Time-frequency Talbot effect as Clifford operations on entangled time-frequency GKP states

TL;DR

This paper demonstrates how the time-frequency Talbot effect can implement Clifford operations on entangled GKP qubits, enabling robust quantum information processing with potential for experimental realization.

Contribution

It introduces the use of the TF Talbot effect as a means to perform Clifford gates on entangled TF-GKP states, linking diffraction phenomena to quantum error correction.

Findings

The TF Talbot effect can implement Clifford operations on TF-GKP states.

The signature of the effect is observable via a generalized Hong-Ou-Mandel interferometer.

Feasibility analysis shows current technology can realize these operations, with comb finesse as a key parameter.

Abstract

The Talbot effect -- a near-field diffraction phenomenon in which a periodic wavefront self-images at regular distances -- can be transposed to the time--frequency domain via the space--time duality between diffraction and dispersive broadening. We exploit this analogy to define the time--frequency (TF) Talbot effect and show that it implements different Clifford operations on TF Gottesman-Kitaev-Preskill (TF-GKP) qubits (Phys. Rev. 102, 012607), a class of qubit states encoded in the discretised frequency and time-of-arrival degrees of freedom of entangled photon pairs, whose logical basis corresponds to even and odd components of an entangled frequency combs. These states are intrinsically robust against small frequency and temporal displacements, which can be further corrected by linear or nonlinear quantum error-correction schemes. We analyse the role of the comb envelope and peak width relative to the free spectral range, and show that a compromise must be made between the gate fidelity of the Clifford gates induced by TF-Talbot operation and the error-correction capacity of the code. We then demonstrate that the signature of the TF-Talbot effect is directly accessible via the generalised Hong-Ou-Mandel interferometer: all six logical GKP states can be unambiguously distinguished by introducing a frequency shift of half the comb periodicity in one interferometer arm. We conclude with a feasibility analysis based on current experimental technology, identifying the comb finesse as the key figure of merit for both gate performance and correctability. This conclusion extends naturally to quadrature GKP states, where a shear in quadrature phase space is precisely a Talbot effect.