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Identifying the boundary beyond which quantum machines provide a computational advantage over their classical counterparts is a crucial step in charting their usefulness. Gaussian Boson Sampling (GBS), in which photons are measured from a highly entangled Gaussian state, is a leading approach in pursuing quantum advantage. State-of-the-art quantum photonics experiments that, once programmed, run in minutes, would require 600 million years to simulate using the best pre-existing classical algorithms. Here, we present substantially faster classical GBS simulation methods, including speed and accuracy improvements to the calculation of loop hafnians, the matrix function at the heart of GBS. We test these on a $\sim \! 100,000$ core supercomputer to emulate a range of different GBS experiments with up to 100 modes and up to 92 photons. This reduces the run-time of classically simulating state-of-the-art GBS experiments to several months -- a nine orders of magnitude improvement over previous estimates. Finally, we introduce a distribution that is efficient to sample from classically and that passes a variety of GBS validation methods, providing an important adversary for future experiments to test against., 18 pages, 16 figures

Encoding qudits into photons can provide improvements to quantum communication and computation tasks. Here, we present new schemes for generating high-dimensional photonic entanglement and show how to construct cluster states for universal qudit quantum computation.

Integrated photonics will play a key role in quantum systems as they grow from few-qubit prototypes to tens of thousands of qubits. The underlying optical quantum technologies can only be realized through the integration of these components onto quantum photonic integrated circuits (QPICs) with accompanying electronics. In the last decade, remarkable advances in quantum photonic integration have enabled table-top experiments to be scaled down to prototype chips with improvements in efficiency, robustness, and key performance metrics. These advances have enabled integrated quantum photonic technologies combining up to 650 optical and electrical components onto a single chip that are capable of programmable quantum information processing, chip-to-chip networking, hybrid quantum system integration, and high-speed communications. In this roadmap article, we highlight the status, current and future challenges, and emerging technologies in several key research areas in integrated quantum photonics, including photonic platforms, quantum and classical light sources, quantum frequency conversion, integrated detectors, and applications in computing, communications, and sensing. With advances in materials, photonic design architectures, fabrication and integration processes, packaging, and testing and benchmarking, in the next decade we can expect a transition from single- and few-function prototypes to large-scale integration of multi-functional and reconfigurable devices that will have a transformative impact on quantum information science and engineering., JPhys Photonics, 4 (1), ISSN:2515-7647

Photonics is a sophisticated platform for the development of novel quantum technologies, from quantum processors to distributed quantum communication. Most linear optical architectures focus on encoding qubits into photons using, for example, polarization or a dual-rail approach. However, encoding higher-dimensional systems - qudits - can in principle provide improved information capacity and noise tolerance in communication, and lower error thresholds in fault-tolerant quantum computation. Here we present new schemes for generating high-dimensional photonic entanglement and discuss how to build cluster states for universal high-dimensional quantum computation.

Photons are natural carriers of high-dimensional quantum information, and, in principle, can benefit from higher quantum information capacity and noise resilience. However, schemes to generate the resources required for high-dimensional quantum computing have so far been lacking in linear optics. Here, we show how to generate GHZ states in arbitrary dimensions and numbers of photons using linear optical circuits described by Fourier transform matrices. Combining our results with recent schemes for qudit Bell measurements, we show that universal linear optical quantum computing can be performed in arbitrary dimensions.

One of the central principles of quantum mechanics is that if there are multiple paths that lead to the same event and there is no way to distinguish between them, interference occurs. It is often assumed that distinguishing information in the preparation, evolution, or measurement of a system is sufficient to destroy interference. However, it is still possible for photons in distinguishable, separable states to interfere due to the indistinguishability of paths corresponding to possible exchange processes. Here we experimentally measure an interference signal that depends only on the multiparticle interference of four photons in a four-port interferometer despite pairs of them occupying distinguishable states.

Here we show that multi-particle quantum interference still occurs even when some of the particles involved are in orthogonal states. We experimentally demonstrate this with four photons.

Quantum interference of two independent particles in pure quantum states is fully described by the particles' distinguishability: the closer the particles are to being identical, the higher the degree of quantum interference. When more than two particles are involved, the situation becomes more complex and interference capability extends beyond pairwise distinguishability, taking on a surprisingly rich character. Here, we study many-particle interference using three photons. We show that the distinguishability between pairs of photons is not sufficient to fully describe the photons' behavior in a scattering process, but that a collective phase, the triad phase, plays a role. We are able to explore the full parameter space of three-photon interference by generating heralded single photons and interfering them in a fiber tritter. Using multiple degrees of freedom-temporal delays and polarization-we isolate three-photon interference from two-photon interference. Our experiment disproves the view that pairwise two-photon distinguishability uniquely determines the degree of nonclassical many-particle interference.

Quantum interference of two independent photons in pure quantum states is fully described by the particles' distinguishability: the closer the particles are to being identical, the higher the degree of quantum interference. When more than two particles are involved, the situation becomes more complex and interference capability extends beyond pairwise distinguishability. Here, we study many-particle interference using three photons. We show that the three distinct distinguishabilities between pairs of photons are not sufficient to fully describe the photons' behaviour in a scattering process, but that additionally a fourth parameter, a collective phase, governs the scattering process. We use heralded single photons and a fibre-optic tritter to explore this full parameter space for the first time and thereby demonstrate genuine three-photon interference. Further, our work challenges the view that using time delays between identical photons alone suffices to fully study multi-photon interference.

Resonance fluorescence arises from the interaction of an optical field with a two-level system and has played a fundamental role in the development of quantum optics and its applications. Despite its conceptual simplicity it entails a wide range of intriguing phenomena, such as the Mollow-triplet emission spectrum and coherent photon emission. One fundamental aspect of resonance fluorescence, reduced quantum fluctuations in the single photon stream from an atom in free space, was predicted more than 30 years ago. However, the requirement to operate in the weak excitation regime, together with the combination of modest oscillator strength of atoms and low collection efficiencies, has continued to cast stringent experimental conditions for the observation of squeezing with atoms. Attempts to circumvent these issues had to sacrifice antibunching due to either stimulated forward scattering from atomic ensembles or multiphoton transitions inside optical cavities. Here, we use an artificial atom with a large optical dipole enabling 100-fold improvement of the photon detection rate over the natural atom counterpart and reach the necessary conditions for the observation of quadrature squeezing in single resonance-fluorescence photons. Implementing phase-dependent homodyne intensity-correlation detection, we demonstrate that the electric field quadrature variance of resonance fluorescence is 3\% below the fundamental limit set by vacuum fluctuations, while the photon statistics remain antibunched. The presence of squeezing and antibunching simultaneously is a fully nonclassical outcome of the wave-particle duality of photons., Supplementary material for this work can be found in the publications section of our website http://www.amop.phy.cam.ac.uk/amop-ma