Efficient Quantum Circuits based on the Quantum Natural Gradient

TL;DR

This paper introduces symmetry-conserving quantum circuits optimized with the quantum natural gradient, enabling efficient state preparation with depth depending on entanglement rather than system size, beneficial for near-term quantum applications.

Contribution

The paper proposes SCom-QAOA circuits that preserve symmetries and optimize their parameters using the quantum natural gradient, reducing circuit depth dependence on system size for certain states.

Findings

Circuit depth depends on entanglement, not system size.

High fidelity states (>99%) achieved with sub-system-size depth.

Enables broader initial state preparation for variational algorithms.

Abstract

Efficient preparation of arbitrary entangled quantum states is crucial for quantum computation. This is particularly important for noisy intermediate scale quantum simulators relying on variational hybrid quantum-classical algorithms. To that end, we propose symmetry-conserving modified quantum approximate optimization algorithm~(SCom-QAOA) circuits. The depths of these circuits depend not only on the desired fidelity to the target state, but also on the amount of entanglement the state contains. The parameters of the SCom-QAOA circuits are optimized using the quantum natural gradient method based on the Fubini-Study metric. The SCom-QAOA circuit transforms an unentangled state into a ground state of a gapped one-dimensional Hamiltonian with a circuit-depth that depends not on the system-size, but rather on the finite correlation length. In contrast, the circuit depth grows proportionally to the system size for preparing low-lying states of critical one-dimensional systems. Even in the latter case, SCom-QAOA circuits with depth less than the system-size were sufficient to generate states with fidelity in excess of 99\%, which is relevant for near-term applications. The proposed scheme enlarges the set of the initial states accessible for variational quantum algorithms and widens the scope of investigation of non-equilibrium phenomena in quantum simulators.