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.
Unitary synthesis underlies universal quantum computation by translating unitary transformations into circuits of elementary gates. We show that for any budget
m≥0 of ancilla, every
n-qubit unitary can be exactly implemented using a quantum circuit consisting of
O(4n) CNOT and single-qubit gates in
O(n+4n/(n+m)) layers attaining the asymptotically optimal depth--ancilla tradeoff while simultaneously achieving optimal circuit size. The key idea is to encode computational basis states as wavefunctions sharing a Gaussian envelope, converting unitary action on amplitudes into coordinate transformations that admit shallow circuit implementations. The continuous encoding is then discretized, with approximation errors removed by exact residual correction. The depth-ancilla tradeoff follows by recursively applying the quantum Shannon decomposition, synthesizing its smaller unitary factors, and reusing ancillary qubits.
High-dimensional photonic operations are an important resource for quantum information processing, yet achieving scalability and long-distance operation remains a formidable challenge. Here, we demonstrate reconfigurable high-dimensional spatial-mode state synthesis using spatial-mode-encoded qu d its in a 20-m-long multimode fiber. By exploiting the ultra-long coherence of heralded single photons from a warm 87 Rb atomic ensemble, we overcome the modal dispersion limits that restricted previous short-distance demonstrations. Using digital optical phase conjugation, we deterministically synthesize spatial-mode states structured by target unitary operations, including generalized Pauli operators and quantum Fourier transforms, through the complex fiber medium. We achieve process fidelities exceeding 92.5(4)% for dimensions up to d = 7. These results establish long multimode fibers as a reconfigurable platform for high-dimensional quantum state synthesis and transport in fiber-based quantum information processing.