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arXiv:1912.02362

Quantum-Assisted Greedy Algorithms

Ramin Ayanzadeh, Milton Halem, John E. Dorband, Tim Finin

Published Dec 8, 2019• 10 citations
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Abstract

We show how to leverage quantum annealers to better select candidates in greedy algorithms. Unlike conventional greedy algorithms that employ problem-specific heuristics for making locally optimal choices at each stage, we use quantum annealers that sample from the ground state of Ising Hamiltonians at cryogenic temperatures and use retrieved samples to estimate the probability distribution of problem variables. More specifically, we look at each spin in the Ising model as a random variable and contract all problem variables whose corresponding uncertainties are negligible. Our empirical results on a D-Wave 2000Q quantum processor revealed that the proposed quantum-assisted greedy algorithm (QAGA) can find remarkably better solutions, compared to the state-of-the-art techniques in the realm of quantum annealing.

DOI
10.13016/m2n5ap-kape

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We show how to leverage quantum annealers to better select candidates in greedy algorithms. Unlike conventional greedy algorithms that employ problem-specific heuristics for making locally optimal choices at each stage, we use quantum annealers that sample from the ground state of Ising Hamiltonians at cryogenic temperatures and use retrieved samples to estimate the probability distribution of problem variables. More specifically, we look at each spin in the Ising model as a random variable and contract all problem variables whose corresponding uncertainties are negligible. Our empirical results on a D-Wave 2000Q quantum processor revealed that the proposed quantum-assisted greedy algorithm (QAGA) can find remarkably better solutions, compared to the state-of-the-art techniques in the realm of quantum annealing.
We show how to leverage quantum annealers (QAs) to better select candidates in greedy algorithms. Unlike conventional greedy algorithms that employ problem-specific heuristics for making locally optimal choices at each stage, we use QAs that sample from the ground state of problem-dependent Hamiltonians at cryogenic temperatures and use retrieved samples to estimate the probability distribution of problem variables. More specifically, we look at each spin of the Ising model as a random variable and contract all problem variables whose corresponding uncertainties are negligible. Our empirical results on a D-Wave 2000Q quantum processor demonstrate that the proposed quantum-assisted greedy algorithm (QAGA) scheme can find notably better solutions compared to the state-of-the-art techniques in the realm of quantum annealing
We show how to leverage quantum annealers (QAs) to better select candidates in greedy algorithms. Unlike conventional greedy algorithms that employ problem-specific heuristics for making locally optimal choices at each stage, we use QAs that sample from the ground state of a problem-dependent Hamiltonians at cryogenic temperatures and use retrieved samples to estimate the probability distribution of problem variables. More specifically, we look at each spin of the Ising model as a random variable and contract all problem variables whose corresponding uncertainties are negligible. Our empirical results on a D-Wave 2000Q quantum proces-sor demonstrate that the proposed quantum-assisted greedy algorithm (QAGA) scheme can find notably better solutions compared to the state-of-the-art techniques in the realm of quantum annealing.
We introduce the reinforcement quantum annealing (RQA) scheme in which an intelligent agent interacts with a quantum annealer that plays the stochastic environment role of learning automata and tries to iteratively find better Ising Hamiltonians for the given problem of interest. As a proof-of-concept, we propose a novel approach for reducing the NP-complete problem of Boolean satisfiability (SAT) to minimizing Ising Hamiltonians and show how to apply the RQA for increasing the probability of finding the global optimum. Our experimental results on two different benchmark SAT problems (namely factoring pseudo-prime numbers and random SAT with phase transitions), using a D-Wave 2000Q quantum processor, demonstrated that RQA finds notably better solutions with fewer samples, compared to state-of-the-art techniques in the realm of quantum annealing.
Genetic algorithms, which mimic evolutionary processes to solve optimization problems, can be enhanced by using powerful semi-local search algorithms as mutation operators. Here, we introduce reverse quantum annealing, a class of quantum evolutions that can be used for performing families of quasi-local or quasi-nonlocal search starting from a classical state, as novel sources of mutations. Reverse annealing enables the development of genetic algorithms that use quantum fluctuation for mutations and classical mechanisms for the crossovers -- we refer to these as Quantum-Assisted Genetic Algorithms (QAGAs). We describe a QAGA and present experimental results using a D-Wave 2000Q quantum annealing processor. On a set of spin-glass inputs, standard (forward) quantum annealing finds good solutions very quickly but struggles to find global optima. In contrast, our QAGA proves effective at finding global optima for these inputs. This successful interplay of non-local classical and quantum fluctuations could provide a promising step toward practical applications of Noisy Intermediate-Scale Quantum (NISQ) devices for heuristic discrete optimization.
Routing and scheduling problems with time windows have long been important optimization problems for logistics and planning. Many classical heuristics and exact methods exist for such problems. However, there are no satisfactory methods for generating routes using quantum computing (QC), for mainly two reasons: inequality constraints, and the trade-off of feasibility and solution quality. Inequality constraints are typically handled using slack variables; and feasible solutions are found by filtering samples. These challenges are amplified in the presence of noise inherent in QC. Here, we propose a greedy algorithm that generates routes by using information from all samples obtained from the quantum computer. By noticing the relationship between qubits in our formulation as a directed acyclic graph (DAG), we designed an algorithm that adaptively constructs a feasible solution. We prove its convergence to a feasible solution, and illustrate its efficacy by solving the Fleet Sizing Vehicle Routing Problem with Time Windows (FSVRPTW). Our computational results show that this method obtains a lower objective value than the current state-of-the-art annealing approaches, both classical and hybrid, for the same amount of time using D-Wave Hybrid Solvers. We also show its robustness to noise on D-Wave Advantage2 through computational results as compared to the filtering approach on DWaveSampler, even when the filtering approach is given a longer annealing time, and a larger sample size.
Quantum processing units (QPUs) executing annealing algorithms have shown promise in optimization and simulation applications. Hybrid algorithms are a natural bridge to larger applications. We present a simple greedy method for solving larger-than-QPU lattice-structured Ising optimization problems. The method, implemented in the open source D-Wave Hybrid framework, uses a QPU coprocessor operating with generic parameters. Performance is evaluated for standard spin-glass problems on two lattice types with up to 11,616 spin variables, double the size that is directly programmable on any available QPU. The proposed method is shown to converge to low-energy solutions faster than an open source simulated annealing method that is either directly employed or substituted as a coprocessor in the hybrid method. Using newer Advantage QPUs in place of D-Wave 2000Q QPUs is shown to enhance convergence of the hybrid method to low energies and to achieve a lower final energy.