Decoherence in adiabatic quantum computation

Abstract

Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time-scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit T2 time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary cancellation methods, designed to improve the fidelity of adiabatic quantum computing in the closed system setting, remain beneficial in the open system setting. To address the high computational cost of master equation simulations, we also demonstrate that a quantum Monte Carlo algorithm that explicitly accounts for a thermal bosonic bath can be used to interpolate between classical and quantum annealing. Our study highlights and clarifies the significantly different role played by decoherence in the adiabatic and circuit models of quantum computing.

The Nature and Correction of Diabatic Errors in Anyon Braiding

“…The Oðt −2 op Þ diabatic transition probability is characteristic of any continuous, but otherwise generic, time dependence. A set of more general results show that errors become smaller as the evolution becomes smoother [9][10][11]. If the first k derivatives of the Hamiltonian exist and are continuous, then the diabatic corrections to the transition probability vanish as Oðt −2k−2 op Þ.…”

“…However, the scaling of diabatic corrections is sensitive to the precise time dependence of the parameters in the Hamiltonian. In particular, the corrections are Oð1=t kþ1 op Þ when the time dependence is C k smooth [9][10][11], and they are exponentially suppressed when the time dependence is analytic [12][13][14][15][16]. (Infinitely smooth C ∞ time dependence may result in stretched exponential decay of corrections.)…”

Adiabatic Quantum Search in Open Systems

“…Furthermore, AQC is affected by noise present in any realistic implementation. It has been suggested that AQC may be inherently robust against noise [12,13] and that the presence of an environment may even improve performance [14]. Adiabatic evolution is particularly susceptible to noise when the gap between the ground state and the excited states is small.…”

Performance of two different quantum annealing correction codes

“…In the closed system setting, starting in the ground state of H(0) and evolving adiabatically, the system is guaranteed to reach the ground state of H I with high probability [15][16][17]. Although adiabatic dynamics is robust against certain forms of decoherence appearing in the more realistic open system setting [10,[18][19][20][21][22][23], it remains susceptible to thermal noise and specification errors [24], which can jeopardize the efficiency of the quantum computation. Therefore, any scalable quantum annealing architecture will require quantum error correction [25].…”