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arXiv:1307.8238 · Physical Review A

Spontaneous parametric down-conversion photon sources are scalable in the asymptotic limit for boson sampling

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

Published Dec 10, 2013• 34 citations
arXivHTMLPDF

Abstract

Boson sampling has emerged as a promising avenue towards postclassical optical quantum computation, and numerous elementary demonstrations have recently been performed. Spontaneous parametric down-conversion (SPDC) is the mainstay for single-photon state preparation, the technique employed in most optical quantum information processing implementations to date. Here we present a simple architecture for boson sampling based on multiplexed SPDC sources and demonstrate that the architecture is limited only by the postselection detection efficiency assuming that other errors, such as spectral impurity, dark counts, and interferometric instability, are negligible. For any given number of input photons, there exists a minimum detector efficiency that allows postselection. If this efficiency is achieved, photon-number errors in the SPDC sources are sufficiently low as to guarantee correct boson sampling most of the time. In this scheme, the required detector efficiency must increase exponentially in the photon number. Thus, we show that idealized SPDC sources will not present a bottleneck for future boson-sampling implementations. Rather, photodetection efficiency is the limiting factor, and thus, future implementations may continue to employ SPDC sources.

DOI
10.1103/physreva.88.063822

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Boson sampling has emerged as a promising avenue towards postclassical optical quantum computation, and numerous elementary demonstrations have recently been performed. Spontaneous parametric down-conversion (SPDC) is the mainstay for single-photon state preparation, the technique employed in most optical quantum information processing implementations to date. Here we present a simple architecture for boson sampling based on multiplexed SPDC sources and demonstrate that the architecture is limited only by the postselection detection efficiency assuming that other errors, such as spectral impurity, dark counts, and interferometric instability, are negligible. For any given number of input photons, there exists a minimum detector efficiency that allows postselection. If this efficiency is achieved, photon-number errors in the SPDC sources are sufficiently low as to guarantee correct boson sampling most of the time. In this scheme, the required detector efficiency must increase exponentially in the photon number. Thus, we show that idealized SPDC sources will not present a bottleneck for future boson-sampling implementations. Rather, photodetection efficiency is the limiting factor, and thus, future implementations may continue to employ SPDC sources.
Heralded spontaneous parametric down-conversion (SPDC) has become the mainstay for single-photon-state preparation in present-day photonics experiments. Because they are heralded, in principle one knows when a single photon has been prepared. However, the heralding efficiencies in experimentally realistic SPDC sources are typically very low. To overcome this, multiplexing techniques have been proposed which employ a bank of SPDC sources in parallel and route successfully heralded photons to the output, thereby effectively boosting the heralding efficiency. However, running a large bank of independent SPDC sources is costly and requires complex switching. We analyze a multiplexing technique based on time-bin encoding that allows the heralding efficiency of just a single SPDC source to be increased. The scheme is simple and experimentally viable using present-day technology. We analyze the operation of the scheme in terms of experimentally realistic considerations, such as losses, detector inefficiency, and pump power.
An important step for photonic quantum technologies is the demonstration of a quantum advantage through boson sampling. In order to prevent classical simulability of boson sampling, the photons need to be almost perfectly identical and almost without losses. These two requirements are connected through spectral filtering: improving one leads to a decrease of the other. A proven method of generating single photons is spontaneous parametric down-conversion (SPDC). We explore the fundamental limits of several important SPDC sources and show that an optimal tradeoff between indistinguishability and losses can always be found. We conclude that a 50-photon scattershot boson-sampling experiment using SPDC sources is possible from a computational complexity point of view. To this end, we numerically optimize SPDC sources under the regime of weak pumping and with a single spatial mode.
A boson-sampling device is a quantum machine expected to perform tasks intractable for a classical computer, yet requiring minimal nonclassical resources as compared to full-scale quantum computers. Photonic implementations to date employed sources based on inefficient processes that only simulate heralded single-photon statistics when strongly reducing emission probabilities. Boson sampling with only single-photon input has thus never been realized. Here, we report on a boson-sampling device operated with a bright solid-state source of single-photon Fock states with high photon-number purity: the emission from an efficient and deterministic quantum dot-micropillar system is demultiplexed into three partially indistinguishable single photons, with a single-photon purity 1-g^{(2)}(0) of 0.990±0.001, interfering in a linear optics network. Our demultiplexed source is between 1 and 2 orders of magnitude more efficient than current heralded multiphoton sources based on spontaneous parametric down-conversion, allowing us to complete the boson-sampling experiment faster than previous equivalent implementations.
Entangled-photon sources with simultaneously near-unity heralding efficiency and indistinguishability are the fundamental elements for scalable photonic quantum technologies. We design and realize a degenerate telecommunication wavelength entangled-photon source from an ultrafast pulsed laser pumped spontaneous parametric down-conversion (SPDC), which shows simultaneously 97% heralding efficiency and 96% indistinguishability between independent single photons without narrow-band filtering. Such a beamlike and frequency-uncorrelated SPDC source allows generation of the first 12-photon genuine entanglement with a state fidelity of 0.572±0.024. We further demonstrate a blueprint of scalable scattershot boson sampling using 12 SPDC sources and a 12×12 mode interferometer for three-, four-, and five-boson sampling, which yields count rates more than 4 orders of magnitude higher than all previous SPDC experiments.
An important open challenge in quantum information processing is to demonstrate a quantum device outperforming a classical computer. One of the most promising ways is by sending single photons through a passive linear-optical network, and sampling their output distribution [1]. However, this requires the nontrivial generation of many spectrally pure (indistinguishable) single photons. Most importantly, -spectral distinguishability reduces the visibility of quantum interference of the photons, but can be mitigated by filtering at the cost of optical losses. Unfortunately, losses are also detrimental to quantum interference. We recently quantified the combined role of spectral imperfections and loss in a multiphoton interference experiment [2]. We now apply these results to the problem of constructing spontaneous parametric down-conversion sources. In particular, we investigate the optimal filter bandwidth for different sources and optimize the down-conversion crystal parameters. Our results show that demonstrating a quantum advantage using photonics is difficult, but possible
A double-heralding technique is presented for producing heralded entangled photon pairs from spontaneous parametric down-conversion (SPDC). Compared to the swap-heralded schemes studied in previous cascaded SPDC and zero-added-loss multiplexing (ZALM) proposals, this double-heralding technique is found to yield the most resource-efficient implementation in terms of minimizing the total number of sources and detectors required to achieve a specified rate and fidelity. This is achieved by reducing the number of modes and mode-sorting optics needed on the heralding path. Specifically, by immediately detecting any two signal photons from an array of down-converters, the corresponding idler photons can be projected onto an anti-correlated pair state which is shown to be unitarily equivalent to the state produced by swap-heralded sources, and hence can be used directly for long-range entanglement distribution in a ZALM architecture. Quasi-deterministic operation through two distinct multiplexing techniques is analyzed. The analysis derives expressions for the heralded pair probability and fidelity assuming realistic detectors with losses, dark counts, and partial photon number resolution (PNR), providing a framework for implementation of the source on a photonic integrated circuit (PIC).