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Whilst holding great promise for low noise, ease of operation and networking, useful photonic quantum computing has been precluded by the need for beyond-state-of-the-art components, manufactured by the millions. Here we introduce a manufacturable platform for quantum computing with photons. We benchmark a set of monolithically-integrated silicon photonics-based modules to generate, manipulate, network, and detect photonic qubits, demonstrating dual-rail photonic qubits with $99.98\% \pm 0.01\%$ state preparation and measurement fidelity, Hong-Ou-Mandel quantum interference between independent photon sources with $99.50\%\pm0.25\%$ visibility, two-qubit fusion with $99.22\%\pm0.12\%$ fidelity, and a chip-to-chip qubit interconnect with $99.72\%\pm0.04\%$ fidelity, not accounting for loss. In addition, we preview a selection of next generation technologies, demonstrating low-loss silicon nitride waveguides and components, fabrication-tolerant photon sources, high-efficiency photon-number-resolving detectors, low-loss chip-to-fiber coupling, and barium titanate electro-optic phase shifters., Comment: 8 pages, 5 figures

Verifying entanglement between parties is essential for creating a secure quantum network, and Bell tests are the most rigorous method for doing so. However, if there is any signaling between the parties, then the violation of these inequalities can no longer be used to draw conclusions about the presence of entanglement. This is because signaling between the parties allows them to coordinate their measurement settings and outcomes, which can give rise to a violation of Bell inequalities even if the parties are not genuinely entangled. There is a pressing need to examine the role of signaling in quantum communication protocols from multiple perspectives, including communication security, physics foundations, and resource utilization while also promoting innovative technological applications. Here, we propose a semi-device independent protocol that allows us to numerically correct for effects of correlations in experimental probability distributions, caused by statistical fluctuations and experimental imperfections. Our noise robust protocol presents a relaxation of a tomography-based optimisation method called the steering robustness, that uses semidefinite programming to numerically identify the optimal quantum steering inequality without the need for resource-intensive tomography. The proposed protocol is numerically and experimentally analyzed in the context of random, misaligned measurements, correcting for signalling where necessary, resulting in a higher probability of violation compared to existing state-of-the-art inequalities. Our work demonstrates the power of semidefinite programming for entanglement verification and brings quantum networks closer to practical applications.

Optical absorption measurements characterize a wide variety of systems from atomic gases to \emph{in-vivo} diagnostics of living organisms. Here we study the potential of non-classical techniques to reduce statistical noise below the shot-noise limit in absorption measurements with concomitant phase shifts imparted by a sample. We consider both cases where there is a known relationship between absorption and a phase shift, and where this relationship is unknown. For each case we derive the fundamental limit and provide a practical strategy to reduce statistical noise. Furthermore, we find an intuitive correspondence between measurements of absorption and of lossy phase shifts, which both show the same scope for precision enhancement. Our results demonstrate that non-classical techniques can aid real-world tasks with present-day laboratory techniques., Comment: 6 page paper, 5 page appendix, 2 figures

Integrated optics is an engineering solution proposed for exquisite control of photonic quantum information. Here we use silicon photonics and the linear combination of quantum operators scheme to realise a fully programmable two-qubit quantum processor. The device is fabricated with readily available CMOS based processing and comprises four nonlinear photon-sources, four filters, eighty-two beam splitters and fifty-eight individually addressable phase shifters. To demonstrate performance, we programmed the device to implement ninety-eight various two-qubit unitary operations (with average quantum process fidelity of 93.2$\pm$4.5%), a two-qubit quantum approximate optimization algorithm and efficient simulation of Szegedy directed quantum walks. This fosters further use of the linear combination architecture with silicon photonics for future photonic quantum processors., Comment: 23 pages, 13 figures

We bring together a cavity-enhanced light-matter interface with a multimode interferometer (MMI) integrated onto a photonic chip and demonstrate the potential of such hybrid systems to tailor distributed entanglement in a quantum network. The MMI is operated with pairs of narrowband photons produced a priori deterministically from a single 87Rb atom strongly coupled to a high-finesse optical cavity. Non-classical coincidences between photon detection events show no loss of coherence when interfering pairs of these photons through the MMI in comparison to the two-photon visibility directly measured using Hong-Ou-Mandel interference on a beam splitter. This demonstrates the ability of integrated multimode circuits to mediate the entanglement of remote stationary nodes in a quantum network interlinked by photonic qubits., Comment: 10 pages, 5 figures

