Open system quantum annealing in mean field models with exponential degeneracy

Real life quantum computers are inevitably affected by intrinsic noise resulting in dissipative non-unitary dynamics realized by these devices. We consider an open system quantum annealing algorithm optimized for a realistic analog quantum device which takes advantage of noise-induced thermalization and relies on incoherent quantum tunneling at finite temperature. We analyze the performance of this algorithm considering a p-spin model which allows for a mean field quasicalssical solution and at the same time demonstrates the 1st order phase transition and exponential degeneracy of states. We demonstrate that finite temperature effects introduced by the noise are particularly important for the dynamics in presence of the exponential degeneracy of metastable states. We determine the optimal regime of the open system quantum annealing algorithm for this model and find that it can outperform simulated annealing in a range of parameters.Comment: 11 pages, 5 figure

Decoherence induced deformation of the ground state in adiabatic quantum computation

Despite more than a decade of research on adiabatic quantum computation (AQC), its decoherence properties are still poorly understood. Many theoretical works have suggested that AQC is more robust against decoherence, but a quantitative relation between its performance and the qubits' coherence properties, such as decoherence time, is still lacking. While the thermal excitations are known to be important sources of errors, they are predominantly dependent on temperature but rather insensitive to the qubits' coherence. Less understood is the role of virtual excitations, which can also reduce the ground state probability even at zero temperature. Here, we introduce normalized ground state fidelity as a measure of the decoherence-induced deformation of the ground state due to virtual transitions. We calculate the normalized fidelity perturbatively at finite temperatures and discuss its relation to the qubits' relaxation and dephasing times, as well as its projected scaling properties.Comment: 10 pages, 3 figure

Solving the Optimal Trading Trajectory Problem Using a Quantum Annealer

We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multi-period portfolio optimization problem we solve is significantly harder than the continuous variable problem. We present insight into how results may be improved using suitable software enhancements, and why current quantum annealing technology limits the size of problem that can be successfully solved today. The formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques.Comment: 7 pages; expanded and update