We present a new technique that improves the scaling of the error in the adiabatic approximation with respect to the evolution duration, thereby permitting faster transfer at a fixed error tolerance. Our method is conceptually different from previously proposed techniques: it exploits a commonly overlooked phase interference effect that occurs predictably at specific evolution times, suppressing transitions away from the adiabatically transferred eigenstate. Our method can be used in concert with existing adiabatic optimization techniques, such as local adiabatic evolutions or boundary cancelation methods. We perform a full error analysis of our phase interference method along with existing boundary cancelation techniques and show a tradeoff between error-scaling and experimental precision. We illustrate these findings using two examples, showing improved error-scaling for an adiabatic search algorithm and a tunable two-qubit quantum logic gate. Acknowledgments 15 References 15The adiabatic approximation underpins many important present-day and future applications, such as stimulated rapid adiabatic passage (STIRAP) [1,2], coherent control of chemical reactions [3] and quantum information processing (QIP) [4,5]. This approximation asserts that a system will remain in an instantaneous eigenstate of a time-varying Hamiltonian if the time-variation happens slowly enough. Errors in this approximation correspond to transitions away from the instantaneous ('adiabatically transferred') eigenstate. For highperformance applications, it is not always practical to minimize errors by slowing things down. Ambitious future technologies, such as quantum computing devices, will demand simultaneous maximization of both accuracy and speed. In this paper, we investigate a phase cancelation effect that appears during an adiabatic evolution and can be exploited to polynomially reduce the probability of a given transition at fixed maximum evolution time. This can lead to speed increases at fixed error probability. Unlike alternative methods that obtain improvements by modifying the adiabatic path [6,7], our technique chooses the evolution time so that destructive interference suppresses the transition. Furthermore, this phase cancelation effect can be exploited to improve existing adiabatic error reduction strategies such as local adiabatic evolutions or boundary cancelation methods. We provide an error analysis of our method and conclude that the accuracy improvements come at the price of increasingly precise knowledge of the time-dependent Hamiltonian; this implies that accuracy is an important and quantifiable resource for quantum protocols utilizing adiabatic passage.
Adiabatic approximationThe adiabatic approximation states that if we consider the evolution of a quantum system under a time-dependent Hamiltonian that varies sufficiently slowly in time, then the time evolution operator approximately maps instantaneous eigenstates of the Hamiltonian at t = 0