The ability to control multidimensional quantum systems is key for the investigation of fundamental science and for the development of advanced quantum technologies. Here we demonstrate a multidimensional integrated quantum photonic platform able to robustly generate, control and analyze high-dimensional entanglement. We realize a programmable bipartite entangled system with dimension up to $15 \times 15$ on a large-scale silicon-photonics quantum circuit. The device integrates more than 550 photonic components on a single chip, including 16 identical photon-pair sources. We verify the high precision, generality and controllability of our multidimensional technology, and further exploit these abilities to demonstrate key quantum applications experimentally unexplored before, such as quantum randomness expansion and self-testing on multidimensional states. Our work provides a prominent experimental platform for the development of multidimensional quantum technologies., Comment: Science, (2018)

Integrated quantum photonic applications, providing physially guaranteed communications security, sub-shot-noise measurement, and tremendous computational power, are nearly within technological reach. Silicon as a technology platform has proven formibable in establishing the micro-electornics revoltution, and it might do so again in the quantum technology revolution. Silicon has has taken photonics by storm, with its promise of scalable manufacture, integration, and compatibility with CMOS microelectronics. These same properties, and a few others, motivate its use for large-scale quantum optics as well. In this article we provide context to the development of quantum optics in silicon. We review the development of the various components which constitute integrated quantum photonic systems, and we identify the challenges which must be faced and their potential solutions for silicon quantum photonics to make quantum technology a reality.

Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, non-fault tolerant, quantum devices. Here we report experimental results demonstrating that this intuition need not be true. We implement a recently proposed adaptive Bayesian approach to quantum phase estimation and use it to simulate molecular energies on a Silicon quantum photonic device. The approach is verified to be well suited for pre-threshold quantum processors by investigating its superior robustness to noise and decoherence compared to the iterative phase estimation algorithm. This shows a promising route to unlock the power of quantum phase estimation much sooner than previously believed.

Efficiently characterising quantum systems, verifying operations of quantum devices and validating underpinning physical models, are central challenges for the development of quantum technologies and for our continued understanding of foundational physics. Machine-learning enhanced by quantum simulators has been proposed as a route to improve the computational cost of performing these studies. Here we interface two different quantum systems through a classical channel - a silicon-photonics quantum simulator and an electron spin in a diamond nitrogen-vacancy centre - and use the former to learn the latter's Hamiltonian via Bayesian inference. We learn the salient Hamiltonian parameter with an uncertainty of approximately $10^{-5}$. Furthermore, an observed saturation in the learning algorithm suggests deficiencies in the underlying Hamiltonian model, which we exploit to further improve the model itself. We go on to implement an interactive version of the protocol and experimentally show its ability to characterise the operation of the quantum photonic device. This work demonstrates powerful new quantum-enhanced techniques for investigating foundational physical models and characterising quantum technologies.

Many existing schemes for linear-optical quantum computing (LOQC) depend on multiplexing (MUX), which uses dynamic routing to enable near-deterministic gates and sources to be constructed using heralded, probabilistic primitives. MUXing accounts for the overwhelming majority of active switching demands in current LOQC architectures. In this manuscript, we introduce relative multiplexing (RMUX), a general-purpose optimization which can dramatically reduce the active switching requirements for MUX in LOQC, and thereby reduce hardware complexity and energy consumption, as well as relaxing demands on performance for various photonic components. We discuss the application of RMUX to the generation of entangled states from probabilistic single-photon sources, and argue that an order of magnitude improvement in the rate of generation of Bell states can be achieved. In addition, we apply RMUX to the proposal for percolation of a 3D cluster state in [PRL 115, 020502 (2015)], and we find that RMUX allows a 2.4x increase in loss tolerance for this architecture., Comment: Published version, New Journal of Physics, Volume 19, June 2017

Integrated photonics offers great potential for quantum communication devices in terms of complexity, robustness and scalability. Silicon photonics in particular is a leading platform for quantum photonic technologies, with further benefits of miniaturisation, cost-effective device manufacture and compatibility with CMOS microelectronics. However, effective techniques for high-speed modulation of quantum states in standard silicon photonic platforms have been limited. Here we overcome this limitation and demonstrate high-speed low-error quantum key distribution modulation with silicon photonic devices combining slow thermo-optic DC biases and fast (10~GHz bandwidth) carrier-depletion modulation. The ability to scale up these integrated circuits and incorporate microelectronics opens the way to new and advanced integrated quantum communication technologies and larger adoption of quantum-secured communications.

