Hybrid annealing: Coupling a quantum simulator to a classical computer

Abstract

Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Annealing strategies, either classical or quantum, explore the configuration space by evolving the system under the influence of thermal or quantum fluctuations. The thermal annealing dynamics can rapidly freeze the system into a low-energy configuration, and it can well be simulated on a classical computer, but it easily gets stuck in local minima. Quantum annealing, on the other hand, can be guaranteed to find the true ground state, and can be implemented in modern quantum simulators, however quantum-adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasi-degenerate ground states.

A hybrid quantum-classical paradigm to mitigate embedding costs in quantum annealing

“…Indeed, cycle graphs permit small embeddings and C 580 can be embedded in the Chimera graph χ 10 with 800 physical qubits 19 while, as mentioned earlier in Section 1.3, K 38 can also be embedded in χ 10 and S 5618 would require a much larger χ 31 graph. 20 However, we emphasise that our algorithm is necessarily general and must thus be applicable to arbitrary problems. Indeed, it is important to note that, if one were to tailor the algorithm for specific graph families, then much more efficient classical algorithms can easily be found.…”

“…We formulate a hybrid approach that can mitigate this cost on problems where many related embeddings must be performed by modifying the problem pipeline to reuse or modify embeddings already performed, thereby allowing any potential advantage to be accessed more directly [14]. A similar type of approach has previously been suggested as a theoretical means to exploiting Grover's algorithm [15], and differs from recent hybrid approaches for quantum annealing [16][17][18][19][20] and computing [21,22] that instead aim to provide quantum advantages in situations where far fewer qubits are available than would be needed to execute a complete quantum algorithm for the problem in question [23][24][25]. Research thus far has focused on using quantum annealing to solve problems for which only a single embedding is required.…”

Predicting quantum advantage by quantum walk with convolutional neural networks

“…Recently speedup problem extensively has been discussed in the framework of quantum computation purposed to accelerate the solution of familiar optimization problems by using quantum hardware [71,72]. However, predicting a quantum speedup in this hardware represents a complex problem that depends on many physical parameters including size and topology of the system [73][74][75][76]. In this paper we proposed a new machine learning method to predict a speedup of quantum transport.…”

Finding spin glass ground states using quantum walks

“…With no prior knowledge of the solution, the equal superposition of all basis states choice that avoids bias. More generally, the initial state can be prepared as weighted or biased superposition, to incorporate prior knowledge about the solution (Perdomo-Ortiz et al 2011,Duan et al 2013, Chancellor 2017, Graß and Lewenstein 2017, Baldwin and Laumann 2018, Kechedzhi et al 2018, Graß 2019.…”