we take the thermodynamic limit. By using solvable spin models, we study how the performance and the bound are affected by phase transitions.

arXiv comment6 pages, 3 figures, minor changes

References in corpus (41)

• Quantum Annealing in the Transverse Ising Model
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Adiabatic Quantum Computing
• Ultimate physical limits to computation
• Shortcuts to adiabaticity: concepts, methods, and applications
• The maximum speed of dynamical evolution
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Quantum annealing with more than one hundred qubits
• Fast optimal frictionless atom cooling in harmonic traps
• Shortcuts to adiabaticity
• Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
• Computational capacity of the universe
• Shortcuts to adiabaticity by counter-diabatic driving
• Quantum speed limit for physical processes
• Quantum speed limit for non-Markovian dynamics
• Quantum speed limits in open system dynamics
• Bounds for the adiabatic approximation with applications to quantum computation
• The fundamental limit on the rate of quantum dynamics: the unified bound is tight
• Classical and quantum shortcuts to adiabaticity for scale-invariant driving
• Minimizing irreversible losses in quantum systems by local counter-diabatic driving
• Trade-off between speed and cost in shortcuts to adiabaticity
• Quantum Adiabatic Brachistochrone
• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Decoherence in adiabatic quantum computation
• Generating shortcuts to adiabaticity in quantum and classical dynamics
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Environment assisted speed-up of the field evolution in cavity QED
• Superadiabatic Controlled Evolutions and Universal Quantum Computation
• Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
• Geometric Speed Limit of Accessible Many-Body State Preparation
• Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
• Necessary Condition for the Quantum Adiabatic Approximation
• A note on the switching adiabatic theorem
• From Classical Nonlinear Integrable Systems to Quantum Shortcuts to Adiabaticity
• Energetic cost of superadiabatic quantum computation
• Steering random spin systems to speed up the quantum adiabatic algorithm
• Hamiltonian engineering for adiabatic quantum computation: Lessons from shortcuts to adiabaticity
• Complex semiclassical analysis of the Loschmidt amplitude and dynamical quantum phase transitions
• Faster annealing schedules for quantum annealing
• Shortcuts to adiabaticity applied to nonequilibrium entropy production: An information geometry viewpoint
• Unitary deformations of counterdiabatic driving

Cited by in corpus (29)

• Unifying Quantum and Classical Speed Limits on Observables
• Controlling and exploring quantum systems by algebraic expression of adiabatic gauge potential
• Shortcuts to Adiabaticity in Krylov Space
• Quantum speed limits on operator flows and correlation functions
• Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
• Speed limits on correlations in bipartite quantum systems
• Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations
• Quantum speed limit for thermal states
• General bound on the performance of counter-diabatic driving acting on dissipative spin systems
• State-dependent error bound for digital quantum simulation of driven systems
• Quantum speed limit for states and observables of perturbed open systems
• Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators
• Exact thermal properties of free-fermionic spin chains
• Quantum speed limits in arbitrary phase spaces
• Quantum Speed Limit under Brachistochrone Evolution
• Quantum lower and upper speed limits
• Scaling of errors in digitized counterdiabatic driving
• Bounds on quantum adiabaticity in driven many-body systems from generalized orthogonality catastrophe and quantum speed limit
• Quantum speed limit for the maximum coherent state under squeezed environment
• Performance evaluation of invariant-based inverse engineering by quantum speed limit
• Quantum work statistics of controlled evolutions
• Lower bounds for adiabatic quantum algorithms by quantum speed limits
• Generalized speed limits for classical stochastic systems and their applications to relaxation, annealing, and pumping processes
• Quantum annealing showing an exponentially small success probability despite a constant energy gap with polynomial energy
• The underlying order induced by orthogonality and the quantum speed limit
• Quantum speed limits in dephasing dynamics of a qubit system coupled to thermal environments
• Quantum speed limits for an open system in contact with a thermal bath
• Implementation of multiparticle quantum speed limits on observables
• Rate Function Modelling of Quantum Many-Body Adiabaticity