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arXiv:1509.04246 · Physical Review A

Recursive multiport schemes for implementing quantum algorithms with photonic integrated circuits

Gelo Noel M. Tabia

Published Jan 14, 2016• 13 citations
arXivHTMLPDF

Abstract

We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on $2d$ modes using a pair of circuits for the same operation on $d$ modes. The circuits operate on path-encoded qudits and realize $d$-dimensional unitary transformations on these states using linear optical networks with $O\left({d}^{2}\right)$ optical elements. To evaluate the schemes against realistic errors, we ran simulations of proof-of-principle experiments using a simple fabrication model of silicon-based photonic integrated devices that employ directional couplers and thermo-optic modulators for beam splitters and phase shifters, respectively. We find that high-fidelity performance is achievable with our multiport circuits for 2-qubit and 3-qubit quantum Fourier transforms, and for quantum search on four-item and eight-item databases.

DOI
10.1103/physreva.93.012323

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We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on 2d2d2d modes using a pair of circuits for the same operation on ddd modes. The circuits operate on path-encoded qudits and realize ddd-dimensional unitary transformations on these states using linear optical networks with O(d2)O\left({d}^{2}\right)O(d2) optical elements. To evaluate the schemes against realistic errors, we ran simulations of proof-of-principle experiments using a simple fabrication model of silicon-based photonic integrated devices that employ directional couplers and thermo-optic modulators for beam splitters and phase shifters, respectively. We find that high-fidelity performance is achievable with our multiport circuits for 2-qubit and 3-qubit quantum Fourier transforms, and for quantum search on four-item and eight-item databases.
Linear optics is a promising physical architecture for the implementation of the quantum computing devices. The key element of the linear optical quantum computer is an optical circuit realizing the sequence of transformations defined by the required quantum algorithm. The most prominent approach is the reconfigurable integrated photonics which allows to miniaturize standard optical setups on the chosen integrated photonic platform. In this paper, we propose a universal linear-optical circuit design comprised of the series of multiport beamsplitters followed by the phaseshifting elements. The proposed unitary composer device can be straightforwardly implemented using standard integrated photonic technologies. We provide guidelines for appropriate multiport beamsplitter fabrication using integrated waveguide lattices. To exemplify the performance of the composer we provide the six-mode CNOT linear optical gate circuit design fitted to described interferometric circuit.
Integrated photonic circuits with many input and output modes are essential in applications ranging from conventional optical telecommunication networks, to the elaboration of photonic qubits in the integrated quantum information framework. In particular, the latter field has been object in the recent years of an increasing interest: the compactness and phase stability of integrated waveguide circuits are enabling experiments unconceivable with bulk-optics set-ups. Linear photonic devices for quantum information are based on quantum and classical interference effects: the desired circuit operation can be achieved only with tight fabrication control on both power repartition in splitting elements and phase retardance in the various paths. Here we report on a novel three-dimensional circuit architecture, made possible by the unique capabilities of femtosecond laser waveguide writing, which enables us to realize integrated multimode devices implementing arbitrary linear transformations. Networks of cascaded directional couplers can be built with independent control on the splitting ratios and the phase shifts in each branch. In detail, we show an arbitrarily designed 5×5 integrated interferometer: characterization with one- and two-photon experiments confirms the accuracy of our fabrication technique. We exploit the fabricated circuit to implement a small instance of the boson-sampling experiments with up to three photons, which is one of the most promising approaches to realize phenomena hard to simulate with classical computers. We will further show how, by studying classical and quantum interference in many random multimode circuits, we may gain deeper insight into the bosonic coalescence phenomenon.
