Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers

Liu, Xiaoyuan; Angone, Anthony; Shaydulin, Ruslan; Safro, Ilya; Alexeev, Yuri; Cincio, Łukasz

doi:10.1109/tqe.2021.3140190

Cited by 55 publications

(40 citation statements)

References 64 publications

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“…Another procedure that has shown promising results is layer wise learning [33,30]. Layers in a quantum circuit are trained one at a time, keeping all other layers fixed.…”

Section: Comparison To Other Methodsmentioning

confidence: 99%

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Matrix Product State Pre-Training for Quantum Machine Learning

Dborin¹,

Barratt²,

Wimalaweera³

et al. 2021

Preprint

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Hybrid Quantum-Classical algorithms are a promising candidate for developing uses for NISQ devices. In particular, Parametrised Quantum Circuits (PQCs) paired with classical optimizers have been used as a basis for quantum chemistry and quantum optimization problems. Training PQCs relies on methods to overcome the fact that the gradients of PQCs vanish exponentially in the size of the circuits used. Tensor network methods are being increasingly used as a classical machine learning tool, as well as a tool for studying quantum systems. We introduce a circuit pretraining method based on matrix product state machine learning methods, and demonstrate that it accelerates training of PQCs for both supervised learning, energy minimization, and combinatorial optimization.

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“…Another procedure that has shown promising results is layer wise learning [33,30]. Layers in a quantum circuit are trained one at a time, keeping all other layers fixed.…”

Section: Comparison To Other Methodsmentioning

confidence: 99%

“…Instead of the standard QAOA scheme, we use a brick wall circuit made up of independent 2-qubit gates. These sorts of circuits have been explored for optimisation problems and their performance is competitive with QAOA [30].…”

Section: Combinatorial Optimizationmentioning

confidence: 99%

Matrix Product State Pre-Training for Quantum Machine Learning

Dborin¹,

Barratt²,

Wimalaweera³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…QAOA solves the combinatorial optimization problem of finding the bitstring corresponding to the lowest energy eigenstate of a Hamiltonian [17]. Performance of QAOA has been improved by exploiting symmetries of graph structures [18]- [21], by introducing classical neural networks or other classical methods to assist in parameter optimization [22], [23], by modifying the circuit ansatz [24]- [26], and by increasing circuit parameterization, at the expense of increased classical optimization [27]. Although increasing the number of independent parameters in QAOA circuits can improve performance in some instances, as the number of parameters increases, nonconvex optimization landscapes can hamper parameter optimization [28]- [32].…”

Section: Introductionmentioning

confidence: 99%

Augmenting QAOA Ansatz with Multiparameter Problem-Independent Layer

Chalupnik¹,

Melo²,

Alexeev³

et al. 2022

Preprint

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The quantum approximate optimization algorithm (QAOA) promises to solve classically intractable computational problems in the area of combinatorial optimization. A growing amount of evidence suggests that the originally proposed form of the QAOA ansatz is not optimal, however. To address this problem, we propose an alternative ansatz, which we call QAOA+, that augments the traditional p = 1 QAOA ansatz with an additional multiparameter problem-independent layer. The QAOA+ ansatz allows obtaining higher approximation ratios than p = 1 QAOA while keeping the circuit depth below that of p = 2 QAOA, as benchmarked on the MaxCut problem for random regular graphs. We additionally show that the proposed QAOA+ ansatz, while using a larger number of trainable classical parameters than with the standard QAOA, in most cases outperforms alternative multiangle QAOA ansätze.

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“…Examples of such hardware include adiabatic quantum computers [19], complementary metal-oxide-semiconductor (CMOS) annealers [1] and coherent Ising machines [17]. The gatebased universal quantum computers can also be used to solve such optimization problems [26]. These novel technologies are all unified by an ability to solve the Ising model or, equivalently, the quadratic unconstrained binary optimization (QUBO) problem.…”

Section: Introductionmentioning

confidence: 99%

Partitioning Dense Graphs with Hardware Accelerators

Liu,

Ushijima-Mwesigwa,

Ghosh

et al. 2022

Preprint

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Graph partitioning is a fundamental combinatorial optimization problem that attracts a lot of attention from theoreticians and practitioners due to its broad applications. From multilevel graph partitioning to more general-purpose optimization solvers such as Gurobi and CPLEX, a wide range of approaches have been developed. Limitations of these approaches are important to study in order to break the computational optimization barriers of this problem. As we approach the limits of Moore's law, there is now a need to explore ways of solving such problems with special-purpose hardware such as quantum computers or quantum-inspired accelerators. In this work, we experiment with solving the graph partitioning on the Fujitsu Digital Annealer (a special-purpose hardware designed for solving combinatorial optimization problems) and compare it with the existing top solvers. We demonstrate limitations of existing solvers on many dense graphs as well as those of the Digital Annealer on sparse graphs which opens an avenue to hybridize these approaches.

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Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers

Abstract: IEEE Transactions on Quantum EngineeringDate of publication xxxx 00, 0000, date of current version xxxx 00, 0000.

Cited by 55 publications

References 64 publications

Matrix Product State Pre-Training for Quantum Machine Learning

Matrix Product State Pre-Training for Quantum Machine Learning

Augmenting QAOA Ansatz with Multiparameter Problem-Independent Layer

Partitioning Dense Graphs with Hardware Accelerators

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