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.
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.
We demonstrate a client-server quantum key distribution (QKD) scheme, with large resources such as laser and detectors situated at the server-side, which is accessible via telecom-fibre, to a client requiring only an on-chip polarisation rotator, tha
t may be integrated into a handheld device. The detrimental effects of unstable fibre birefringence are overcome by employing the reference frame independent QKD protocol for polarisation qubits in polarisation maintaining fibre, 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-fibre tethering.
Integrated quantum photonics is an appealing platform for quantum information processing, quantum communication and quantum metrology. In all these applications it is necessary not only to be able to create and detect Fock states of light but also to
program the photonic circuits that implements some desired logical operation. Here we demonstrate a reconfigurable controlled two-qubit operation on a chip using a multiwaveguide interferometer with a tunable phase shifter. We find excellent agreement between theory and experiment, with a 0.98 pm 0.02 average similarity between measured and ideal operations.
