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We propose novel methods for the exact synthesis of single-qubit unitarieswith high success probability and gate fidelity, considering both time-bin andfrequency-bin encodings. The proposed schemes are experimentally implementablewith a spectral linear-optical quantum computation (S- LOQC) platform, composedof electro-optic phase modulators and phase-only programmable filters (pulseshapers). We assess the performances in terms of fidelity and probability ofthe two simplest 3-components configurations for arbitrary gate generation inboth encodings and give an exact analytical solution for the synthesis of anarbitrary single-qubit unitary in the time-bin encoding, using a single-toneRadio Frequency (RF) driving of the EOMs. We further investigate theparallelization of arbitrary single-qubit gates over multiple qubits with acompact experimental setup, both for spectral and temporal encodings. Wesystematically evaluate and discuss the impact of the RF bandwidth - thatconditions the number of tones driving the modulators - and of the choice ofencoding for different targeted gates. We moreover quantify the number of highfidelity Hadamard gates that can be synthesized in parallel, with minimal andincreasing resources in terms of driving RF tones in a realistic system. Ouranalysis positions spectral S-LOQC as a promising platform to conduct massivelyparallel single qubit operations, with potential applications to quantummetrology and quantum tomography.

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