On the experimental verification of quantum complexity in linear optics

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 welcom

Testing foundations of quantum mechanics with photons

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 articl

Quantum interferometry with three-dimensional geometry

Quantum interferometry uses quantum resources to improve phase estimation with respect to classical methods. Here we propose and theoretically investigate a new quantum interferometric scheme based on three-dimensional waveguide devices. These can be implemented by femtosecond laser waveguide writing, recently adopted for quantum applications. In particular, multiarm interferometers include "tritter" and "quarter" as basic elements, corresponding to the generalization of a beam splitter to a 3- and 4-port splitter, respectively. By injecting Fock states in the input ports of such interferometers, fringe patterns characterized by nonclassical visibilities are expected. This enables outperforming the quantum Fisher information obtained with classical fields in phase estimation. We also discuss the possibility of achieving the simultaneous estimation of more than one optical phase. This approach is expected to open new perspectives to quantum enhanced sensing and metrology performed in integrated photonic.Comment: 7 pages (+4 Supplementary Information), 5 figure

Quantum teleportation on a photonic chip

Quantum teleportation is a fundamental concept in quantum physics which now finds important applications at the heart of quantum technology including quantum relays, quantum repeaters and linear optics quantum computing (LOQC). Photonic implementations have largely focussed on achieving long distance teleportation due to its suitability for decoherence-free communication. Teleportation also plays a vital role in the scalability of photonic quantum computing, for which large linear optical networks will likely require an integrated architecture. Here we report the first demonstration of quantum teleportation in which all key parts - entanglement preparation, Bell-state analysis and quantum state tomography - are performed on a reconfigurable integrated photonic chip. We also show that a novel element-wise characterisation method is critical to mitigate component errors, a key technique which will become increasingly important as integrated circuits reach higher complexities necessary for quantum enhanced operation.Comment: Originally submitted version - refer to online journal for accepted manuscript; Nature Photonics (2014

Guaranteed violation of a Bell inequality without aligned reference frames or calibrated devices

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 figure

On-chip quantum interference between silicon photon-pair sources

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

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers