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Quantum 2.0 Conference and Exhibition

Demonstration of a compiled version of Shor’s algorithm using frequency and time single-photon qudits

Jinwon Yoo, Nicola Montaut, Matteo Piccolini, Stefania Sciara, Rosario Lo Franco, Roberto Morandotti

Published Jan 1, 2025• 0 citations
Publisher

Abstract

We present a resource-efficient compiled version of Shor's algorithm by employing frequency and time qudits within a single photon and utilizing fiber-optic devices. Our results demonstrate successful factorization of the number 15 with high fidelity.
DOI
10.1364/quantum.2025.qtu3a.17

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Shor's quantum factoring algorithm finds the prime factors of a large number exponentially faster than any other known method, a task that lies at the heart of modern information security, particularly on the Internet. This algorithm requires a quantum computer, a device that harnesses the massive parallelism afforded by quantum superposition and entanglement of quantum bits (or qubits). We report the demonstration of a compiled version of Shor's algorithm on an integrated waveguide silica-on-silicon chip that guides four single-photon qubits through the computation to factor 15.
Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation. Here, we implement a compiled version in a photonic system. For the first time, we demonstrate the core processes, coherent control, and resultant entangled states required in a full-scale implementation. These are necessary steps on the path towards scalable quantum computing. Our results highlight that the algorithm performance is not the same as that of the underlying quantum circuit and stress the importance of developing techniques for characterizing quantum algorithms.
We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period r=2 and exploit a simplified linear optical network to coherently implement the quantum circuits of the modular exponential execution and semiclassical quantum Fourier transformation. During this computation, genuine multiparticle entanglement is observed which well supports its quantum nature. This experiment represents an essential step toward full realization of Shor's algorithm and scalable linear optics quantum computation.