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arXiv:1403.4007 · Physical Review Letters

Scalable Boson Sampling with Time-Bin Encoding Using a Loop-Based Architecture

Keith R. Motes, Alexei Gilchrist, Jonathan P. Dowling, Peter P. Rohde

Published Sep 18, 2014• 141 citations
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Abstract

We present an architecture for arbitrarily scalable boson sampling using two nested fiber loops. The architecture has fixed experimental complexity, irrespective of the size of the desired interferometer, whose scale is limited only by fiber and switch loss rates. The architecture employs time-bin encoding, whereby the incident photons form a pulse train, which enters the loops. Dynamically controlled loop coupling ratios allow the construction of the arbitrary linear optics interferometers required for boson sampling. The architecture employs only a single point of interference and may thus be easier to stabilize than other approaches. The scheme has polynomial complexity and could be realized using demonstrated present-day technologies.

DOI
10.1103/physrevlett.113.120501

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We present an architecture for arbitrarily scalable boson sampling using two nested fiber loops. The architecture has fixed experimental complexity, irrespective of the size of the desired interferometer, whose scale is limited only by fiber and switch loss rates. The architecture employs time-bin encoding, whereby the incident photons form a pulse train, which enters the loops. Dynamically controlled loop coupling ratios allow the construction of the arbitrary linear optics interferometers required for boson sampling. The architecture employs only a single point of interference and may thus be easier to stabilize than other approaches. The scheme has polynomial complexity and could be realized using demonstrated present-day technologies.
Recently, Motes, Gilchrist, Dowling, and Rohde [Phys. Rev. Lett. 113, 120501 (2014).] presented a scheme for photonic boson sampling using a fiber-loop architecture. Here we show that the same architecture can be modified to implement full, universal linear-optics quantum computing, in various incarnations. The scheme employs two embedded fiber loops, a single push-button photon source, three dynamically controlled beamsplitters, and a single time-resolved photodetector. The architecture has only a single point of interference, and thus may be significantly easier to align than other schemes. The experimental complexity of the scheme is constant, irrespective of the size of the computation, limited only by fiber lengths and their respective loss rates.
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It was recently shown by Motes, Gilchrist, Dowling, and Rohde [Phys. Rev. Lett. 113, 120501 (2014)] that a time-bin encoded fiber-loop architecture can implement an arbitrary passive linear optics transformation. This was shown in the case of an ideal scheme whereby the architecture has no sources of error. In any realistic implementation, however, physical errors are present, which corrupt the output of the transformation. We investigate the dominant sources of error in this architecture---loss and mode mismatch---and consider how it affects the BosonSampling protocol, a key application for passive linear optics. For our loss analysis we consider two major components that contribute to loss---fiber and switches---and calculate how this affects the success probability and fidelity of the device. Interestingly, we find that errors due to loss are not uniform (unique to time-bin encoding), which asymmetrically biases the implemented unitary. Thus loss necessarily limits the class of unitaries that may be implemented, and therefore future implementations must prioritize minimizing loss rates if arbitrary unitaries are to be implemented. Our formalism for mode mismatch is generalized to account for various phenomenon that may cause mode mismatch, but we focus on two---errors in fiber-loop lengths and time jitter of the photon source. These results provide a guideline for how well future experimental implementations might perform in light of these error mechanisms.
Boson sampling arising from multiphoton interference in linear-optical networks is a prominent non-universal model for quantum computation. Here, by encoding the multi-qubit state to bosonic Fock state, we present a scalable quantum-circuit framework for simulating boson sampling on a universal quantum computing platform. Beginning with balanced beam-splitter transformations on the single- and two-photon sectors, we derive equivalent quantum-circuit implementations and unify them within a common Hilbert-space representation using an ancilla-assisted encoding. This construction is then generalized to arbitrary interferometers by replacing each optical beam splitter with a repeating quantum-circuit unit that selectively acts only within the relevant local interference subspace, requiring N+1N+1N+1 qubits for a two-photon NNN-mode interferometer and a linear-overhead subspace-identification procedure. Using this framework, gate-based quantum circuit for a four-mode boson-sampling circuit is developed and experimentally implemented on a four-qubit gate-based photonic qubit system. The qubit framework for emulating boson sampling of n−n-n−photons in m−m-m−mode will be useful to solve a broad class of sampling complexity problem on a gate-based quantum computers.
The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.
A major challenge for postclassical boson sampling experiments is the need for a large number of coupled optical modes, detectors, and single-photon sources. Here we show that these requirements can be greatly eased by time-bin encoding and dispersive optics-based unitary transformations. Detecting consecutively heralded photons after time-independent dispersion performs boson sampling from unitaries for which an efficient classical algorithm is lacking. We also show that time-dependent dispersion can implement general single-particle unitary operations. More generally, this scheme promises an efficient architecture for a range of other linear optics experiments.