arXiv subjects

Sergey Knysh

Publications and source records attributed to Sergey Knysh.

10 recordsLinked to original sources

arXiv2020

Quantum annealing speedup of embedded problems via suppression of Griffiths singularities

Optimal parameter setting for applications problems embedded into hardware graphs is key to practical quantum annealers (QA). Embedding chains typically crop up as harmful Griffiths phases, but can be used as a resource as we show here: to balance out singularities in the logical problem changing its universality class. Smart choice of embedding parameters reduces annealing times for random Ising chain from $O(exp[c\sqrt N])$ to $O(N^2)$. Dramatic reduction in time-to-solution for QA is confirmed by numerics, for which we developed a custom integrator to overcome convergence issues.

quant-ph↗

arXiv2019

Supplementary information for "Quantum supremacy using a programmable superconducting processor"

This is an updated version of supplementary information to accompany "Quantum supremacy using a programmable superconducting processor", an article published in the October 24, 2019 issue of Nature. The main article is freely available at https://www.nature.com/articles/s41586-019-1666-5. Summary of changes since arXiv:1910.11333v1 (submitted 23 Oct 2019): added URL for qFlex source code; added Erratum section; added Figure S41 comparing statistical and total uncertainty for log and linear XEB; new References [1,65]; miscellaneous updates for clarity and style consistency; miscellaneous typographical and formatting corrections.

quant-ph↗

arXiv2019

Noise amplification at spin-glass bottlenecks of quantum annealing: a solvable model

To gain better insight into the complexity theory of quantum annealing, we propose and solve a class of spin systems which contain bottlenecks of the kind expected to dominate the runtime of quantum annealing as it tries to solve difficult optimization problems. We uncover a noise amplification effect at these bottlenecks, whereby tunneling rates caused by flux-qubit noise scale in proportion to the number of qubits $N$ in the limit that $N\to \infty$. By solving the incoherent annealing dynamics exactly, we find a wide range of regimes where the probability that a quantum annealer remains in the ground-state upon exiting the bottleneck is close to one-half. We corroborate our analysis with detailed simulations of the performance of the D-Wave 2X quantum annealer on our class of computational problems.

quant-ph↗

arXiv2017

A NASA Perspective on Quantum Computing: Opportunities and Challenges

In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can provide an advantage, and if so by how much, or how to design quantum algorithms that realize such advantages. Many of the most challenging computational problems arising in the practical world are tackled today by heuristic algorithms that have not been mathematically proven to outperform other approaches but have been shown to be effective empirically. While quantum heuristic algorithms have been proposed, empirical testing becomes possible only as quantum computation hardware is built. The next few years will be exciting as empirical testing of quantum heuristic algorithms becomes more and more feasible. While large-scale universal quantum computers are likely decades away, special-purpose quantum computational hardware has begun to emerge that will become more powerful over time, as well as some small-scale universal quantum computers.

quant-ph↗

arXiv2016

Computational Bottlenecks of Quantum Annealing

A promising approach to solving hard binary optimisation problems is quantum adiabatic annealing (QA) in a transverse magnetic field. An instantaneous ground state --- initially a symmetric superposition of all possible assignments of $N$ qubits --- is closely tracked as it becomes more and more localised near the global minimum of the classical energy. Regions where the energy gap to excited states is small (e.g. at the phase transition) are the algorithm's bottlenecks. Here I show how for large problems the complexity becomes dominated by $O(\log N)$ bottlenecks inside the spin glass phase, where the gap scales as a stretched exponential. For smaller $N$, only the gap at the critical point is relevant, where it scales polynomially, as long as the phase transition is second order. This phenomenon is demonstrated rigorously for the two-pattern Gaussian Hopfield Model. Qualitative comparison with the Sherrington-Kirkpatrick Model leads to similar conclusions.

quant-ph↗

arXiv2015

Quantum annealing via environment-mediated quantum diffusion

We show that quantum diffusion near the quantum critical point can provide a highly very efficient mechanism of open-system quantum annealing. It is based on the diffusion-mediated recombination of excitations. For an Ising spin chain coupled to a bosonic bath, excitation diffusion in a transverse field sharply slows down as the system moves away from the quantum critical region. This leads to spatial correlations and effective freezing of the excitation density. We find that obtaining an approximate solution via the diffusion-mediated quantum annealing can be faster than via closed-system quantum annealing or Glauber dynamics.

quant-ph↗

arXiv2014

Comparative Study of the Performance of Quantum Annealing and Simulated Annealing

Relations of simulated annealing and quantum annealing are studied by a mapping from the transition matrix of classical Markovian dynamics of the Ising model to a quantum Hamiltonian and vice versa. It is shown that these two operators, the transition matrix and the Hamiltonian, share the eigenvalue spectrum. Thus, if simulated annealing with slow temperature change does not encounter a difficulty caused by an exponentially long relaxation time at a first-order phase transition, the same is true for the corresponding process of quantum annealing in the adiabatic limit. One of the important differences between the classical-to-quantum mapping and the converse quantum-to-classical mapping is that the Markovian dynamics of a short-range Ising model is mapped to a short-range quantum system, but the converse mapping from a short-range quantum system to a classical one results in long-range interactions. This leads to a difference in efficiencies that simulated annealing can be efficiently simulated by quantum annealing but the converse is not necessarily true. We conclude that quantum annealing is easier to implement and is more flexible than simulated annealing. We also point out that the present mapping can be extended to accommodate explicit time dependence of temperature, which is used to justify the quantum-mechanical analysis of simulated annealing by Somma, Batista, and Ortiz. Additionally, an alternative method to solve the non-equilibrium dynamics of the one-dimensional Ising model is provided through the classical-to-quantum mapping.

quant-ph↗

arXiv2014

Quantum Optimization of Fully-Connected Spin Glasses

The Sherrington-Kirkpatrick model with random $\pm1$ couplings is programmed on the D-Wave Two annealer featuring 509 qubits interacting on a Chimera-type graph. The performance of the optimizer compares and correlates to simulated annealing. When considering the effect of the static noise, which degrades the performance of the annealer, one can estimate an improvement on the comparative scaling of the two methods in favor of the D-Wave machine. The optimal choice of parameters of the embedding on the Chimera graph is shown to be associated to the emergence of the spin-glass critical temperature of the embedded problem.

cond-mat.dis-nn↗

arXiv2010

Scaling laws for precision in quantum interferometry and bifurcation landscape of optimal state

Phase precision in optimal 2-channel quantum interferometry is studied in the limit of large photon number $N\gg 1$, for losses occurring in either one or both channels. For losses in one channel an optimal state undergoes an intriguing sequence of local bifurcations as the losses or the number of photons increase. We further show that fixing the loss paramater determines a scale for quantum metrology -- a crossover value of the photon number $N_c$ beyond which the supra-classical precision is progressively lost. For large losses the optimal state also has a different structure from those considered previously.

quant-ph↗

arXiv1998

Superconductivity in a two-dimensional Electron Gas

In a series of recent experiments, Kravchenko and colleagues observed unexpectedly that a two-dimensional electron gas in zero magnetic field can be a conductor. The two-dimensionality was imposed by confining the electron gas to move laterally at the interface between two semiconductors. The observation of a conductor in two dimensions (2D) is surprising as the conventional theory of metals precludes the presence of a metallic state at zero temperature in 2D. Nonetheless, there are now several experiments confirming the existence of the new conducting phase in a dilute two-dimensional electron gas in zero magnetic field. Here we argue based on an analysis of the experiments and general theoretical grounds that this phase is a zero-temperature superconductor with an inhomogeneous charge density.

cond-mat.str-el↗