Quantum Sampling Algorithms for Near-Term Devices

Wild, Dominik S.; Sels, Dries; Pichler, Hannes; Zanoci, Cristian; Lukin, Mikhail D.

doi:10.1103/physrevlett.127.100504

Cited by 14 publications

(9 citation statements)

References 45 publications

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“…Among many quantum sampling algorithms, we adopt the algorithm developed in Refs. [13,14]. We define the parent Hamiltonian…”

Section: Algorithmsmentioning

confidence: 99%

“…The minimum action state is 2 15 -fold degenerate before gauge fixing but non-degenerate after gauge fixing. We adopted the quantum adiabatic calculation to obtain the ground state of the parent Hamiltonian (13). The evolution operator in Eq.…”

Section: Benchmark Testmentioning

confidence: 99%

“…Since the path integral of lattice gauge theory is multiple integral over classical numbers, it can be regarded as the partition function of a classical statistical system. There are many proposals for quantum sampling of classical statistical systems [7][8][9][10][11][12][13][14]. In classical Monte Carlo sampling, configurations are generated by a Markov chain with classical random numbers.…”

Section: Introductionmentioning

confidence: 99%

“…In quantum sampling, configurations are generated by quantum fluctuation. Quantum sampling algorithms can achieve quadratic speedup over classical Markov-chain algorithms [9,10] or further speedup [11][12][13][14] although the degree of speedup is sensitive to the algorithm and system. In any case, quantum sampling would be a promising approach to large-scale statistics.…”

Section: Introductionmentioning

confidence: 99%

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Quantum sampling for the Euclidean path integral of lattice gauge theory

Yamamoto

2022

Preprint

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Although the Hamiltonian formalism is so far favored for quantum computation of lattice gauge theory, the path integral formalism would never be useless. The advantages of the path integral formalism are the knowledge and experience accumulated by classical lattice simulation and manifest Lorentz invariance. We discuss quantum computation of lattice gauge theory in the path integral formalism. We utilize a quantum sampling algorithm to generate gauge configurations, and demonstrate a benchmark test of Z2 lattice gauge theory on a four-dimensional hypercube.

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“…Among many quantum sampling algorithms, we adopt the algorithm developed in Refs. [13,14]. We define the parent Hamiltonian…”

Section: Algorithmsmentioning

confidence: 99%

Section: Benchmark Testmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Quantum sampling for the Euclidean path integral of lattice gauge theory

Yamamoto

2022

Preprint

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“…In our recent work, reference [12], we introduced a family of quantum algorithms that provide unbiased samples by preparing a state that encodes the entire Gibbs distribution. We showed that this approach leads to a speedup over a classical Markov chain algorithm for several examples.…”

Section: Introductionmentioning

confidence: 99%

Quantum Sampling Algorithms, Phase Transitions, and Computational Complexity

Wild,

Sels,

Pichler

et al. 2021

Preprint

Self Cite

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Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum computer by preparing a quantum state that encodes the entire probability distribution followed by a projective measurement. We investigate the complexity of adiabatically preparing such quantum states for the Gibbs distributions of various classical models including the Ising chain, hard-sphere models on different graphs, and a model encoding the unstructured search problem. By constructing a parent Hamiltonian, whose ground state is the desired quantum state, we relate the asymptotic scaling of the state preparation time to the nature of transitions between distinct quantum phases. These insights enable us to identify adiabatic paths that achieve a quantum speedup over classical Markov chain algorithms. In addition, we show that parent Hamiltonians for the problem of sampling from independent sets on certain graphs can be naturally realized with neutral atoms interacting via highly excited Rydberg states.

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Quantum science with optical tweezer arrays of ultracold atoms and molecules

Kaufman

2021

Nat. Phys.

200

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Quantum Sampling Algorithms for Near-Term Devices

Cited by 14 publications

References 45 publications

Quantum sampling for the Euclidean path integral of lattice gauge theory

Quantum sampling for the Euclidean path integral of lattice gauge theory

Quantum Sampling Algorithms, Phase Transitions, and Computational Complexity

Quantum science with optical tweezer arrays of ultracold atoms and molecules

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