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IEEE Dallas Circuits and Systems Conference (DCAS)

A Two-Qubit Controlled-NOT Gate for Multi-Color Quantum Photonic Systems

Hiva Shahoei, Duncan L. MacFarlane, Mitchell Aaron Thornton

Published Apr 10, 2026• 0 citations
Publisher

Abstract

We present a conceptual KLM-style implementation of a two-qubit controlled-NOT (CNOT) gate for frequency-encoded (multi-color) photonic qubits. The CNOT operation is constructed through an$\mathrm{H}-\text{CZ}-\mathrm{H}$decomposition, where programmable frequency-domain Hadamard transformations are implemented using a parallel frequency-mixing architecture. This parallel configuration enables controlled redistribution of probability amplitudes among frequency bins while maintaining scalability and reduced parasitic loss compared to serial architectures. The nonlinearity required for the CZ gate is realized through two-photon interference at a partial beam splitter within an otherwise linear optical system, without requiring auxiliary photons. This approach provides a resource-efficient and scalable framework for frequency-domain quantum logic and multi-color photonic quantum information processing.

DOI
10.1109/dcas69364.2026.11544593

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Photonic quantum gates are fundamental building blocks for a wide range of optical quantum information processing tasks. We propose an efficient linear-optical scheme for implementing a post-selected three-qubit fan-out gate (also known as a controlled-NOT-NOT gate) using only two ancillary single photons and linear optical elements. The scheme can be generalized to an nnn-qubit fan-out gate, requiring (n−1)(n-1)(n−1) ancillary single photons and (3n−3)(3n-3)(3n−3) polarizing beam splitters (PBSs), with a success probability of (14)n−1\left(\frac{1}{4}\right)^{n-1}(41​)n−1. Compared to the standard gate decomposition approach, which requires (2n−2)(2n-2)(2n−2) ancillary single photons, (5n−5)(5n-5)(5n−5) PBSs, and yields a success probability of (18)n−1\left(\frac{1}{8}\right)^{n-1}(81​)n−1. Our scheme significantly reduces the resource overhead and improves the success probability. We further evaluate the gate performance and demonstrate improved robustness compared to gate decomposition-based methods.