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...

Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms 1-3 . Shor's quantum algorithm 4 for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer 5 . However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations 6-9 . Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol [10][11][12] . Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N = 21. The algorithmic output is distinguishable from noise, in contrast to previous demonstrations. These results point to larger-scale implementations of Shor's algorithm by harnessing scalable resource reductions applicable to all physical architectures.Shor's factoring algorithm consists of a quantum order finding algorithm, preceded and succeeded by various classical routines. While the classical tasks are known to be efficient on a classical computer, order finding is understood to be intractable classically. However, it is known that this part of the algorithm can be performed efficiently on a quantum computer. To determine the prime factors of an odd integer N , one chooses a coprime of N , x. The order r relates x to N according to x r mod N = 1, and can be used to obtain the factors, given by the greatest common divisor gcd(x r 2 ± 1, N ). The quantum order finding circuit involves two registers: a work register and a control register. In the standard protocol, the work register performs modular arithmetic with m = log 2 N qubits, enough to encode the number N , and the n qubit control register provides the algorithmic output, with n bits of precision.Measuring the control register in the computational basis will yield a result of k2 n /r where k is an integer between 0 and r − 1, with the value of k occurring probabilistically. Dividing the result by 2 n gives the first n bits of k/r and r may be found with classical processing, using the continued fraction algorithm. For large n, and a perfectly functioning circuit, the output probability distribution of the control register is a series of well defined peaks at values of k2 n /r (Fig. 1b). (See Appendix for details.)Here we implement an iterative version of the order finding algorithm 10,11 , in which the control register contains only a single qubit which is recycled n times, using a sequence of measurement and feed-forward operations, with each step providing an additional bit of precision (Fig. 1a). Reducing the number of qubits in quantum simulations and quantum chemistry has been achieved with recursive phase estimation 13-16 , while ground state projections have been demonstrated by exploiting similar techniques in NMR 17 .The iterative version of...

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.

We demonstrate a client-server quantum key distribution (QKD) scheme. Large resources such as laser and detectors are situated at the server side, which is accessible via telecom fiber to a client requiring only an on-chip polarization rotator, which may be integrated into a handheld device. The detrimental effects of unstable fiber birefringence are overcome by employing the reference-frame-independent QKD protocol for polarization qubits in polarization maintaining fiber, where standard QKD protocols fail, as we show for comparison. This opens the way for quantum enhanced secure communications between companies and members of the general public equipped with handheld mobile devices, via telecom-fiber tethering.

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Quantum algorithms are computational routines that exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum factoring algorithm [1] is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the large number of resources required, to date, there have been only four small scale demonstrations [2][3][4][5].Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol [6]. Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N = 21 [7]. Significantly, the algorithmic output exhibits structure that is distinguishable from noise, in contrast to previous demonstrations. 0 1 0 1 2 00 01 10 11 0 1 8 1 4 3 8 000 011 101 0 0.35 0000 0101 1011 0 0.35 0 0 0 0 0 0 1 Fig. 1. (a) Measurement of the control qubit after each controlled unitary gives the next most significant bit in the output and the outcome is fed forward to the iterated (semi-classical) Fourier transform, which applies either the identity operation I or the appropriate phase gate R, prior to the Hadamard H. (b) As the number of iterations increases the precision increases. (c) For two bits of precision the controlled unitary operations can be constructed with this arrangement of controlled-swap gates.The correct algorithmic output from the quantum order finding circuit for factoring N = 21 is confirmed by the experimental results with a fidelity of 99 ± 4% with the ideal probability distribution. The experimental output has a critical dependence on decoherence: phase instability drives the output toward a uniform probability distribution, in contrast with previous experimental demonstrations of Shor's algorithm, all of them for N = 15, in which a uniform probability distribution is the expected outcome. We confirmed this analysis experimentally [7].These results point to larger-scale implementations of Shor's algorithm by harnessing substantial but scalable resource reductions applicable to all physical architectures.

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