General error estimate for adiabatic quantum computing

Abstract

Most investigations devoted to the conditions for adiabatic quantum computing are based on the first-order correction $⟨{\Psi }_{\mathrm{ground}}(t)|\dot{H}(t)|{\Psi }_{\mathrm{excited}}(t)⟩/\Delta E^2(t)\ll 1$. However, it is demonstrated that this first-order correction does not yield a good estimate for the computational error. Therefore, a more general criterion is proposed, which includes higher-order corrections as well and shows that the computational error can be made exponentially small -- which facilitates significantly shorter evolution times than the above first-order estimate in certain situations. Based on this criterion and rather general arguments and assumptions, it can be demonstrated that a run-time $T$ of order of the inverse minimum energy gap $\Delta E_{\min }$ is sufficient and necessary, i.e., $T=\ord(ΔE_{\rm min}^{-1})$. For some examples, these analytical investigations are confirmed by numerical simulations. PACS: 03.67.Lx, 03.67.-a.

8 pages, 6 figures, several modifications

References in corpus (3)

• Adiabatic Quantum Computation in Open Systems
• Exponential complexity of an adiabatic algorithm for an NP-complete problem
• Scaling of running time of quantum adiabatic algorithm for propositional satisfiability

Cited by in corpus (41)

• Shortcuts to adiabaticity: concepts, methods, and applications
• Bounds for the adiabatic approximation with applications to quantum computation
• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• Fast adiabatic qubit gates using only ${\sigma }_z$ control
• Error correcting codes for adiabatic quantum computation
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Preservation of Positivity by Dynamical Coarse-Graining
• First Order Quantum Phase Transition in Adiabatic Quantum Computation
• Adiabatic Preparation of Topological Order
• Accuracy vs run time in adiabatic quantum search
• Transport Statistics of Interacting Double Dot Systems: Coherent and Non-Markovian Effects
• Adiabatic Gate Teleportation
• Collective performance of a finite-time quantum Otto cycle
• Necessary Condition for the Quantum Adiabatic Approximation
• Non-Markovian decoherence in the adiabatic quantum search algorithm
• Decoherence in the dynamical quantum phase transition of the transverse Ising chain
• Schedule path optimization for quantum annealing and adiabatic quantum computing
• A Cooper-Pair Box Coupled to Two Resonators: An Architecture for a Quantum Refrigerator
• Adiabatic Cluster State Quantum Computing
• Adiabatic preparation without Quantum Phase Transitions
• Nonadiabatic dynamics of the excited states for the Lipkin-Meshkov-Glick model
• Cooperative efficiency boost for quantum heat engines
• Adiabatic evolution under quantum control
• Adiabatic Quantum Transistors
• Continuous-Time Quantum Algorithms for Unstructured Problems
• Error suppression in adiabatic quantum computing with qubit ensembles
• The three phases of quantum annealing: fast, slow, and very slow
• Demonstrating Majorana non-Abelian properties using fast adiabatic charge-transfer
• Quantum adiabatic optimization with Rydberg arrays: localization phenomena and encoding strategies
• How Fast Can Quantum Annealers Count?
• Dynamical quantum phase transitions
• Non-Adiabatic Quantum Dynamics of Grover's Adiabatic Search Algorithm
• Quantum dynamics with an ensemble of Hamiltonians
• Why the Quantitative Condition Fails to Reveal Quantum Adiabaticity
• Decoherence in a dynamical quantum phase transition
• Probing nonlinear adiabatic paths with a universal integrator
• Ultrafast coherent control of spinor Bose-Einstein condensates using stimulated Raman adiabatic passage
• Pechukas-Yukawa formalism for Landau-Zener transitions in the presence of external noise
• Pechukas-Yukawa approach to the evolution of the quantum state of a parametrically perturbed system
• General conditions for a quantum adiabatic evolution
• Bounding Run-Times of Local Adiabatic Algorithms