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arXiv:2210.11830 · Physical Review A

Parallelizable synthesis of arbitrary single-qubit gates with linear optics and time-frequency encoding

Antoine Henry, R. Raghunathan, Guillaume Ricard, Baptiste Lefaucher, Filippo M. Miatto, Nadia Belabas, Isabelle Zaquine, Romain Alléaume

Published Jun 26, 2023• 12 citations

Abstract

We propose 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 three-component 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 rf driving of the electro-optic modulators. 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, which 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.

DOI: 10.1103/physreva.107.062610

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Accurate control of two-level systems is a longstanding problem in quantum mechanics. One such quantum system is the frequency-bin qubit: a single photon existing in superposition of two discrete frequency modes. In this Letter, we demonstrate fully arbitrary control of frequency-bin qubits in a quantum frequency processor for the first time. We numerically establish optimal settings for multiple configurations of electro-optic phase modulators and pulse shapers, experimentally confirming near-unity mode-transformation fidelity for all fundamental rotations. Performance at the single-photon level is validated through the rotation of a single frequency-bin qubit to 41 points spread over the entire Bloch sphere, as well as tracking of the state path followed by the output of a tunable frequency beam splitter, with Bayesian tomography confirming state fidelities F_{ρ}>0.98 for all cases. Such high-fidelity transformations expand the practical potential of frequency encoding in quantum communications, offering exceptional precision and low noise in general qubit manipulation.

We demonstrate high-fidelity, tunable, and ultrafine-resolution on-chip frequency beamsplitters using a quantum frequency processor based on an integrated pulse shaper with six spectral channels. Near-ideal Hadamard gate performance is achieved, with fidelity F > 0.9995 and modified success probability P > 0.9621 maintained across frequency spacings from 2-5 GHz and down to as few as four spectral pulse shaper channels. The system's support of frequency spacings as narrow as 2 GHz significantly surpasses prior bulk demonstrations and enables arbitrary splitting ratios via spectral phase or modulation index control. These results establish a scalable and resource-efficient platform for integrated frequency-bin quantum photonics, opening new directions in quantum information processing, including densely parallel single-qubit operations and multidimensional gate implementations.

Among the objectives toward large-scale quantum computation is the quantum interconnect: a device which uses photons to interface qubits that otherwise could not interact. However, current approaches require photons indistinguishable in frequency---a major challenge for systems experiencing different local environments or of different physical compositions altogether. Here we develop an entirely new platform which actually exploits such frequency mismatch for processing quantum information. Labeled "spectral linear optical quantum computation" (spectral LOQC), our protocol offers favorable linear scaling of optical resources and enjoys an unprecedented degree of parallelism, as an arbitrary

N

-qubit quantum gate may be performed in parallel on multiple

N

-qubit sets in the same linear optical device. Not only does spectral LOQC offer new potential for optical interconnects; it also brings the ubiquitous technology of high-speed fiber optics to bear on photonic quantum information, making wavelength-configurable and robust optical quantum systems within reach.