Reconfigurable devices which can implement arbitrary unitary operations are crucial for photonic quantum computation, optical neural networks, and boson sampling. Here, we address the problem of, using multiport interferometers, approximating with a given infidelity any pure-state preparation and any unitary operation. By means of numerical calculations, we show that pure states, in any dimension ddd, can be prepared with infidelity $\ensuremath{\le}{10}^{\ensuremath{-}15}$ with three layers of ddd-dimensional Fourier transforms and three layers of configurable phase shifters. We also present numerical evidence that d+1d+1d+1 layers of ddd-dimensional Fourier transforms and d+2d+2d+2 layers of configurable phase shifters can produce any unitary operation with infidelity $\ensuremath{\le}{10}^{\ensuremath{-}14}$. The conclusions are achieved by numerical simulations in the range from d=3d=3d=3 to d=10d=10d=10. These results are interesting in light of the recent availability of multicore fiber-integrated multiport interferometers.
ABSTRACT Unitary operations lie at the heart of quantum computing, enabling the manipulation of quantum states in a reversible and coherent manner. In photonic integrated circuits, these operations are realized using photonic waveguide architectures composed of passive beam splitters and reconfigurable phase shifters. This review provides an overview of photonic circuit architectures designed to implement unitary transformations. We examine various design strategies, material platforms, and the current state‐of‐the‐art in realizing high‐fidelity photonic unitaries. In addition, we explore the theoretical underpinnings of photon transport in such circuits, shedding light on the quantum behavior of light in unitary photonic systems. Finally, we introduce a simulation framework for modeling and analyzing these photonic networks, offering a practical tool for research and development in this rapidly growing field.
Quantum information science aims to harness uniquely quantum mechanical properties to enhance measurement and information technologies, and to explore fundamental aspects of quantum physics. Of the various approaches to quantum computing [1], photons are particularly appealing for their low-noise properties and ease of manipulation at the single qubit level [2,3]. Encoding quantum information in photons is also an appealing approach to quantum communication, metrology (eg. [4]), measurement (eg. [5]) and other quantum technologies [6]. However, the implementation of optical quantum circuits with bulk optics has reached practical limits. We have developed an integrated waveguide approach to photonic quantum circuits for high performance, miniaturization and scalability [7]. Here we report high-fidelity silica-on-silicon integrated optical realizations of key quantum photonic circuits, including two-photon quantum interference and a controlled-NOT logic gate [8]. We have demonstrated controlled manipulation of up to four photons on-chip, including highfidelity single qubit operations, using a lithographically patterned resistive phase shifter [9]. We have used this architecture to implement a small-scale compiled version of Shor's quantum factoring algorithm [10], demonstrated heralded generation of tunable four photon entangled states from a six photon input [11], a reconfigurable two-qubit circuit [12], and combined waveguide photonic circuits with superconducting single photon detectors [13]. We describe complex quantum interference behavior in multi-mode interference devices with up to eight inputs and outputs [14], and quantum walks of correlated particles in arrays of coupled waveguides [15]. Finally, we give an overview of our recent work on fundamental aspects of quantum measurement [16,17] and diamond [18,19] and nonlinear [20,21] photon sources.
Quantum information science aims to harness uniquely quantum mechanical properties to enhance measurement and information technologies, and to explore fundamental aspects of quantum physics. Of the various approaches to quantum computing [1], photons are particularly appealing for their low-noise properties and ease of manipulation at the single qubit level [2]. Encoding quantum information in photons is also an appealing approach to quantum communication, metrology (eg. [3]), measurement (eg. [4]) and other quantum technologies [5]. However, the implementation of optical quantum circuits with bulk optics has reached practical limits. We have developed an integrated waveguide approach to photonic quantum circuits for high performance, miniaturisation and scalability [6]. Here we report high-fidelity silica-on-silicon integrated optical realisations of key quantum photonic circuits, including two-photon quantum interference and a controlled-NOT logic gate [7]. We have demonstrated controlled manipulation of up to four photons on-chip, including high-fidelity single qubit operations, using a lithographically patterned resistive phase shifter [8]. We have used this architecture to implement a small-scale compiled version of Shorʼs quantum factoring algorithm [9] and demonstrated heralded generation of tuneable four photon entangled states from a six photon input [10]. We have combined waveguide photonic circuits with superconducting single photon detectors [11]. We describe complex quantum interference behaviour in multi-mode interference devices with up to eight inputs and outputs [12], and quantum walks of correlated particles in arrays of coupled waveguides [13]. Finally, we give an overview of our recent work on fundamental aspects of quantum measurement [14,15] and single photon sources [16,17].