The relationship between minimum gap and success probability in adiabatic quantum computing

Abstract

We explore the relationship between two figures of merit for an adiabatic quantum computation process: the success probability $P$ and the minimum gap ${\Delta }_{min}$ between the ground and first excited states, investigating to what extent the success probability for an ensemble of problem Hamiltonians can be fitted by a function of ${\Delta }_{min}$ and the computation time $T$. We study a generic adiabatic algorithm and show that a rich structure exists in the distribution of $P$ and ${\Delta }_{min}$. In the case of two qubits, $P$ is to a good approximation a function of ${\Delta }_{min}$, of the stage in the evolution at which the minimum occurs and of $T$. This structure persists in examples of larger systems.

13 pages, 6 figures. Substantially updated, with further discussion of the phase diagram and the relation between one- and two-qubit evolution, as well as a greatly extended list of references

References in corpus (8)

• Landau-Zener-Stuckelberg interferometry
• Bounds for the adiabatic approximation with applications to quantum computation
• Simple proof of equivalence between adiabatic quantum computation and the circuit model
• Noise resistance of adiabatic quantum computation using random matrix theory
• Decoherence in a scalable adiabatic quantum computer
• Improved Error-Scaling for Adiabatic Quantum State Transfer
• Ramsey numbers and adiabatic quantum computing
• Optimal parametrizations of adiabatic paths

Cited by in corpus (3)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Schedule path optimization for quantum annealing and adiabatic quantum computing
• Recursive simulation of quantum annealing