Linear optics underpins tests of fundamental quantum mechanics and computer science, as well as quantum technologies. Here we experimentally demonstrate the longstanding goal of a single reprogrammable optical circuit that is sufficient to implement all possible linear optical protocols up to the size of that circuit. Our six-mode universal system consists of a cascade of 15 MachZehnder interferometers with 30 thermo-optic phase shifters integrated into a single photonic chip that is electrically and optically interfaced for arbitrary setting of all phase shifters, input of up to six photons and their measurement with a 12 single-photon detector system. We programmed this system to implement heralded quantum logic and entangling gates, boson sampling with verification tests, and six-dimensional complex Hadamards. We implemented 100 Haar random unitaries with average fidelity 0.999 ± 0.001. Our system is capable of switching between these and any other linear optical protocol in seconds. These results point the way to applications across fundamental science and quantum technologies.Photonics has been crucial in establishing the foundations of quantum mechanics [1], and more recently has pushed the vanguard of efforts in understanding new non-classical computational possibilities. Typical protocols involve nonlinear operations, such as the generation of quantum states of light through optical frequency conversion [2,3], or measurement-induced nonlinearities for quantum logic gates [4], together with linear operations between optical modes to implement core processing functions [5]. Encoding qubits in the polarisation of photons has been particularly appealing for the ability to implement arbitrary linear operations on the two polarisation modes using a series of wave plates [6]. For path encoding the same operations can be mapped to a sequence of beamsplitters and phase shifters. In fact, since any linear optical (LO) circuit is described by a unitary operator, and a specific array of basic two-mode operations is mathematically sufficient to implement any unitary operator on optical modes [7], it is theoretically possible to construct a single device with sufficient versatility to implement any possible LO operation up to the specified number of modes.Here we report the realisation of this longstanding goal with a six-mode device that is completely reprogrammable and universal for LO. We demonstrate the versatility of this universal LO processor (LPU) by applying it to several quantum information protocols, including tasks that were previously not possible. We im- * anthony.laing@bristol.ac.uk plement heralded quantum logic gates at the heart of the circuit model of LO quantum computing [4] and new heralded entangling gates that underpin the measurementbased model of LO quantum computing [8][9][10], both of which are the first of their kind in integrated photonics. We perform 100 different boson sampling [11][12][13][14][15] experiments and simultaneously realise new verification protocols. Finally, we use multi-p...

The first quantum technologies to solve computational problems that are beyond the capabilities of classical computers are likely to be devices that exploit characteristics inherent to a particular physical system, to tackle a bespoke problem suited to those characteristics. Evidence implies that the detection of ensembles of photons, which have propagated through a linear optical circuit, is equivalent to sampling from a probability distribution that is intractable to classical simulation. However, it is probable that the complexity of this type of sampling problem means that its solution is classically unverifiable within a feasible number of trials, and the task of establishing correct operation becomes one of gathering sufficiently convincing circumstantial evidence. Here, we develop scalable methods to experimentally establish correct operation for this class of sampling algorithm, which we implement with two different types of optical circuits for 3, 4, and 5 photons, on Hilbert spaces of up to 50, 000 dimensions. With only a small number of trials, we establish a confidence > 99% that we are not sampling from a uniform distribution or a classical distribution, and we demonstrate a unitary specific witness that functions robustly for small amounts of data. Like the algorithmic operations they endorse, our methods exploit the characteristics native to the quantum system in question. Here we observe and make an application of a "bosonic clouding" phenomenon, interesting in its own right, where photons are found in local groups of modes superposed across two locations. Our broad approach is likely to be practical for all architectures for quantum technologies where formal verification methods for quantum algorithms are either intractable or unknown.The construction of a universal quantum computer, capable of implementing any quantum computation or quantum simulation, is a major long term experimental objective. However, it is expected that non-universal quantum machines, that exploit characteristics of their own physical system to solve specific problems, will outperform classical computers in the near-term [1]. Ensembles of single photons in linear optical circuits are a recently proposed example: despite being non-interacting particles, their detection statistics are described by functions that are intractable to classical computers -matrix permanents [2]. It is therefore believed that linear optics constitutes a platform for the efficient sampling of probability distributions that cannot be simulated by classical computers, with strong evidence provided in the case of circuits described by large random matrices [3][4][5][6][7].A universal quantum computer, running for example Shor's factoring algorithm [8], creates an exponentially large probability distribution with individual peaks at highly regular intervals that facilitate the solution to the factoring problem allowing efficient classical verification, as is the case for all problems in the NP complexity class [9]. Accordingly, correct operation of the...

