Adiabatic quantum optimization in the presence of discrete noise: Reducing the problem dimensionality

  title={Adiabatic quantum optimization in the presence of discrete noise: Reducing the problem dimensionality},
  author={Salvatore Mandr{\`a} and Gian Giacomo Guerreschi and Al{\'a}n Aspuru-Guzik},
  journal={Physical Review A},
Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the minimum energy gap encountered during the dynamics. Unfortunately, the direct calculation of the gap is strongly limited by the exponential growth in the dimensionality of the Hilbert space associated to the quantum system. Although many special-purpose… 

Figures and Tables from this paper

Threshold theorem in isolated quantum dynamics with stochastic control errors

We investigate the effect of stochastic control errors in the time-dependent Hamiltonian on isolated quantum dynamics. The control errors are formulated as time-dependent stochastic noise in the

Evaluation of Quantum Approximate Optimization Algorithm based on the approximation ratio of single samples

By selecting a suitable optimizer for the variational parameters and reducing the number of function evaluations, QAOA performance improves by up to 2 orders of magnitude compared to previous estimates and decreases the performance gap with classical alternatives.

Analog nature of quantum adiabatic unstructured search

It is found that the unstructured search algorithm’s quadratic speedup is generally not robust to the presence of any one of the above non-idealities, and in some cases it imposes unrealistic conditions on how the strength of these noise sources must scale to maintain the quadratics speedup.

Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

The proposed quantum algorithm is faster than the classical WalkSAT and Adiabatic Quantum Optimization for random instances with a density of constraints close to the satisfiability threshold, the regime in which instances are typically the hardest to solve.

Maximum-Entropy Inference with a Programmable Annealer

This work shows experimentally that finite temperature maximum entropy decoding can give slightly better bit-error-rates than the maximum likelihood approach, and introduces a bit-by-bit analytical method which is agnostic to the specific application and shows that the annealer samples from a highly Boltzmann-like distribution.

Strengths and weaknesses of weak-strong cluster problems: A detailed overview of state-of-the-art classical heuristics versus quantum approaches

To date, a conclusive detection of quantum speedup remains elusive. Recently, a team by Google Inc.~[V.~S.~Denchev {\em et al}., Phys.~Rev.~X {\bf 6}, 031015 (2016)] proposed a weak-strong cluster

Hard combinatorial problems and minor embeddings on lattice graphs

  • A. Lucas
  • Computer Science
    Quantum Inf. Process.
  • 2019
While this work focuses on embedding problems onto Chimera lattices, the techniques used generalize to any non-planar lattice graph, and may be more effective on future quantum annealing hardware.

Hard combinatorial problems and minor embeddings on lattice graphs

  • Andrew Lucas
  • Computer Science
    Quantum Information Processing
  • 2019
While this work focuses on embedding problems onto Chimera lattices, the techniques used generalize to any non-planar lattice graph, and may be more effective on future quantum annealing hardware.

Evaluation of QAOA based on the approximation ratio of individual samples

In particular for three-regular random graphs, QAOA performance shows improvement by up to two orders of magnitude compared to previous estimates, strongly reducing the performance gap with classical alternatives.

Adiabatic speedup in cutting a spin chain by pulse control in a laboratory frame

This paper adds an LEO Hamiltonian directly in a laboratory frame and finds that the required pulse conditions obtained in the adiabatic frame are no longer valid, and obtains the new pulse conditions in the laboratory frame.



The quantum adiabatic optimization algorithm and local minima

It is proved that for a constant range of values for the transverse field, the spectral gap is exponentially small in the sector length, and there are exponentially many eigenvalues all exponentially close to the ground state energy.

Decoherence in adiabatic quantum computation

Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is

Anderson localization makes adiabatic quantum optimization fail

It turns out that due to a phenomenon similar to Anderson localization, exponentially small gaps appear close to the end of the adiabatic algorithm for large random instances of NP-complete problems, which implies that unfortunately, adiABatic quantum optimization fails: the system gets trapped in one of the numerous local minima.

Quantum search by local adiabatic evolution

The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state, which

How powerful is adiabatic quantum computation?

It is argued that the adiabatic approach may be thought of as a kind of 'quantum local search', and a family of minimization problems that is hard for such local search heuristics are designed, and an exponential lower bound is established for the ad iabatic algorithm for these problems.

Thermally assisted quantum annealing of a 16-qubit problem.

It is experimentally demonstrated that, even with annealing times eight orders of magnitude longer than the predicted single-qubit decoherence time, the probabilities of performing a successful computation are similar to those expected for a fully coherent system.

Quantum annealing in the transverse Ising model

We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between

A variational eigenvalue solver on a photonic quantum processor

The proposed approach drastically reduces the coherence time requirements and combines this method with a new approach to state preparation based on ansätze and classical optimization, enhancing the potential of quantum resources available today and in the near future.

Optimization through quantum annealing: theory and some applications

The theory and the practical implementation of both classical and quantum annealing are illustrated – highlighting the crucial differences between these two methods – by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems.

Non-markovian decoherence in the adiabatic quantum search algorithm

We consider an adiabatic quantum algorithm (Grover's search routine) weakly coupled to a rather general environment, i.e., without using the Markov approximation. Markovian errors generally require