The ability to control multidimensional quantum systems is central to the development of advanced quantum technologies. We demonstrate a multidimensional integrated quantum photonic platform able to generate, control, and analyze high-dimensional entanglement. A programmable bipartite entangled system is realized with dimensions up to 15 × 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 previously unexplored quantum applications, such as quantum randomness expansion and self-testing on multidimensional states. Our work provides an experimental platform for the development of multidimensional quantum technologies.

We introduce the concept of an eigenstate witness and use it to find energies of quantum systems with quantum computers.

Complex-valued neural networks have many advantages over their real-valued counterparts. Conventional digital electronic computing platforms are incapable of executing truly complex-valued representations and operations. In contrast, optical computing platforms that encode information in both phase and magnitude can execute complex arithmetic by optical interference, offering significantly enhanced computational speed and energy efficiency. However, to date, most demonstrations of optical neural networks still only utilize conventional real-valued frameworks that are designed for digital computers, forfeiting many of the advantages of optical computing such as efficient complex-valued operations. In this article, we highlight an optical neural chip (ONC) that implements truly complex-valued neural networks. We benchmark the performance of our complex-valued ONC in four settings: simple Boolean tasks, species classification of an Iris dataset, classifying nonlinear datasets (Circle and Spiral), and handwriting recognition. Strong learning capabilities (i.e., high accuracy, fast convergence and the capability to construct nonlinear decision boundaries) are achieved by our complex-valued ONC compared to its real-valued counterpart.

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Efficiently characterising quantum systems [1-3], verifying operations of quantum devices [4-6] and validating underpinning physical models [7,8], are central challenges for the development of quantum technologies [9-11] and for our continued understanding of foundational physics [12,13]. Machine-learning enhanced by quantum simulators has been proposed as a route to improve the computational cost of performing these studies [14, 15]. 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.In science and engineering [16,17], physical systems are approximated by simplified models to allow the comprehension of their essential features. The utility of the model hinges upon the fidelity of the approximation to the actual physical system, and can be measured by the consistency of the model predictions with the real experimental data. However, predicting behaviour in the exponentially large configuration space of quantum systems is known to be intractable to classical computing machines [18,19]. A fundamental question therefore naturally arises: How can underpinning theoretical models of quantum systems be validated?To address this question, quantum Hamiltonian learning (QHL) was recently proposed [14,15] as a technique that exploits classical machine learning with quantum simulations to efficiently validate Hamiltonian models and verify the predictions of quantum systems or devices. QHL is tractable in cases in which other known methods fail because quantum simulation is exponentially faster than existing techniques [18][19][20] for simulating broad classes of complex quantum systems [21][22][23][24]. Our experimental demonstration of QHL uses a programmable silicon-photonics quantum simulator, shown in Figs. 1a,b, to learn the electron spin dynamics of a negatively charged nitrogen-vacancy (NV − ) centre in bulk diamond, shown in Figs. 1c,d. We further demonstrate an interactive QHL protocol that allows us to characterise and verify single-qubit gates using other trusted gates on the same quantum photonic device. arXiv:1703.05402v1 [quant-ph]

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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, nonfault 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 prethreshold 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.

While integrated photonics is a robust platform for quantum information processing, architectures for photonic quantum computing place stringent demands on high quality information carriers. Sources of single photons that are highly indistinguishable and pure, that are either near-deterministic or heralded with high efficiency, and that are suitable for massmanufacture, have been elusive. Here, we demonstrate on-chip photon sources that simultaneously meet each of these requirements. Our photon sources are fabricated in silicon using mature processes, and exploit a dual-mode pump-delayed excitation scheme to engineer the emission of spectrally pure photon pairs through intermodal spontaneous fourwave mixing in low-loss spiralled multi-mode waveguides. We simultaneously measure a spectral purity of 0.9904 ± 0.0006, a mutual indistinguishability of 0.987 ± 0.002, and >90% intrinsic heralding efficiency. We measure on-chip quantum interference with a visibility of 0.96 ± 0.02 between heralded photons from different sources.