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The goal of integrated quantum photonics is to combine components for the generation, manipulation, and detection of non-classical light in a phase stable and efficient platform. Solid-state quantum emitters have recently reached outstanding performance as single photon sources. In parallel, photonic integrated circuits have been advanced to the point that thousands of components can be controlled on a chip with high efficiency and phase stability. Consequently, researchers are now beginning to combine these leading quantum emitters and photonic integrated circuit platforms to realize the best properties of each technology. In this article, we review recent advances in integrated quantum photonics based on such hybrid systems. Although hybrid integration solves many limitations of individual platforms, it also introduces new challenges that arise from interfacing different materials. We review various issues in solid-state quantum emitters and photonic integrated circuits, the hybrid integration techniques that bridge these two systems, and methods for chip-based manipulation of photons and emitters. Finally, we discuss the remaining challenges and future prospects of on-chip quantum photonics with integrated quantum emitters. PHOTONIC INTEGRATED CIRCUIETS FOR QUANTUM PHOTONICSPICs provide a compact, phase stable, and high-bandwidth platform to transmit, manipulate, and detect light on-chip. By leveraging advances in semiconductor manufacturing for classical communication, PICs have been demonstrated with over a thousand active components in a few square mm [50]. Now, with many foundries offering multi-26. I. Aharonovich, D. Englund, and M. Toth, "Solid-state single-photon emitters," Nat. Photonics 10, 631 (2016) , "Neardeterministic activation of room-temperature quantum emitters in hexagonal boron nitride," Optica 5, 1128-1134 (2018)

Advances in control techniques for vibrational quantum states in molecules present new challenges for modelling such systems, which could be amenable to quantum simulation methods. Here, by exploiting a natural mapping between vibrations in molecules and photons in waveguides, we demonstrate a reprogrammable photonic chip as a versatile simulation platform for a range of quantum dynamic behaviour in different molecules. We begin by simulating the time evolution of vibrational excitations in the harmonic approximation for several four-atom molecules, including HCS, SO, HNCO, HFHF, N and P. We then simulate coherent and dephased energy transport in the simplest model of the peptide bond in proteins-N-methylacetamide-and simulate thermal relaxation and the effect of anharmonicities in HO. Finally, we use multi-photon statistics with a feedback control algorithm to iteratively identify quantum states that increase a particular dissociation pathway of NH. These methods point to powerful new simulation tools for molecular quantum dynamics and the field of femtochemistry.

Physically motivated quantum algorithms for specific near-term quantum hardware will likely be the next frontier in quantum information science. Here, we show how many of the features of neural networks for machine learning can naturally be mapped into the quantum optical domain by introducing the quantum optical neural network (QONN). Through numerical simulation and analysis we train the QONN to perform a range of quantum information processing tasks, including newly developed protocols for quantum optical state compression, reinforcement learning, and blackbox quantum simulation. We consistently demonstrate our system can generalize from only a small set of training data onto states for which it has not been trained. Our results indicate QONNs are a powerful design tool for quantum optical systems and, leveraging advances in integrated quantum photonics, a promising architecture for next generation quantum processors.

denotes equal contribution.Conventional computing architectures have no known efficient algorithms for combinatorial optimization tasks, which are encountered in fundamental areas and real-world practical problems including logistics, social networks, and cryptography. Physical machines have recently been proposed and implemented as an alternative to conventional exact and heuristic solvers for the Ising problem, one such optimization task that requires finding the ground state spin configuration of an arbitrary Ising graph. However, these physical approaches usually suffer from decreased ground state convergence probability or universality for high edge-density graphs or arbitrary graph weights, respectively. We experimentally demonstrate a proof-of-principle integrated nanophotonic recurrent Ising sampler (INPRIS) capable of converging to the ground state of various 4-spin graphs with high probability. The INPRIS exploits experimental physical noise as a resource to speed up the ground state search. By injecting additional extrinsic noise during the algorithm iterations, the INPRIS explores larger regions of the phase space, thus allowing one to probe noise-dependent physical observables. Since the recurrent photonic transformation that our machine imparts is a fixed function of the graph problem, and could thus be implemented with optoelectronic architectures that enable GHz clock rates (such as passive or non-volatile photonic circuits that do not require reprogramming at each iteration), our work paves a way for orders-of-magnitude speedups in exploring the solution space of combinatorially hard problems.Combinatorial optimization is critical for a broad array of tasks, including artificial intelligence, bioinformatics, cryptography, scheduling, trajectory planning, and circuit design [1-3]. However, combinatorial problems typically fall into the nondeterministic-polynomial hard (NP-hard) problem class, becoming computationally intractable at large scale for traditional algorithms. This challenge motivates the search for alternatives to conventional (von Neumann) computing architectures that can efficiently solve such problems. The Ising problem, which consists of finding the ground state spin configuration of a quadratic Hamiltonian defined by a symmetric matrix K and spins of unit amplitude σ 1≤i≤N ∈ {−1, 1} N ,has garnered significant attention as many other combinatorial problems can be polynomially reduced to an Ising problem [4, 5]. Therefore, any technique for finding the ground state of arbitrary Ising problems, which is an NP-hard computational task, may extend to a wide range of other computationally intensive optimization problems. There is currently no known efficient classical algorithm to find the exact ground state of an arbitrary Ising graph, so heuristic and meta-heuristic algorithms are often implemented as a means of quickly obtaining approximate solutions [6]. Various physical systems have been proposed as Ising machines, as the evolution of many natural systems (ferromagnets [7], lipid m...

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