We generate photon pairs in a-Si:H microrings using a CW pump, and find the Kerr coefficient of a-Si:H to be $3.73 \pm 0.25 \times 10^{-17}m^2/W$. By measuring the Q factor with coupled power we find that the loss in the a-Si:H micro-rings scales linearly with power, and therefore cannot originate from two photon absorption. Theoretically comparing a-Si:H and c-Si micro-ring pair sources, we show that the high Kerr coefficient of this sample of a-Si:H is best utilized for microrings with Q factors below $10^3$, but that for higher Q factor devices the photon pair rate is greatly suppressed due to the first order loss., Comment: 10 pages, 5 figures

Quantum metrology enables estimation of optical phase shifts with precision beyond the shot-noise limit. One way to exceed this limit is to use squeezed states, where the quantum noise of one observable is reduced at the expense of increased quantum noise for its complementary partner. Because shot-noise limits the phase sensitivity of all classical states, reduced noise in the average value for the observable being measured allows for improved phase sensitivity. However, additional phase sensitivity can be achieved using phase estimation strategies that account for the full distribution of measurement outcomes. Here we experimentally investigate the phase sensitivity of a five-particle optical spin-squeezed state generated by photon subtraction from a parametric downconversion photon source. The Fisher information for all photon-number outcomes shows it is possible to obtain a quantum advantage of 1.58 compared to the shot-noise limit, even though due to experimental imperfection, the average noise for the relevant spin-observable does not achieve sub-shot-noise precision. Our demonstration implies improved performance of spin squeezing for applications to quantum metrology., Comment: 8 pages, 5 figures

Imperfections in integrated photonics manufacturing have a detrimental effect on the maximal achievable visibility in interferometric architectures. These limits have profound implications for further photonics technological developments and in particular for quantum photonics technologies. Active optimisation approaches, together with reconfigurable photonics, have been proposed as a solution to overcome this. In this paper, we demonstrate an ultra-high (>60 dB) extinction ratio in a silicon photonic device consisting of cascaded Mach-Zehnder interferometers, in which additional interferometers function as variable beamsplitters. The imperfections of fabricated beamsplitters are compensated using an automated progressive optimization algorithm with no requirement for pre-calibration. This work shows the possibility of integrating and accurately controlling linear-optical components for large-scale quantum information processing and other applications., Comment: 4 pages, 3 figures

Client-server models enable computations to be hosted remotely on quantum servers. We present a novel protocol for realizing this task, with practical advantages when using technology feasible in the near term. Client tasks are realized as linear combinations of operations implemented by the server, where the linear coefficients are hidden from the server. We report on an experimental demonstration of our protocol using linear optics, which realizes linear combination of two single-qubit operations by a remote single-qubit control. In addition, we explain when our protocol can remain efficient for larger computations, as well as some ways in which privacy can be maintained using our protocol., Comment: 26 pages, 9 figures

Quantum metrology promises high-precision measurements beyond the capability of any classical techniques, and has the potential to be integral to investigative techniques. However, all sensors must tolerate imperfections if they are to be practical. Here we show that photons with perfectly overlapped modes, which are therefore fully indistinguishable, are not required for quantum-enhanced measurement, and that partially-distinguishable photons do not have to be engineered to mitigate the adverse effects of distinguishability. We quantify the effect of distinguishability on quantum metrology experiments, and report results of an experiment to verify that two- and four-photon states containing partially-distinguishable photons can achieve quantum-enhanced sensitivity with low-visibility quantum interference. This demonstrates that sources producing photons with mixed spectral states can be readily utilized for quantum metrology., Comment: 4 + 3 pages, 3 + 0 figures, comments welcome

