Abstract We consider quantum chaos diagnostics of the variational circuit states at random parameters and explore their connection to the circuit expressibility and optimizability. By measuring the operator spreading coefficient and the eigenvalue spectrum of the modular Hamiltonian of the reduced density matrix, we identify the emergence of universal random matrix ensembles in high-depth circuit states. The diagnostics that use the eigenvalue spectrum, e.g. operator spreading and entanglement entropy, turn out to be more accurate measures of the variational quantum algorithm optimization efficiency than those that use the level spacing distribution of the entanglement spectrum, such as r -statistics or spectral form factors.
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Entanglement diagnostics for efficient VQA optimization
Abstract We consider information spreading measures in randomly initialized variational quantum circuits and introduce entanglement diagnostics for efficient variational quantum/classical computations. We establish a robust connection between entanglement measures and optimization accuracy by solving two eigensolver problems for Ising Hamiltonians with nearest-neighbor and long-range spin interactions. As the circuit depth affects the average entanglement of random circuit states, the entanglement diagnostics can identify a high-performing depth range for optimization tasks encoded in local Hamiltonians. We argue, based on an eigensolver problem for the Sachdev–Ye–Kitaev model, that entanglement alone is insufficient as a diagnostic to the approximation of volume-law entangled target states and that a large number of circuit parameters is needed for such an optimization task.
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- Award ID(s):
- 1911298
- NSF-PAR ID:
- 10345931
- Date Published:
- Journal Name:
- Journal of Statistical Mechanics: Theory and Experiment
- Volume:
- 2022
- Issue:
- 7
- ISSN:
- 1742-5468
- Page Range / eLocation ID:
- 073101
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schrödinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for near-term quantum devices. Here we demonstrate that when combined with the Rayleigh–Ritz variational principle for mixed quantum states, the ground-state contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two
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Abstract Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary
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Variational Quantum Algorithms (VQAs) rely upon the iterative optimization of a parameterized unitary circuit with respect to an objective function. Since quantum machines are noisy and expensive resources, it is imperative to choose a VQA's ansatz appropriately and its initial parameters to be close to optimal. This work tackles the problem of finding initial ansatz parameters by proposing CAFQA, a Clifford ansatz for quantum accuracy. The CAFQA ansatz is a hardware-efficient circuit built with only Clifford gates. In this ansatz, the initial parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation, thereby producing a suitable stabilizer state. The stabilizer states produced are shown to always equal or outperform traditional classical initialization (e.g., Hartree-Fock), and often produce high accuracy estimations prior to quantum exploration. Furthermore, the technique is classically suited since a) Clifford circuits can be exactly simulated classically in polynomial time and b) the discrete Clifford space, while scaling exponentially in the number of qubits, is searched efficiently via Bayesian Optimization. For the Variational Quantum Eigensolver (VQE) task of molecular ground state energy estimation up to 20 qubits, CAFQA's Clifford Ansatz achieves a mean accuracy of near 99%, recovering as much as 99.99% of the correlation energy over Hartree-Fock. Notably, the scalability of the approach allows for preliminary ground state energy estimation of the challenging Chromium dimer with an accuracy greater than Hartree-Fock. With CAFQA's initialization, VQA convergence is accelerated by a factor of 2.5x. In all, this work shows that stabilizer states are an accurate ansatz initialization for VQAs. Furthermore, it highlights the potential for quantum-inspired classical techniques to support VQAs.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1742-5468/ac7791
