Accelerating variational quantum Monte Carlo using the variational quantum eigensolver

Variational Monte Carlo (VMC) methods are used to sample classically from distributions corresponding to quantum states which have an efficient classical description. VMC methods are based on performing a number of steps of a Markov chain starting with samples from a simple initial distribution. Here we propose replacing this initial distribution with samples produced using a quantum computer, for example using the variational quantum eigensolver (VQE). We show that, based on the use of initial distributions generated by numerical simulations and by experiments on quantum hardware, convergence to the target distribution can be accelerated compared with classical samples; the energy can be reduced compared with the energy of the state produced by VQE; and VQE states produced by small quantum computers can be used to accelerate large instances of VMC. Quantum-enhanced VMC makes minimal requirements of the quantum computer and offers the prospect of accelerating classical methods using noisy samples from near-term quantum computers which are not yet able to accurately represent ground states of complex quantum systems.Comment: 11 pages, 9 figures; v2: added references and additional result

Generating entanglement with linear optics

Entanglement is the basic building block of linear optical quantum computation, and as such understanding how to generate it in detail is of great importance for optical architectures. We prove that Bell states cannot be generated using only 3 photons in the dual-rail encoding, and give strong numerical evidence for the optimality of the existing 4 photon schemes. In a setup with a single photon in each input mode, we find a fundamental limit on the possible entanglement between a single mode Alice and arbitrary Bob. We investigate and compare other setups aimed at characterizing entanglement in settings more general than dual-rail encoding. The results draw attention to the trade-off between the entanglement a state has and the probability of postselecting that state, which can give surprising constant bounds on entanglement even with increasing numbers of photons.Comment: 13 pages, 10 figures, 1 table, comments welcom

Discriminating distinguishability

Particle distinguishability is a significant challenge for quantum technologies, in particular photonics where the Hong-Ou-Mandel (HOM) effect clearly demonstrates it is detrimental to quantum interference. We take a representation theoretic approach in first quantisation, separating particles' Hilbert spaces into degrees of freedom that we control and those we do not, yielding a quantum information inspired bipartite model where distinguishability can arise as correlation with an environment carried by the particles themselves. This makes clear that the HOM experiment is an instance of a (mixed) state discrimination protocol, which can be generalised to interferometers that discriminate unambiguously between ideal indistinguishable states and interesting distinguishable states, leading to bounds on the success probability of an arbitrary HOM generalisation for multiple particles and modes. After setting out the first quantised formalism in detail, we consider several scenarios and provide a combination of analytical and numerical results for up to nine photons in nine modes. Although the Quantum Fourier Transform features prominently, we see that it is suboptimal for discriminating completely distinguishable states.Comment: 17 pages, 2 Tables, 2 figure

Integrated Silicon Photonics for High-Speed Quantum Key Distribution

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

Strategies for solving the Fermi-Hubbard model on near-term quantum computers

The Fermi-Hubbard model is of fundamental importance in condensed-matter physics, yet is extremely challenging to solve numerically. Finding the ground state of the Hubbard model using variational methods has been predicted to be one of the first applications of near-term quantum computers. Here we carry out a detailed analysis and optimisation of the complexity of variational quantum algorithms for finding the ground state of the Hubbard model, including costs associated with mapping to a real-world hardware platform. The depth complexities we find are substantially lower than previous work. We performed extensive numerical experiments for systems with up to 12 sites. The results suggest that the variational ans\"atze we used -- an efficient variant of the Hamiltonian Variational ansatz and a novel generalisation thereof -- will be able to find the ground state of the Hubbard model with high fidelity in relatively low quantum circuit depth. Our experiments include the effect of realistic measurements and depolarising noise. If our numerical results on small lattice sizes are representative of the somewhat larger lattices accessible to near-term quantum hardware, they suggest that optimising over quantum circuits with a gate depth less than a thousand could be sufficient to solve instances of the Hubbard model beyond the capacity of classical exact diagonalisation.Comment: 14+11 pages, 19 figures, 5 tables; v3: publication versio

Advances in quantum machine learning

Here we discuss advances in the field of quantum machine learning. The following document offers a hybrid discussion; both reviewing the field as it is currently, and suggesting directions for further research. We include both algorithms and experimental implementations in the discussion. The field's outlook is generally positive, showing significant promise. However, we believe there are appreciable hurdles to overcome before one can claim that it is a primary application of quantum computation.Comment: 38 pages, 17 Figure