A Hybrid Approach for Solving Optimization Problems on Small Quantum Computers

Shaydulin, Ruslan; Ushijima‐Mwesigwa, Hayato; Negre, Christian F. A.; Safro, Ilya; Mniszewski, Susan M.; Alexeev, Yuri

doi:10.1109/mc.2019.2908942

Cited by 55 publications

(40 citation statements)

References 13 publications

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“…First of all, we look at current noisy quantum computers and quantum optimization algorithms, in particular VQE and QAOA. We do not touch upon quantum annealing, but the interested reader can find studies in the works of [51]- [54] and references therein. VQE and QAOA are currently under major scrutiny and discussions on their performance, e.g., [9], [18], [55]- [58], especially for the solution of unconstrained binary optimization problems, of which MaxCut is one important embodiment.…”

Section: Quantum Computing For Qubosmentioning

confidence: 99%

Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers

Gambella

Simonetto

2020

IEEE Trans. Quantum Eng.

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Solving combinatorial optimization problems on current noisy quantum devices is currently being advocated for (and restricted to) binary polynomial optimization with equality constraints via quantum heuristic approaches. This is achieved using, for example, the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). In this article, we present a decomposition-based approach to extend the applicability of current approaches to "quadratic plus convex" mixed binary optimization (MBO) problems, so as to solve a broad class of real-world optimization problems. In the MBO framework, we show that the alternating direction method of multipliers (ADMM) can split the MBO into a binary unconstrained problem (that can be solved with quantum algorithms), and continuous constrained convex subproblems (that can be solved cheaply with classical optimization solvers). The validity of the approach is then showcased by numerical results obtained on several optimization problems via simulations with VQE and QAOA on the quantum circuits implemented in Qiskit, an open-source quantum computing software development framework.

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Section: Quantum Computing For Qubosmentioning

confidence: 99%

Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers

Gambella

Simonetto

2020

IEEE Trans. Quantum Eng.

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“…Graph problems are of particular interest to the study and near-term applications of QAOA and have been studied extensively in recent years. Problems considered include MaxCut [15], [35], [36], Maximum-k-Cut [17], Maximum Independent Set [37], [38], Community Detection [5], [39], [40], Graph Vertex k-Coloring [41], Maximum k-Colorable Subgraph [42], Graph Partitioning [8], and many more [43]- [45]. The combination of hardness and sparsity make graph problems especially appealing as an early application of QAOA, as evidenced by the fact that a number of recent experimental demonstrations apply QAOA to graph problems [4], [46].…”

Section: Accelerating Qaoa Training By Using Fast Graph Automorphism Solversmentioning

confidence: 99%

Exploiting Symmetry Reduces the Cost of Training QAOA

Shaydulin

Wild

2021

IEEE Trans. Quantum Eng.

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A promising approach to the practical application of the Quantum Approximate Optimization Algorithm (QAOA) is finding QAOA parameters classically in simulation and sampling the solutions from QAOA with optimized parameters on a quantum computer. Doing so requires repeated evaluations of QAOA energy in simulation. We propose a novel approach for accelerating the evaluation of QAOA energy by leveraging the symmetry of the problem. We show a connection between classical symmetries of the objective function and the symmetries of the terms of the cost Hamiltonian with respect to the QAOA energy. We show how by considering only the terms that are not connected by symmetry, we can significantly reduce the cost of evaluating the QAOA energy. Our approach is general and applies to any known subgroup of symmetries and is not limited to graph problems. Our results are directly applicable to nonlocal QAOA generalization RQAOA. We outline how available fast graph automorphism solvers can be leveraged for computing the symmetries of the problem in practice. We implement the proposed approach on the MaxCut problem using a state-of-the-art tensor network simulator and a graph automorphism solver on a benchmark of 48 graphs with up to 10,000 nodes. Our approach provides an improvement for p = 1 on 71.7% of the graphs considered, with a median speedup of 4.06, on a benchmark where 62.5% of the graphs are known to be hard for automorphism solvers.

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“…This can be achieved by using either of the two available forms of quantum computation: gate-based quantum computing and adiabatic quantum computing. Current quantum computers are hardware-limited in both the number and quality of qubits, qubit connectivity, presence of high noise levels, and the need for full error-correction 13 . Noisy gate-based quantum computers are currently available at the scale of ~50 to 70 qubits Adiabatic quantum computers are available in the form of quantum annealers, such as the D-Wave 2000Q (with ~2048 qubits) and the new D-Wave Advantage machine (with ~5000 qubits).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the largest fully connected graph that can be embedded is 65. A hybrid quantum-classical approach is required to address larger numbers of variables as nodes (here representing SDs) 13 . We use the D-Wave developed qbsolv classical solver 29 to orchestrate the QUBO solution process between the central processing unit (CPU) and QPU.…”

Section: Introductionmentioning

confidence: 99%

Reduction of the molecular hamiltonian matrix using quantum community detection

Mniszewski

Dub

Tretiak

et al. 2021

Sci Rep

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Quantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

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A Hybrid Approach for Solving Optimization Problems on Small Quantum Computers

Cited by 55 publications

References 13 publications

Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers

Multiblock ADMM Heuristics for Mixed-Binary Optimization on Classical and Quantum Computers

Exploiting Symmetry Reduces the Cost of Training QAOA

Reduction of the molecular hamiltonian matrix using quantum community detection

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