Abstract
The quantum alternating operator ansatz (QAOA) is a prominent example of variational quantum algorithms. We propose a generalized QAOA called CD-QAOA, which is inspired by the counterdiabatic 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 generators of 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 consider 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 and Lipkin-Meshkov-Glick models, and for the suitability 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.
Highlights
The ability to prepare a quantum many-body system in its ground state is an important milestone in the quest for understanding and identifying novel collective quantum phenomena
In stark contrast to conventional quantum alternating operator ansatz (QAOA), adding just the zero-order term H3 1⁄4 Y from the gauge potential series (Appendix E 3), we find that CD-QAOA already gives a significantly improved protocol; this is achieved by the high-level discrete optimization, which selects the order of the operators in the sequence
We find that CD-QAOA shows superior performance for all three ordered ground states: While the gain over conventional QAOA for the Haldane state is already a faster protocol, we clearly see how the gauge potential terms can prove essential for reaching the ground state in the FM and XY phases within the available durations
Summary
The ability to prepare a quantum many-body system in its ground state is an important milestone in the quest for understanding and identifying novel collective quantum phenomena. Quantum simulators—such as ultracold and Rydberg atoms [1,2], trapped ions [3,4,5,6], nitrogen vacancy centers [7,8,9], and superconducting qubits [6,10]—all require the development of state preparation schemes via real-time dynamical processes Despite their high level of controllability, finding short protocols to prepare strongly correlated ground states under platform-specific constraints is a challenging problem in AMO-based quantum simulation platforms because of the exponentially large Hilbert space dimensions of quantum many-body systems. On this background, speed-efficient protocols become progressively more important for near-term quantum computing devices [11], where simulation errors grow with the protocol duration due to imperfections in the implementation of the basic gate operations
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