Understanding the fundamental limits on the precision to which an optical phase can be estimated is of key interest for many investigative techniques utilized across science and technology. We study the estimation of a fixed optical phase shift due to a sample which has an associated optical loss, and compare phase estimation strategies using classical and non-classical probe states. These comparisons are based on the attainable (quantum) Fisher information calculated per number of photons absorbed or scattered by the sample throughout the sensing process. We find that, for a given number of incident photons upon the unknown phase, non-classical techniques in principle provide less than a 20% reduction in root-mean-square-error (RMSE) in comparison with ideal classical techniques in multi-pass optical setups. Using classical techniques in a new optical setup we analyze, which incorporates additional stages of interference during the sensing process, the achievable reduction in RMSE afforded by non-classical techniques falls to only ~4%. We explain how these conclusions change when non-classical techniques are compared to classical probe states in non-ideal multi-pass optical setups, with additional photon losses due to the measurement apparatus., Comment: Expanded text to match published version

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms. In this paper, we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks which could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle we have experimentally implemented the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor., Comment: 10 pages, 5 figures

Improvement in secure transmission of information is an urgent practical need for governments, corporations and individuals. Quantum key distribution (QKD) promises security based on the laws of physics and has rapidly grown from proof-of-concept to robust demonstrations and even deployment of commercial systems. Despite these advances, QKD has not been widely adopted, and practical large-scale deployment will likely require integrated chip-based devices for improved performance, miniaturisation and enhanced functionality, fully integrated into classical communication networks. Here we report low error rate, GHz clocked QKD operation of an InP transmitter chip and a SiO$_x$N$_y$ receiver chip --- monolithically integrated devices that use state-of-the-art components and manufacturing processes from the telecom industry. We use the reconfigurability of these devices to demonstrate three important QKD protocols --- BB84, Coherent One Way (COW) and Differential Phase Shift (DPS) --- with performance comparable to state-of-the-art. These devices, when combined with integrated single photon detectors, satisfy the requirements at each of the levels of future QKD networks --- from point-of-use through to backbone --- and open the way to operation in existing and emerging classical communication networks., Comment: 5 pages, 3 figures, 1 table

Increasing control of single photons enables new applications of photonic quantum-enhanced technology and further experimental exploration of fundamental quantum phenomena. Here, we demonstrate quantum logic using narrow linewidth photons that are produced under nearly perfect quantum control from a single ^87Rb atom strongly coupled to a high-finesse cavity. We use a controlled- NOT gate integrated into a photonic chip to entangle these photons, and we observe non-classical correlations between events separated by periods exceeding the travel time across the chip by three orders of magnitude. This enables quantum technology that will use the properties of both narrowband single photon sources and integrated quantum photonics, such as networked quantum computing, narrow linewidth quantum enhanced sensing and atomic memories., Comment: 5 pates, 3 figures

Integrated photonics has enabled much progress towards quantum technologies. Many applications, including quantum communication, sensing, and distributed and cloud quantum computing, will require coherent photonic interconnection between separate chip-based sub-systems. Large-scale quantum computing systems and architectures may ultimately require quantum interconnects to enable scaling beyond the limits of a single wafer and towards "multi-chip" systems. However, coherently interconnecting separate chips is challenging due to the fragility of these quantum states and the demanding challenges of transmitting photons in at least two media within a single coherent system. Distribution and manipulation of qubit entanglement between multiple devices is one of the most stringent requirements of the interconnected system. Here, we report a quantum photonic interconnect demonstrating high-fidelity entanglement distribution and manipulation between two separate chips, implemented using state-of-the-art silicon photonics. Path-entangled states are generated and manipulated on-chip, and distributed between the chips by interconverting between path-encoding and polarisation-encoding. We use integrated state analysers to confirm a Bell-type violation of $S$=2.638+-0.039 between two chips. With improvements in loss, this quantum interconnect will provide new levels of flexible systems and architectures for quantum technologies., Comment: 12 pages, 10 figures

Absorption spectroscopy is routinely used to characterise chemical and biological samples. For the state-of-the-art in absorption spectroscopy, precision is theoretically limited by shot-noise due to the fundamental Poisson-distribution of photon number in laser radiation. In practice, the shot-noise limit can only be achieved when all other sources of noise are eliminated. Here, we use wavelength-correlated and tuneable photon pairs to demonstrate sub-shot-noise absorption spectroscopy. We measure the absorption spectra of spectrally-similar biological samples---oxyhaemoglobin and carboxyhaemoglobin---and show that obtaining a given precision in resolution requires fewer heralded single probe photons compared to using an ideal laser., Comment: 5 pages, 4 figures

Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics. We describe an operationally simple method to directly implement Haar random unitary matrices in optical circuits, with no requirement for prior or explicit matrix calculations. Our physically-motivated and compact representation directly maps independent probability density functions for parameters in Haar random unitary matrices, to optical circuit components. We go on to extend the results to the case of random unitaries for qubits.

