Exact Ising model simulation on a quantum computer

We present an exact simulation of a one-dimensional transverse Ising spin chain with a quantum computer. We construct an efficient quantum circuit that diagonalizes the Ising Hamiltonian and allows to obtain all eigenstates of the model by just preparing the computational basis states. With an explicit example of that circuit for $n=4$ spins, we compute the expected value of the ground state magnetization, the time evolution simulation and provide a method to also simulate thermal evolution. All circuits are run in IBM and Rigetti quantum devices to test and compare them qualitatively.Comment: The program used for this work for the IBM quantum devices was awarded with the IBM "Teach Me QISKit" award. Accepted in Quantum journal (2018-12-18

Simulating 0+1 Dimensional Quantum Gravity on Quantum Computers: Mini-Superspace Quantum Cosmology and the World Line Approach in Quantum Field Theory

Quantum computers are a promising candidate to radically expand computational science through increased computing power and more effective algorithms. In particular quantum computing could have a tremendous impact in the field of quantum cosmology. The goal of quantum cosmology is to describe the evolution of the Universe through the Wheeler-DeWitt equation or path integral methods without having to first formulate a full theory of quantum gravity. The quantum computer provides an advantage in this endeavor because it can perform path integrals in Lorentzian space and does not require constructing contour integrations in Euclidean gravity. Also quantum computers can provide advantages in systems with fermions which are difficult to analyze on classical computers. In this study, we first employed classical computational methods to analyze a Friedmann-Robertson-Walker mini-superspace with a scalar field and visualize the calculated wave function of the Universe for a variety of different values of the spatial curvature and cosmological constant. We them used IBM's Quantum Information Science Kit Python library and the variational quantum eigensolver to study the same systems on a quantum computer. The framework can also be extended to the world line approach to quantum field theory.Comment: 5 pages, 4 figure

Exact Numerical Solution of the BCS Pairing Problem

We propose a new simulation computational method to solve the reduced BCS Hamiltonian based on spin analogy and submatrix diagonalization. Then we further apply this method to solve superconducting energy gap and the results are well consistent with those obtained by Bogoliubov transformation method. The exponential problem of 2^{N}-dimension matrix is reduced to the polynomial problem of N-dimension matrix. It is essential to validate this method on a real quantumComment: 7 pages, 3 figure

Quantum walks of correlated photon pairs in two-dimensional waveguide arrays

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 figure

Fractal Fidelity as a signature of Quantum Chaos

We analyze the fidelity of a quantum simulation and we show that it displays fractal fluctuations iff the simulated dynamics is chaotic. This analysis allows us to investigate a given simulated dynamics without any prior knowledge. In the case of integrable dynamics, the appearance of fidelity fractal fluctuations is a signal of a highly corrupted simulation. We conjecture that fidelity fractal fluctuations are a signature of the appearance of quantum chaos. Our analysis can be realized already by a few qubit quantum processor.Comment: 5 pages, 5 figure

Simulating chemistry using quantum computers

The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.Comment: 27 pages. Submitted to Ann. Rev. Phys. Che