Quantum Autoencoders to Denoise Quantum Data

Bondarenko, Dmytro; Feldmann, Polina

doi:10.1103/physrevlett.124.130502

Cited by 99 publications

(66 citation statements)

References 45 publications

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“…Optimizing such protocols may involve automatization of the creation and analysis of QSMs, e.g., for finding an optimal basis automatically, in similarity with quantum annealing, but now at the level of measurement operators. Finally, one may envision using machine learning to find more optimal navigation protocols (see [36,37] for related work in the context of Hamiltonian feedback and open-loop control). Given the delayed-reward setting at hand, a reinforcement learning strategy such as Q-learning [38] or SARSA [39] might be the most appropriate choice.…”

Section: Discussionmentioning

confidence: 99%

Measurement-driven navigation in many-body Hilbert space: Active-decision steering

Herasymenko¹,

Gornyi²,

Gefen³

2021

Preprint

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The challenge of preparing a system in a designated state spans diverse facets of quantum mechanics. To complete this task of steering quantum states, one can employ quantum control through a sequence of generalized measurements which direct the system towards the target state. In an active version of this protocol, the obtained measurement readouts are used to adjust the protocol on-the-go, with a possibility for accelerated performance or fidelity increase. In this work, we consider such active measurement-driven steering as applied to the challenging case of many-body quantum systems. The target states of highest interest would be those with multipartite entanglement. Such state preparation in a measurement-based protocol is limited by the natural constraints for system-detector couplings. We develop a framework for finding such physically feasible couplings, based on parent Hamiltonian construction. For helpful decision-making strategies, we offer Hilbert-space-orientation techniques, comparable to those used in navigation. The first one is to tie the active-decision protocol to the fastest accumulation of the cost function, such as the target state fidelity. We show the potential of 9.5-fold speedup, employing this approach for generating the ground state of the Affleck-Lieb-Kennedy-Tasaki spin chain. The second wayfinding technique is to map out the available measurement actions onto a Quantum State Machine. A decision-making protocol can be based on such a representation, using semiclassical heuristics. This approach has advantages and limitations complementary to the cost function-based method. We give an example of a W-state preparation which is accelerated with this method by a factor of 12.5.

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Section: Discussionmentioning

confidence: 99%

Measurement-driven navigation in many-body Hilbert space: Active-decision steering

Herasymenko¹,

Gornyi²,

Gefen³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Consequently, traditional optimization methods including the Adam optimizer utilized in our numerical experiments are impacted. This trainability issue happens even when the ansatz is short depth [61] and the work [62] showed that the barren plateau phenomenon could also arise in the architecture of dissipative quantum neural networks [63][64][65].…”

Section: Barren Plateausmentioning

confidence: 99%

Variational Quantum Singular Value Decomposition

Wang

Song

Wang

2021

Quantum

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Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.

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“…First experiments show promising results for systems of small and increasing size [74,123,124]. Various strategies of error mitigation were proposed that can further improve the performance of algorithms when run on physical devices [125][126][127][128][129][130][131][132]. Finally, considering linear algebra problems, several VQAs were also proposed to solve LSEs [133][134][135][136][137][138], and ongoing efforts are directed towards improving their workflow.…”

Section: Introductionmentioning

confidence: 99%

Solving nonlinear differential equations with differentiable quantum circuits

2021

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We propose a quantum algorithm to solve systems of nonlinear differential equations. Using a quantum feature map encoding, we define functions as expectation values of parametrized quantum circuits. We use automatic differentiation to represent function derivatives in an analytical form as differentiable quantum circuits (DQCs), thus avoiding inaccurate finite difference procedures for calculating gradients. We describe a hybrid quantum-classical workflow where DQCs are trained to satisfy differential equations and specified boundary conditions. As a particular example setting, we show how this approach can implement a spectral method for solving differential equations in a high-dimensional feature space. From a technical perspective, we design a Chebyshev quantum feature map that offers a powerful basis set of fitting polynomials and possesses rich expressivity. We simulate the algorithm to solve an instance of Navier-Stokes equations and compute density, temperature, and velocity profiles for the fluid flow in a convergent-divergent nozzle.

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Quantum Autoencoders to Denoise Quantum Data

Cited by 99 publications

References 45 publications

Measurement-driven navigation in many-body Hilbert space: Active-decision steering

Measurement-driven navigation in many-body Hilbert space: Active-decision steering

Variational Quantum Singular Value Decomposition

Solving nonlinear differential equations with differentiable quantum circuits

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