Parallelizable Synthesis of Arbitrary Single-Qubit Gates with Linear Optics and Time-Frequency Encoding

TL;DR

This paper introduces novel, experimentally feasible methods for the exact synthesis and parallelization of arbitrary single-qubit gates using spectral and temporal linear optical quantum computing, with high fidelity and success probability.

Contribution

It presents a new analytical approach for single-qubit gate synthesis in time-bin encoding and explores parallelization strategies in spectral and temporal encodings with practical experimental setups.

Findings

High-fidelity arbitrary single-qubit gates can be synthesized with minimal RF tones.

Parallelization of multiple Hadamard gates is feasible with optimized resource use.

Spectral S-LOQC enables massively parallel single-qubit operations.

Abstract

We propose novel methods for the exact synthesis of single-qubit unitaries with high success probability and gate fidelity, considering both time-bin and frequency-bin encodings. The proposed schemes are experimentally implementable with a spectral linear-optical quantum computation (S- LOQC) platform, composed of electro-optic phase modulators and phase-only programmable filters (pulse shapers). We assess the performances in terms of fidelity and probability of the two simplest 3-components configurations for arbitrary gate generation in both encodings and give an exact analytical solution for the synthesis of an arbitrary single-qubit unitary in the time-bin encoding, using a single-tone Radio Frequency (RF) driving of the EOMs. We further investigate the parallelization of arbitrary single-qubit gates over multiple qubits with a compact experimental setup, both for spectral and temporal encodings. We systematically evaluate and discuss the impact of the RF bandwidth - that conditions the number of tones driving the modulators - and of the choice of encoding for different targeted gates. We moreover quantify the number of high fidelity Hadamard gates that can be synthesized in parallel, with minimal and increasing resources in terms of driving RF tones in a realistic system. Our analysis positions spectral S-LOQC as a promising platform to conduct massively parallel single qubit operations, with potential applications to quantum metrology and quantum tomography.