Variational quantum Boltzmann machines

Zoufal, Christa; Lucchi, Aurélien; Woerner, Stefan

doi:10.1007/s42484-020-00033-7

Cited by 94 publications

(103 citation statements)

References 77 publications

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“…with the Boltzmann constant k B , system temperature T and partition function Z = Tr[e − Ĥω/(kBT ) ]. Depending on the construction of Ĥω and the choice of the loss function, QBMs can be used for various machine learning tasks, such as generative or discriminative learning [18]. Throughout the training, the Gibbs state ρ Gibbs ( Ĥω ) is repeatedly prepared and measured for different parameter values ω.…”

Section: Quantum Boltzmann Machinesmentioning

confidence: 99%

“…In the variational approach, the state of the 2n qubits is represented by a parameterized quantum circuit with parameters θ. For Var-QBMs, the initial parameter values θ (0) must be chosen such that each qubit pair is in a Bell state [18].…”

Section: Quantum Boltzmann Machinesmentioning

confidence: 99%

“…We choose to apply the suggested method to a generative learning example, investigated in Ref. [18], where the aim is to prepare a Gibbs state whose sampling probabilities correspond to a given target probability density function.…”

Section: Quantum Boltzmann Machinesmentioning

confidence: 99%

“…In this context, Variational Quantum Imaginary Time Evolution (VarQITE) techniques are particularly promising and received a lot of in-Stefan Woerner: wor@zurich.ibm.com terest recently [16][17][18]. These methods approximate Quantum Imaginary Time Evolution by mapping the quantum state evolution to the evolution of parameters in a parameterized quantum circuit, which serves as an ansatz for the evolved state.…”

Section: Introductionmentioning

confidence: 99%

“…These methods approximate Quantum Imaginary Time Evolution by mapping the quantum state evolution to the evolution of parameters in a parameterized quantum circuit, which serves as an ansatz for the evolved state. The interest in these approaches stems from the fact that imaginary time evolution is an integral part of many quantum algorithms and can, for instance, be used to find ground states of given Hamiltonians [16] or to prepare corresponding Gibbs states [17][18][19][20]. The former is important, e.g., for quantum chemistry or combinatorial optimization, while the latter finds applications, e.g., in the simulation of many-body systems [21], quantum semi-definite program solvers [22], as well as in evaluating and training Quantum Boltzmann Machines (QBMs) [23].…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

Gacon

Zoufal

Carleo

et al. 2021

Quantum

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The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with d parameters, however, is computationally expensive and generally requires O(d2) function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFIM at a constant cost. We present the resulting algorithm and successfully apply it to prepare Hamiltonian ground states and train Variational Quantum Boltzmann Machines.

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Section: Quantum Boltzmann Machinesmentioning

confidence: 99%

Section: Quantum Boltzmann Machinesmentioning

confidence: 99%

Section: Quantum Boltzmann Machinesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

Gacon

Zoufal

Carleo

et al. 2021

Quantum

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Perspectives of quantum computing for chemical engineering

et al. 2022

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Quantum computing has been attracting public attention recently. This interest is driven by the advancements in hardware, software, and algorithms required for its successful usage and the promise that it entails the potential acceleration of computational tasks compared to classical computing. This perspective article presents a short review on quantum computing, how this computational approach solves problems, and three fields that quantum computing can potentially impact the most while relevant to chemical engineering: computational chemistry, optimization, and machine learning. Here, we present a series of chemical engineering applications, the developments, potential improvements with respect to classical computing, and challenges that quantum computing faces for each of these fields. This article intends to provide a clear picture of the challenges and potential advantages that quantum technology may yield for chemical engineering, together with an invitation for our colleagues to join us in the adoption and development of quantum computing.

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Simulating noisy variational quantum eigensolver with local noise models

Zeng

Cao

et al. 2021

Quantum Engineering

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The variational quantum eigensolver (VQE) is a promising algorithm to demonstrate quantum advantage on near‐term noisy‐intermediate‐scale quantum (NISQ) computers. One central problem of VQE is the effect of noise, especially physical noise, on realistic quantum computers. We systematically study the effect of noise for the VQE algorithm by performing numerical simulations with various local noise models, including amplitude damping, dephasing, and depolarizing noise. We show that the ground state energy will deviate from the exact value as the noise probability increase, and typically, the noise will accumulate as the circuit depth increase. The results suggest that the noisy quantum system can remain entanglement at the noise level of NISQ devices by comparing the VQE solution with the mean‐field solution for the many‐body ground state problem. We build a noise model to capture the noise in a real quantum computer, and the corresponding numerical simulation is consistent with experimental results on IBM Quantum computers through cloud. Our work sheds new light on the practical research of noisy VQE, and the deep understanding of the noise effect of VQE will also help develop error mitigation techniques on near‐term quantum computers.

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Variational quantum Boltzmann machines

Cited by 94 publications

References 77 publications

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

Simultaneous Perturbation Stochastic Approximation of the Quantum Fisher Information

Perspectives of quantum computing for chemical engineering

Simulating noisy variational quantum eigensolver with local noise models

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