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Research in Optical Sciences

Linear Optical Quantum Computing in a Single Spatial Mode

Peter C. Humphreys, Benjamin J. Metcalf, Justin B. Spring, Merritt Moore, Xian‐Min Jin, Marco Barbieri, W. Steven Kolthammer, Ian A. Walmsley

Published Jan 1, 2014• 1 citation
Publisher

Abstract

We present a scheme for linear-optical quantum computing using time-bin encoded qubits in a single spatial mode. Our protocol has the potential to dramatically increase the quantum information capacity of fixed spatial resources.
DOI
10.1364/qim.2014.qth2a.4

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We present a scheme for linear optical quantum computing using time-bin-encoded qubits in a single spatial mode. We show methods for single-qubit operations and heralded controlled-phase (cphase) gates, providing a sufficient set of operations for universal quantum computing with the Knill-Laflamme-Milburn [Nature (London) 409, 46 (2001)] scheme. Our protocol is suited to currently available photonic devices and ideally allows arbitrary numbers of qubits to be encoded in the same spatial mode, demonstrating the potential for time-frequency modes to dramatically increase the quantum information capacity of fixed spatial resources. As a test of our scheme, we demonstrate the first entirely single spatial mode implementation of a two-qubit quantum gate and show its operation with an average fidelity of 0.84±0.07.
We suggest an efficient scheme for quantum computation with linear optical elements, where the qubits are encoded in single photon states. The scheme reduces the resources required per logical gate by several orders of magnitude, compared to an earlier proposal of Knill, Laflamme, and Milburn, while the resource overhead per gate is independent of the length of the computation. A central feature of the scheme, enabling these improvements, is the prior construction of a "linked" photon state designed according to the particular quantum circuit one wishes to process. Once this state has been successfully prepared, the computation is pursued deterministically by a sequence of teleportation steps.
We propose a scalable scheme for optical quantum computing using measurement-induced continuous-variable quantum gates in a loop-based architecture. Here, time-bin-encoded quantum information in a single spatial mode is deterministically processed in a nested loop by an electrically programmable gate sequence. This architecture can process any input state and an arbitrary number of modes with almost minimum resources, and offers a universal gate set for both qubits and continuous variables. Furthermore, quantum computing can be performed fault tolerantly by a known scheme for encoding a qubit in an infinite-dimensional Hilbert space of a single light mode.
Quantum entanglement is a fundamental resource for secure information processing and communications. The canonical optical quantum information processing encodes a single qubit per photon, with remarkable demonstrations of secure quantum communications, linear optical quantum computing amongst others. Often the polarization qubit, a discrete variable with entangled Bell states, is used. Continuous variables such as energy-time modes and spatial modes, however, present a dramatically larger Hilbert space for quantum information processing. The high-dimensional entanglement capture more qubits per photon, enabling dramatically higher secure key rates over longer distances and with better error resilience. Here I will describe our results on high-dimensional entanglement in quantum frequency combs for dense quantum communications. We first demonstrate revival of the Hong-Ou-Mandel interferences, long postulated by theorists more than a decade ago, up to 19-dimensions and with visibilities up to 96.5%. The mode-locked two-photon state in high-dimensions is further witnessed through a stabilized Franson interferometer, as a generalized Bell’s inequality test and hyperentangled through multiple degrees-of-freedom. Entanglement revivals of the non-local interference at discrete time-bins are uncovered, up to 97.8% visibility, as a fundamental resource for dense secure information processing.