A hybrid algorithm framework for small quantum computers with application to finding Hamiltonian cycles

Ge, Yimin; Dunjko, Vedran

doi:10.1063/1.5119235

Cited by 9 publications

(24 citation statements)

References 26 publications

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“…The former is to decompose a large problem into smaller subproblems, each of which is solved by a small quantum computer. Examples include quantizing classical divideand-conquer algorithms to solve combinatorial optimization problems [13,14], and Fujii et al's deep variational quantum eigensolver framework [15], which is suitable for simulating physical systems when interactions between subsystems are weak. Partially quantizing a tensor network may also fall into this category [16,17].…”

mentioning

confidence: 99%

Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits

Chen¹,

Cheng²,

Zhao³

et al. 2022

Preprint

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Although near-term quantum computing devices are still limited by the quantity and quality of qubits in the so-called NISQ era, quantum computational advantage has been experimentally demonstrated. Moreover, hybrid architectures of quantum and classical computing have become the main paradigm for exhibiting NISQ applications, where low-depth quantum circuits are repeatedly applied. In order to further scale up the problem size solvable by the NISQ devices, it is also possible to reduce the number of physical qubits by "cutting" the quantum circuit into different pieces. In this work, we experimentally demonstrated a circuit-cutting method for simulating quantum circuits involving many logical qubits, using only a few physical superconducting qubits. By exploiting the symmetry of linear-cluster states, we can estimate the effectiveness of circuit-cutting for simulating up to 33-qubit linear-cluster states, using at most 4 physical qubits for each subcircuit. Specifically, for the 12-qubit linear-cluster state, we found that the experimental fidelity bound can reach as much as 0.734, which is about 19% higher than a direct simulation on the same 12-qubit superconducting processor. Our results indicate that circuit-cutting represents a feasible approach of simulating quantum circuits using much fewer qubits, while achieving a much higher circuit fidelity.

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mentioning

confidence: 99%

Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits

Chen¹,

Cheng²,

Zhao³

et al. 2022

Preprint

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show abstract

“…We would then study if performances of both GW and QAOA are improved on the sparser instance. Third, an obvious limitation to this type of study is the size of the graph we can handle; to this end it would be interesting if divide-and-conquer type methods explored in [11] can be utilized to increase the size of datasets we can consider. Additionally, in our work, we did not tackle the important question of how the choice of QAOA optimization procedures influences the advantage gained.…”

Section: Discussionmentioning

confidence: 99%

To quantum or not to quantum: towards algorithm selection in near-term quantum optimization

Moussa,

Calandra,

Dunjko

2020

Preprint

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The Quantum Approximate Optimization Algorithm (QAOA) constitutes one of the often mentioned candidates expected to yield a quantum boost in the era of near-term quantum computing. In practice, quantum optimization will have to compete with cheaper classical heuristic methods, which have the advantage of decades of empirical domain-specific enhancements. Consequently, to achieve optimal performance we will face the issue of algorithm selection, well-studied in practical computing. Here we introduce this problem to the quantum optimization domain.Specifically, we study the problem of detecting those problem instances of where QAOA is most likely to yield an advantage over a conventional algorithm. As our case study, we compare QAOA against the well-understood approximation algorithm of Goemans and Williamson (GW) on the Max-Cut problem. As exactly predicting the performance of algorithms can be intractable, we utilize machine learning to identify when to resort to the quantum algorithm. We achieve cross-validated accuracy well over 96%, which would yield a substantial practical advantage. In the process, we highlight a number of features of instances rendering them better suited for QAOA. While we work with simulated idealised algorithms, the flexibility of ML methods we employed provides confidence that our methods will be equally applicable to broader classes of classical heuristics, and to QAOA running on real-world noisy devices.

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“…Solving large problems on small NISQ hardware: Dunjko et al [8] proposed a hybrid algorithm for solving 3SAT problems on quantum computers with limited number of qubits. Ge & Dunjko [9] proposed another hybrid algorithm to enhance Eppstein's algorithm for finding cubic Hamiltonian circle in degree-3 graphs. However, these hybrid algorithms do not apply to the MaxCut problem addressed in this paper.…”

Section: Related Work and Motivationmentioning

confidence: 99%

Large-scale Quantum Approximate Optimization via Divide-and-Conquer

Li¹,

Alam²,

Ghosh³

2021

Preprint

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Quantum Approximate Optimization Algorithm (QAOA) is a promising hybrid quantum-classical algorithm for solving combinatorial optimization problems. However, it cannot overcome qubit limitation for large-scale problems. Furthermore, the execution time of QAOA scales exponentially with the problem size. We propose a Divide-and-Conquer QAOA (DC-QAOA) to address the above challenges for graph maximum cut (Max-Cut) problem. The algorithm works by recursively partitioning a larger graph into smaller ones whose MaxCut solutions are obtained with small-size NISQ computers. The overall solution is retrieved from the sub-solutions by applying the combination policy of quantum state reconstruction. Multiple partitioning and reconstruction methods are proposed/ compared. DC-QAOA achieves 97.14% approximation ratio (20.32% higher than classical counterpart), and 94.79% expectation value (15.80% higher than quantum annealing). DC-QAOA also reduces the time complexity of conventional QAOA from exponential to quadratic.

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A hybrid algorithm framework for small quantum computers with application to finding Hamiltonian cycles

Cited by 9 publications

References 26 publications

Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits

Experimental Simulation of Larger Quantum Circuits with Fewer Superconducting Qubits

To quantum or not to quantum: towards algorithm selection in near-term quantum optimization

Large-scale Quantum Approximate Optimization via Divide-and-Conquer

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