Measurement-Based Variational Quantum Eigensolver

Ferguson, R. S.; Dellantonio, Luca; Balushi, Abdulrahim Al; Jansen, Karl; Dür, W.; Muschik, Christine A.

doi:10.1103/physrevlett.126.220501

Cited by 51 publications

(36 citation statements)

References 57 publications

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“…Alternating minimization has also proven useful in QAOA protocols [15,[58][59][60], as has other perturbations, such as filtered measurements [61]. Because L MBE is calculated from singlequbit measurements, it is a form of measurement-based quantum computation [62][63][64]. Moreover, as the number of possible single-qubit measurements scales linearly with circuit width, L MBE represents up to a quadratic reduction in the number of observables required to solve complete graphs from ∼ n 2 (specifically n(n − 1)/2 twooperator Pauli strings) to ∼ 2n (two single-qubit measurements per qubit), lowering the measurement complexity and runtime of the algorithm on real quantum hardware [65,66].…”

Section: Resultsmentioning

confidence: 99%

Variational Quantum Optimization with Multi-Basis Encodings

Kossaifi²,

Anandkumar

et al. 2021

Preprint

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Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization landscapes. We tackle these challenges by introducing a new variational quantum algorithm that utilizes multi-basis graph encodings and nonlinear activation functions. Our technique results in increased optimization performance, a factor of two increase in effective quantum resources, and a quadratic reduction in measurement complexity. While the classical simulation of many qubits with traditional quantum formalism is impossible due to its exponential scaling, we mitigate this limitation with exact circuit representations using factorized tensor rings. In particular, the shallow circuits permitted by our technique, combined with efficient factorized tensor-based simulation, enable us to successfully optimize the MaxCut of the nonlocal 512-vertex DIMACS library graphs on a single GPU. By improving the performance of quantum optimization algorithms while requiring fewer quantum resources and utilizing shallower, more error-resistant circuits, we offer tangible progress for variational quantum optimization.

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Section: Resultsmentioning

confidence: 99%

Variational Quantum Optimization with Multi-Basis Encodings

Kossaifi²,

Anandkumar

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…Specific structures of quantum algorithms can be identified for quantum optimization which is a key aspect in the development of new algorithms [412]. A novel class of variational quantum eigensolvers is obtained by combining optimization and measurement processes, leading to advantages in terms of resources and times [221]. Insight from QOCT on overcoming barren plateaus may help overcome convergence problems in quantum machine learning [94,288] or in variational quantum algorithms [358].…”

Section: Quantum Algorithmsmentioning

confidence: 99%

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Koch,

Boscain,

Calarco

et al. 2022

Preprint

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Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments.

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“…As L p is calculated from single-qubit measurements, it can be considered a form of measurement-based quantum computation (MBQC) [43][44][45]. Moreover, as the subpartitions (maximum value per qubit is 1) vs fraction of calculated MaxCut convergence for nonlinear loss functions.…”

Section: Parallel Vqa (Np-vqa)mentioning

confidence: 99%

Nonlinear Quantum Optimization Algorithms via Efficient Ising Model Encodings

Kossaifi²,

Anandkumar

et al. 2021

Preprint

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Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization landscapes. We tackle these challenges to quantum advantage with two new variational quantum algorithms, which utilize multi-basis graph encodings and nonlinear activation functions to outperform existing methods with remarkably shallow quantum circuits. Both algorithms provide a polynomial reduction in measurement complexity and either a factor of two speedup a factor of two reduction in quantum resources. Typically, the classical simulation of such algorithms with many qubits is impossible due to the exponential scaling of traditional quantum formalism and the limitations of tensor networks. Nonetheless, the shallow circuits and moderate entanglement of our algorithms, combined with efficient tensor method-based simulation, enable us to successfully optimize the MaxCut of high-connectivity global graphs with up to 512 nodes (qubits) on a single GPU.

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Measurement-Based Variational Quantum Eigensolver

Cited by 51 publications

References 57 publications

Variational Quantum Optimization with Multi-Basis Encodings

Variational Quantum Optimization with Multi-Basis Encodings

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Nonlinear Quantum Optimization Algorithms via Efficient Ising Model Encodings

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