Repeat-until-success cubic phase gate for universal continuous-variable quantum computation

Abstract

In order to achieve universal quantum computation using continuous variables, one needs to jump out of the set of Gaussian operations and have a non-Gaussian element, such as the cubic phase gate. However, such a gate is currently very difficult to implement in practice. Here we introduce an experimentally viable 'repeat-untilsuccess' approach to generating the cubic phase gate, which is achieved using sequential photon subtractions and Gaussian operations. We find that our scheme offers benefits in terms of the expected time until success, although we require a primitive quantum memory.

Quantum Machine Learning over Infinite Dimensions

“…The operations in C cc S can be implemented with the quartic gate introduced in [38,47]. See Supplementary Material for more detail.…”

“…which can be efficiently implemented by a cubic phase gate and linear optics [27,38]. In practice, the success of the algorithm relies on the distinguishability of |γλ i q , which depends on the spectrum of eigenvalues, the degree of squeezing s of the auxiliary state, and the magnitude of error.…”

“…1). This serves as an input to the phase-dependent gates outlined in [38], which can be used to construct the exponential swap gate. The rotation gate in Eq.…”

“…It can be implemented by treating the auxiliary mode, R, as the ancilla in the phase-dependent gate. Thus, the principle component analysis problem essentially relies on repeated application of the 'repeat-until-success' phase gate [38]. In a realistic scenario, R is in a single-mode squeezed state with finite squeezing (see Supplementary Section), which is experimentally straightforward using a belowthreshold optical parametric amplifier (OPA).…”

“…which can be implemented efficiently [38]. The state then becomes e iγAp RpS |b |0 q,R |0 q,S = i b i |e i |p p,R |γλ i p q,S dp,…”