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Frontiers in Optics

A compiled version of Shor’s quantum factoring algorithm on a waveguide chip

Jonathan C. F. Matthews, Alberto Politi, Jeremy L. O’Brien

Published Jan 1, 2009• 2 citations
Publisher

Abstract

We report the realization of a compiled version of Shor’s quantum factoring algorithm on an integrated waveguide chip. This demonstration serves as an illustration to the importance of using integrated optics for quantum optical experiments.
DOI
10.1364/fio.2009.pdpa6

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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.
Although practical realisation of a fully functioning quantum computer is still a long way off, recent progress both experimentally and theoretically is paving the way for possible implementations. One of the leading approaches is quantum optics, where photons are used as carriers of quantum information, and are manipulated in both linear and non-linear optical circuits. More recently, advances in integrated quantum photonics are enabling the realisation of compact and stable quantum gates and circuits. This approach provides routes to enhancing the complexity of quantum optic experiments, and ultimately towards the development of advanced quantum technologies. This study presents an overview of recent developments in the field of integrated waveguide quantum circuits. Key building blocks required for the realisation of quantum circuits are presented, and a rudimentary version of Shor's quantum factoring algorithm is demonstrated. Planar waveguide quantum circuits provide a high-performance platform from which quantum technologies and experimental quantum physics using single photons can be developed, and a new generation of quantum information and computing devices can be monolithically integrated onto a single optical chip.
Quantum information science has shown that harnessing quantum mechanical effects can dramatically improve performance for certain tasks in communication, computation and measurement. Of the various physical systems being pursued, single particles of light - photons - are often the logical choice [1]. In addition to single photon sources and detectors, photonic quantum technologies will rely on sophisticated optical circuits [2]. Recently we reported the implementation of quantum optic integrated circuits, which not only dramatically reduces the footprint of quantum circuits, but allows unprecedented stability and higher performance. We demonstrated silica on silicon circuits that implement key components for quantum information, including CNOT gates [3] and single-qubit operations [4]. These components show promising progresses toward fault tolerance operation [5]. We also used integrated waveguides to implement a circuit that performs a compiled version of Shor's quantum algorithm [6] to factorize 15. Here we report the demonstration of circuits that extend the capabilities of the components already demonstrated, to take full advantage of the integrated optics architecture.
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.