Encoding quantum information in continuous variables (CV)---as the quadrature of electromagnetic fields---is a powerful approach to quantum information science and technology. CV entanglement---light beams in Einstein-Podolsky-Rosen (EPR) states---is a key resource for quantum information protocols; and enables hybridisation between CV and single photon discrete variable (DV) qubit systems. However, CV systems are currently limited by their implementation in free-space optical networks: increased complexity, low loss, high-precision alignment and stability, as well as hybridisation, demand an alternative approach. Here we show an integrated photonic implementation of the key capabilities for CV quantum technologies---generation and characterisation of EPR beams in a photonic chip. Combined with integrated squeezing and non-Gaussian operation, these results open the way to universal quantum information processing with light.

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 Mach-Zehnder 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 $\pm$ 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., Comment: Comments welcome

Photonic qubits constitute a leading platform to disruptive quantum technologies due to their unique low-noise properties. The cost of the photonic approach is the non-deterministic nature of many of the processes, including single-photon generation, which arises from parametric sources and negligible interaction between photons. Active temporal multiplexing - repeating a generation process in time and rerouting to single modes using an optical switching network - is a promising approach to overcome this challenge and will likely be essential for large-scale applications with greatly reduced resource complexity and system sizes. Requirements include the precise synchronization of a system of low-loss switches, delay lines, fast photon detectors, and feed-forward. Here we demonstrate temporal multiplexing of 8 'bins' from a double-passed heralded photon source and observe an increase in the heralding and heralded photon rates. This system points the way to harnessing temporal multiplexing in quantum technologies, from single-photon sources to large-scale computation., Comment: Minor revisions

The foundational ideas of quantum mechanics continue to give rise to counterintuitive theories and physical effects that are in conflict with a classical description of Nature. Experiments with light at the single photon level have historically been at the forefront of tests of fundamental quantum theory and new developments in photonics engineering continue to enable new experiments. Here we review recent photonic experiments to test two foundational themes in quantum mechanics: wave-particle duality, central to recent complementarity and delayed-choice experiments; and Bell nonlocality where recent theoretical and technological advances have allowed all controversial loopholes to be separately addressed in different photonics experiments., Comment: 10 pages, 5 figures, published as a Nature Physics Insight review article

Entanglement--one of the most delicate phenomena in nature--is an essential resource for quantum information applications. Large entangled cluster states have been predicted to enable universal quantum computation, with the required single- qubit measurements readily implemented with photons. Useful large-scale systems must generate and control qubit entanglement on-chip, where quantum information is naturally encoded in photon path. Here we report a silicon photonic chip which integrates resonant-enhanced sources, filters, and reconfigurable optics to generate a path-entangled two-qubit state--the smallest non-trivial cluster state--and analyse its entanglement. We show that ring-resonator-based spontaneous four-wave mixing sources can be made highly indistinguishable, despite their nonlinear dynamics, and the first evidence that their frequency correlations are small, as predicted. We use quantum state tomography, and the strict Bell-CHSH inequality to quantify entanglement in the device, confirming its high performance. This work integrates essential components for building devices and systems to harness quantum entanglement on the large scale.

