Quantifying the efficiency of state preparation via quantum variational eigensolvers

Matos, Gabriel; Johri, Sonika; Papić, Zlatko

doi:10.48550/arxiv.2007.14338

Cited by 2 publications

(3 citation statements)

References 37 publications

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“…For the interacting system, J > 0, applying conventional QAOA using the two gates U j = e −iαj Hj with H 1 = Z|Z +Z and H 2 = X is straightforward, but it does not yield a high-fidelity protocol [Fig. 1 It was recently reported that much better energies can be obtained, using a three-step QAOA which consists of the three terms in the Hamiltonian (3), Z|Z, X, and Z, applied in a fixed order [87]; invoking again an Euler angles argument provides an explanation: the X and Z terms effectively generate the Y gauge potential term.…”

Section: A Nonintegrable Spin-1/2 Ising Chainmentioning

confidence: 99%

“…The better solutions are located in the lower left corner. The proliferation of local minima across the quantum speed limit has recently been studied in the context of RL [78] and QAOA [87]. This behavior indicates the importance of running many different SLSQP realizations, or else we may mis-evaluate the reward of a given sequence and the policy gradient will perform poorly.…”

Section: Appendix C: Many-body Control Landscapementioning

confidence: 99%

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Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving

Yao,

Lin,

Bukov

2020

Preprint

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The Quantum Approximate Optimization Ansatz (QAOA) is a prominent example of variational quantum algorithms. We propose a generalized QAOA ansatz called CD-QAOA, which is inspired by the counter-diabatic (CD) driving procedure, designed for quantum many-body systems, and optimized using a reinforcement learning (RL) approach. The resulting hybrid control algorithm proves versatile in preparing the ground state of quantum-chaotic many-body spin chains, by minimizing the energy. We show that using terms occurring in the adiabatic gauge potential as additional control unitaries, it is possible to achieve fast high-fidelity many-body control away from the adiabatic regime. While each unitary retains the conventional QAOA-intrinsic continuous control degree of freedom such as the time duration, we take into account the order of the multiple available unitaries appearing in the control sequence as an additional discrete optimization problem. Endowing the policy gradient algorithm with an autoregressive deep learning architecture to capture causality, we train the RL agent to construct optimal sequences of unitaries. The algorithm has no access to the quantum state, and we find that the protocol learned on small systems may generalize to larger systems. By scanning a range of protocol durations, we present numerical evidence for a finite quantum speed limit in the nonintegrable mixed-field spin-1/2 Ising model, and for the suitability of the ansatz to prepare ground states of the spin-1 Heisenberg chain in the long-range and topologically ordered parameter regimes. This work paves the way to incorporate recent success from deep learning for the purpose of quantum many-body control.

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Section: A Nonintegrable Spin-1/2 Ising Chainmentioning

confidence: 99%

Section: Appendix C: Many-body Control Landscapementioning

confidence: 99%

Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving

Yao,

Lin,

Bukov

2020

Preprint

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“…In Ref. (Matos et al, 2020), using QAOA it was shown that this region of parameter space appears most challenging in the noise-free system. We initialize the system in the z-polarized product state |ψ i = |↑ • • • ↑ , and aim to prepare the ground state of H. We use the negative energy density −E = −E/N as a reward for the RL agent, cf.…”

Section: Application: Quantum Ising Model In the Presence Of Noisementioning

confidence: 99%

Noise-Robust End-to-End Quantum Control using Deep Autoregressive Policy Networks

Yao¹,

Köttering²,

Gundlach³

et al. 2020

Preprint

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Variational quantum eigensolvers have recently received increased attention, as they enable the use of quantum computing devices to find solutions to complex problems, such as the ground energy and ground state of strongly-correlated quantum many-body systems. In many applications, it is the optimization of both continuous and discrete parameters that poses a formidable challenge. Using reinforcement learning (RL), we present a hybrid policy gradient algorithm capable of simultaneously optimizing continuous and discrete degrees of freedom in an uncertainty-resilient way. The hybrid policy is modeled by a deep autoregressive neural network to capture causality. We employ the algorithm to prepare the ground state of the nonintegrable quantum Ising model in a unitary process, parametrized by a generalized quantum approximate optimization ansatz: the RL agent solves the discrete combinatorial problem of constructing the optimal sequences of unitaries out of a predefined set and, at the same time, it optimizes the continuous durations for which these unitaries are applied. We demonstrate the noise-robust features of the agent by considering three sources of uncertainty: classical and quantum measurement noise, and errors in the control unitary durations. Our work exhibits the beneficial synergy between reinforcement learning and quantum control.

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Quantifying the efficiency of state preparation via quantum variational eigensolvers

Cited by 2 publications

References 37 publications

Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving

Reinforcement Learning for Many-Body Ground-State Preparation Inspired by Counterdiabatic Driving

Noise-Robust End-to-End Quantum Control using Deep Autoregressive Policy Networks

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