High-fidelity universal quantum gates through quantum interfer- ence

Twisted rapid passage is a type of non-adiabatic rapid passage that gives rise to controllable quantum interference effects that were first observed experimentally in 2003. We show that twisted rapid passage sweeps can be used to implement a universal set of quantum gates that operate with high-fidelity. For each gate in the universal set, sweep parameter values are provided which simulations indicate will yield a quantum gate with error probability Pe < 10 . Note that all gates in this universal set are driven by a single type of control field (twisted rapid passage), and the error probability for each gate falls below the rough-and-ready estimate for the accuracy threshold Pa ∼ 10 . The simulations suggest that the universal gate set produced by twisted rapid passage shows promise for use in a fault-tolerant scheme for quantum computing. Introduction. – The physical context for our discussion is the accuracy threshold theorem [1–8] which established that a quantum computation of arbitrary duration could be done, with arbitrarily small error probability, in the presence of noise, and using imperfect quantum gates, under the following conditions. (1) The computational data is protected by a sufficiently layered concatenated quantum error correcting code. (2) Fault-tolerant protocols for quantum computation, error correction, and measurement are used. (3) A universal set of unencoded quantum gates is available with the property that each gate in the set has an error probability Pe that falls below a value Pa known as the accuracy threshold. The value of the threshold is model-dependent, though for many, Pa ∼ 10 has become a rough-and-ready estimate. Thus gates are anticipated to be approaching the accuracies needed for fault-tolerant quantum computing when Pe < 10 . One of the principal challenges facing the field of quantum computing is finding a way to implement a universal set of unencoded quantum gates for which all gate error probabilities satisfy Pe < 10 . In this Letter numerical simulation results are presented which suggest that a class of non-adiabatic rapid passage sweeps, first realized experimentally in 1991 [9], and known as twisted rapid passage (TRP), should be capable of implementing a universal set of unencoded quantum gates Gu that operate non-adiabatically, and with gate error probabilities satisfying Pe < 10 . Gu consists of the one-qubit Hadamard and NOT gates, together with variants of the one-qubit π/8 and phase gates, and the twoqubit controlled-phase gate. The universality of Gu was demonstrated in Ref. [10]. This level of gate accuracy is due to controllable quantum interference effects that arise during a TRP sweep [11,12], and which were observed using NMR in 2003 [13]. To find sweep parameter values that yield such high-performance gates, it proved necessary: (i) to combine the simulations with an optimization procedure that searches for minima of Pe [10,12]; and (ii) for the modified controlled-phase gate, to also apply the symmetrized evolution of Ref. [14]. The outline of this Letter is as follows. We begin with a summary of the essential properties of TRP. This is followed by a discussion of how the simulation and optimization are done, and how symmetrized evolution is incorporated into the two-qubit dynamics. We then present our simulation results for the different gates in Gu. We close with a discussion of our results and of future work. Preliminaries. – To introduce TRP [11,12], we consider a single qubit interacting with an external control