An on-demand single-photon source is a key requirement for scaling many optical quantum technologies. A promising approach to realize an on-demand single-photon source is to multiplex an array of heralded single-photon sources using an active optical switching network. However, the performance of multiplexed sources is degraded by photon loss in the optical components and the non-unit detection efficiency of the heralding detectors. We provide a theoretical description of a general multiplexed single-photon source with lossy components and derive expressions for the output probabilities of single-photon emission and multi-photon contamination. We apply these expressions to three specific multiplexing source architectures and consider their tradeoffs in design and performance. To assess the effect of lossy components on near- and long-term experimental goals, we simulate the multiplexed sources when used for many-photon state generation under various amounts of component loss. We find that with a multiplexed source composed of switches with ~0.2-0.4 dB loss and high efficiency number-resolving detectors, a single-photon source capable of efficiently producing 20-40 photon states with low multi-photon contamination is possible, offering the possibility of unlocking new classes of experiments and technologies., Comment: Journal version

A fair gambling is hard to be made between two spatially separated parties without introducing a trusted third party. Here we propose a novel gambling protocol, which enables fair gambling between two distant parties without the help of a third party. By incorporating the key concepts and methods of game theory, our protocol will force the two parties to move their strategies to a Nash-equilibrium point which guarantees the fairness through the physical laws of quantum mechanics. Furthermore, we show that our protocol can be easily adapted to a biased version, which would find applications in lottery, casino, etc. A proof-of-principle optical demonstration of this protocol is reported as well.

Integrated quantum photonics is a promising approach for future practical and large-scale quantum information processing technologies, with the prospect of on-chip generation, manipulation and measurement of complex quantum states of light. The gallium arsenide (GaAs) material system is a promising technology platform, and has already successfully demonstrated key components including waveguide integrated single-photon sources and integrated single-photon detectors. However, quantum circuits capable of manipulating quantum states of light have so far not been investigated in this material system. Here, we report GaAs photonic circuits for the manipulation of single-photon and two-photon states. Two-photon quantum interference with a visibility of 94.9 +/- 1.3% was observed in GaAs directional couplers. Classical and quantum interference fringes with visibilities of 98.6 +/- 1.3% and 84.4 +/- 1.5% respectively were demonstrated in Mach-Zehnder interferometers exploiting the electro-optic Pockels effect. This work paves the way for a fully integrated quantum technology platform based on the GaAs material system., Comment: 10 pages, 4 figures

A fundamental task in photonics is to characterise an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Amongst many ways to achieve this, single-photon probes can be used in a method called quantum process tomography (QPT). Furthermore, QPT is an essential method in determining how a process acts on quantum mechanical states. For example for quantum technology, QPT is used to characterise multi-qubit processors and quantum communication channels; across quantum physics QPT of some form is often the first experimental investigation of a new physical process, as shown in the recent research into coherent transport in biological mechanisms. However, the precision of QPT is limited by the fact that measurements with single-particle probes are subject to unavoidable shot noise---this holds for both single photon and laser probes. In situations where measurement resources are limited, for example, where the process is rapidly changing or the time bandwidth is constrained, it becomes essential to overcome this precision limit. Here we devise and demonstrate a scheme for tomography which exploits non-classical input states and quantum interferences; unlike previous QPT methods our scheme capitalises upon the possibility to use simultaneously multiple photons per mode. The efficiency---quantified by precision per photon used---scales with larger photon number input states. Our demonstration uses four-photon states and our results show a substantial reduction of statistical fluctuations compared to traditional QPT methods---in the ideal case one four-photon probe state yields the same amount of statistical information as twelve single probe photons.

Generating and characterising randomness is fundamentally important in both classical and quantum information science. Here we report the experimental demonstration of ensembles of pseudorandom optical processes comprising what are known as t-designs. We show that in practical scenarios, certain finite ensembles of two-mode transformations---1- and 2-designs---are indistinguishable from truly random operations for 1- and 2-photon quantum interference, but they fail to mimic randomness for 2- and 3-photon cases, respectively. This provides a novel optical test of pseudo randomness. We make use of the fact that t-photon behaviour is governed by degree-2t polynomials in the parameters of the optical process to experimentally verify the ensembles' behaviour for complete bases of polynomials. This ensures that outputs will be uniform for arbitrary configurations, satisfying the strict definition of pseudorandomness implicit in the mathematical definition., Comment: 10 pages, 12 figures (including appendix)

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., Comment: Comments welcome

We demonstrate quantum walks of correlated photons in a 2D network of directly laser written waveguides coupled in a 'swiss cross' arrangement. The correlated detection events show high-visibility quantum interference and unique composite behaviour: strong correlation and independence of the quantum walkers, between and within the planes of the cross. Violations of a classically defined inequality, for photons injected in the same plane and in orthogonal planes, reveal non-classical behaviour in a non-planar structure., Comment: 5 pages, 5 figures

