Matrix Product State Pre-Training for Quantum Machine Learning

Dborin, James; Barratt, Fergus; Wimalaweera, Vinul; Wright, Lewis; Green, Andrew G.

doi:10.48550/arxiv.2106.05742

Cited by 5 publications

(8 citation statements)

References 26 publications

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“…The severity of the barren plateau problem depends on the cost function [29] and the PQC architecture [28,30,31]. A plethora of proposals exist to avoid barren plateaus in certain cases [29,[31][32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Barren plateaus in quantum tensor network optimization

Martín

Plekhanov²,

Lubasch³

2023

Quantum

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We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider as the cost function the expectation value of a Hamiltonian that is a sum of local terms. For randomly chosen variational parameters we show that the variance of the cost function gradient decreases exponentially with the distance of a Hamiltonian term from the canonical centre in the quantum tensor network. Therefore, as a function of qubit count, for qMPS most gradient variances decrease exponentially and for qTTN as well as qMERA they decrease polynomially. We also show that the calculation of these gradients is exponentially more efficient on a classical computer than on a quantum computer.

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Section: Introductionmentioning

confidence: 99%

Barren plateaus in quantum tensor network optimization

Martín

Plekhanov²,

Lubasch³

2023

Quantum

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“…Nevertheless, there already exist efficient encoding strategies that map MPS into quantum circuits [61][62][63]. Moreover, several proposals were recently developed in which MPS are harnessed for quantum machine learning tasks, for example as part of hybrid classical-quantum algorithms [64,65] or as classical pre-training methods [66,67]. Similar ideas can be applied to the QMPS architecture by mapping the trainable MPS to a parametrized quantum circuit, thus directly integrating the QMPS framework in quantum computations with NISQ devices.…”

Section: Discussion/outlookmentioning

confidence: 99%

Self-Correcting Quantum Many-Body Control using Reinforcement Learning with Tensor Networks

Metz¹,

Bukov²

2022

Preprint

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Quantum many-body control is a central milestone en route to harnessing quantum technologies. However, the exponential growth of the Hilbert space dimension with the number of qubits makes it challenging to classically simulate quantum many-body systems and consequently, to devise reliable and robust optimal control protocols. Here, we present a novel framework for efficiently controlling quantum many-body systems based on reinforcement learning (RL). We tackle the quantum control problem by leveraging matrix product states (i) for representing the many-body state and, (ii) as part of the trainable machine learning architecture for our RL agent. The framework is applied to prepare ground states of the quantum Ising chain, including critical states. It allows us to control systems far larger than neural-network-only architectures permit, while retaining the advantages of deep learning algorithms, such as generalizability and trainable robustness to noise. In particular, we demonstrate that RL agents are capable of finding universal controls, of learning how to optimally steer previously unseen many-body states, and of adapting control protocols on-the-fly when the quantum dynamics is subject to stochastic perturbations.

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“…The VQE algorithm requires a parameterised ansatz circuit U (θ) to construct the trial wave function |ψ(θ) , combined with a classical optimisation that minimizes the expectation value ψ(θ)| H |ψ(θ) for some opera-tor H (which is decomposed into a weighted sum of Pauli strings). Selecting the structure and initial parameters for this ansatz circuit is an active area of VQE research [19,[24][25][26]. For typical ansatz circuits, there is a finite set of parameter points that implement a Clifford circuit, with the resulting states being the so-called stabilizer states, Fig.…”

Section: Clifford Pre-optimisationmentioning

confidence: 99%

Clifford Circuit Initialisation for Variational Quantum Algorithms

Cheng¹,

Khosla²,

Self³

et al. 2022

Preprint

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We present an initialisation method for variational quantum algorithms applicable to intermediate scale quantum computers. The method uses simulated annealing of the efficiently simulable Clifford parameter points as a pre-optimisation to find a low energy initial condition. We numerically demonstrate the effectiveness of the technique, and how it depends on Hamiltonian structure, number of qubits and circuit depth. While a range of different problems are considered, we note that the method is particularly useful for quantum chemistry problems. This presented method could help achieve a quantum advantage in noisy or fault-tolerant intermediate scale devices, even though we prove in general that the method is not arbitrarily scalable.

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Matrix Product State Pre-Training for Quantum Machine Learning

Cited by 5 publications

References 26 publications

Barren plateaus in quantum tensor network optimization

Barren plateaus in quantum tensor network optimization

Self-Correcting Quantum Many-Body Control using Reinforcement Learning with Tensor Networks

Clifford Circuit Initialisation for Variational Quantum Algorithms

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