Quantum metrology research promises approaches to build new sensors that achieve the ultimate level of precision measurement and perform fundamentally better than modern sensors. Practical schemes that tolerate realistic fabrication imperfections and environmental noise are required in order to realise quantum-enhanced sensors and to enable their real-world application. We have demonstrated the key enabling principles of a practical, loss-tolerant approach to photonic quantum metrology designed to harness all multi-photon components in spontaneous parametric downconversion---a method for generating multiple photons that we show requires no further fundamental state engineering for use in practical quantum metrology. We observe a quantum advantage of 28% in precision measurement of optical phase using the four-photon detection component of this scheme, despite 83% system loss. This opens the way to new quantum sensors based on current quantum-optical capabilities., Comment: 8 pages, 7 figures, 2 tables

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm can efficiently find the eigenvalue of a given eigenvector but requires fully coherent evolution. We present an alternative approach that greatly reduces the requirements for coherent evolution and we combine this method with a new approach to state preparation based on ans\"atze and classical optimization. We have implemented the algorithm by combining a small-scale photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry: calculating the ground state molecular energy for He-H+, to within chemical accuracy. The proposed approach, by drastically reducing the coherence time requirements, enhances the potential of the quantum resources available today and in the near future.

Large-scale integrated quantum photonic technologies will require the on-chip integration of identical photon sources with reconfigurable waveguide circuits. Relatively complex quantum circuits have already been demonstrated, but few studies acknowledge the pressing need to integrate photon sources and waveguide circuits together on-chip. A key step towards such large-scale quantum technologies is the integration of just two individual photon sources within a waveguide circuit, and the demonstration of high-visibility quantum interference between them. Here, we report a silicon-on-insulator device combining two four-wave mixing sources, in an interferometer with a reconfigurable phase shifter. We configure the device to create and manipulate two-colour (non-degenerate) or same-colour (degenerate), path-entangled or path-unentangled photon pairs. We observe up to 100.0+/-0.4% visibility quantum interference on-chip, and up to 95+/-4% off-chip. Our device removes the need for external photon sources, provides a path to increasing the complexity of quantum photonic circuits, and is a first step towards fully-integrated quantum technologies.

Multi-photon quantum walks in integrated optics are an attractive controlled quantum system, that can mimic less readily accessible quantum systems and exhibit behavior that cannot in general be accurately replicated by classical light without an exponential overhead in resources. The ability to observe time evolution of such systems is important for characterising multi-particle quantum dynamics---notably this includes the effects of boundary conditions for walks in spaces of finite size. Here we demonstrate the coherent evolution of quantum walks of two indistinguishable photons using planar arrays of 21 evanescently coupled waveguides fabricated in silicon oxynitride technology. We compare three time evolutions, that follow closely a model assuming unitary evolution, corresponding to three different lengths of the array---in each case we observe quantum interference features that violate classical predictions. The longest array includes reflecting boundary conditions., Comment: 7 pages,7 figures

Linear optical circuits of growing complexity are playing an increasing role in emerging photonic quantum technologies. Individual photonic devices are typically described by a unitary matrix containing amplitude and phase information, the characterisation of which is a key task. We present a constructive scheme to retrieve the unitary matrix describing an arbitrary linear optical device using data obtained from one-photon and two-photon ensembles. The scheme is stable on the arbitrarily increasable length scale of the photon packet and independent of photon loss at input and output ports of the device. We find a one-to-one correspondence between ideal data and unitary matrix, and identify the class of non-unitary matrices capable of reproducing the data. The method is extended for coherent state probes, which can simulate two-photon statistics with a reduced visibility. We analyse the performance of reconstruction to simulated noise., Comment: Comments welcome

Quantum systems exhibit particle-like or wave-like behaviour depending on the experimental apparatus they are confronted by. This wave-particle duality is at the heart of quantum mechanics, and is fully captured in Wheeler's famous delayed choice gedanken experiment. In this variant of the double slit experiment, the observer chooses to test either the particle or wave nature of a photon after it has passed through the slits. Here we report on a quantum delayed choice experiment, based on a quantum controlled beam-splitter, in which both particle and wave behaviours can be investigated simultaneously. The genuinely quantum nature of the photon's behaviour is tested via a Bell inequality, which here replaces the delayed choice of the observer. We observe strong Bell inequality violations, thus showing that no model in which the photon knows in advance what type of experiment it will be confronted by, hence behaving either as a particle or as wave, can account for the experimental data.

Emerging models of quantum computation driven by multi-photon quantum interference, while not universal, may offer an exponential advantage over classical computers for certain problems. Implementing these circuits via geometric phase gates could mitigate requirements for error correction to achieve fault tolerance while retaining their relative physical simplicity. We report an experiment in which a geometric phase is embedded in an optical network with no closed-loops, enabling quantum interference between two photons as a function of the phase., Comment: Comments welcome

Photon sources are fundamental components for any quantum photonic technology. The ability to generate high count-rate and low-noise correlated photon pairs via spontaneous parametric down-conversion using bulk crystals has been the cornerstone of modern quantum optics. However, future practical quantum technologies will require a scalable integration approach, and waveguide-based photon sources with high-count rate and low-noise characteristics will be an essential part of chip-based quantum technologies. Here, we demonstrate photon pair generation through spontaneous four-wave mixing in a silicon micro-ring resonator, reporting a maximum coincidence-to-accidental (CAR) ratio of 602 (+-) 37, and a maximum photon pair generation rate of 123 MHz (+-) 11 KHz. To overcome free-carrier related performance degradations we have investigated reverse biased p-i-n structures, demonstrating an improvement in the pair generation rate by a factor of up to 2, with negligible impact on CAR., Comment: 5 pages, 3 figures

Large cross-section GaN waveguides are proposed as a suitable architecture to achieve integrated quantum photonic circuits. Directional couplers with this geometry have been designed with aid of the beam propagation method and fabricated using inductively coupled plasma etching. Scanning electron microscopy inspection shows high quality facets for end coupling and a well defined gap between rib pairs in the coupling region. Optical characterization at 800 nm shows single-mode operation and coupling-length-dependent splitting ratios. Two photon interference of degenerate photon pairs has been observed in the directional coupler by measurement of the Hong-Ou-Mandel dip with 96% visibility., Comment: 4 pages, 5 figures

Integrated quantum photonic waveguide circuits are a promising approach to realizing future photonic quantum technologies. Here, we present an integrated photonic quantum technology platform utilising the silicon-on-insulator material system, where quantum interference and the manipulation of quantum states of light are demonstrated in components orders of magnitude smaller than in previous implementations. Two-photon quantum interference is presented in a multi-mode interference coupler, and manipulation of entanglement is demonstrated in a Mach-Zehnder interferometer, opening the way to an all-silicon photonic quantum technology platform., Comment: 7 pages

Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations. 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. 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., Comment: 7 pages, 3 figures

Bell tests---the experimental demonstration of a Bell inequality violation---are central to understanding the foundations of quantum mechanics, underpin quantum technologies, and are a powerful diagnostic tool for technological developments in these areas. To date, Bell tests have relied on careful calibration of the measurement devices and alignment of a shared reference frame between the two parties---both technically demanding tasks in general. Surprisingly, we show that neither of these operations are necessary, violating Bell inequalities with near certainty with (i) unaligned, but calibrated, measurement devices, and (ii) uncalibrated and unaligned devices. We demonstrate generic quantum nonlocality with randomly chosen local measurements on a singlet state of two photons implemented with reconfigurable integrated optical waveguide circuits based on voltage-controlled phase shifters. The observed results demonstrate the robustness of our schemes to imperfections and statistical noise. This new approach is likely to have important applications in both fundamental science and in quantum technologies, including device independent quantum key distribution., Comment: 7 pages, 7 figures

Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct the algorithm. We have implemented the complete quantum phase estimation algorithm for a single qubit unitary in which the answer is calculated by the algorithm. We use a new approach to implementing the controlled-unitary operations that lie at the heart of the majority of quantum algorithms that is more efficient and does not require the eigenvalues of the unitary to be known. These results point the way to efficient quantum simulations and quantum metrology applications in the near term, and to factoring large numbers in the longer term. This approach is architecture independent and thus can be used in other physical implementations.