Triangularized Orthogonalization-free Method for Solving Extreme Eigenvalue Problems

Gao, Weiguo; Li, Yingzhou; Lu, Bichen

doi:10.48550/arxiv.2005.12161

Cited by 2 publications

(1 citation statement)

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“…The objective function in SSVQE is convex, while with the consideration of the orthogonality constraint and the parametrization of the ansatz circuits, the energy landscape of SSVQE becomes non-convex. On the other hand, the objective function of qOMM, by itself, is non-convex but has no spurious local minima. ,, When the parametrization of the ansatz circuits is taken into consideration, the energy landscape of qOMM is non-convex and could have spurious local minima. For non-convex energy landscapes, usual optimizers, including L-BFGS-B, are efficient in a neighborhood of local minima whereas, around strict saddle points, without second-order information, the optimizers could stall there for a long time.…”

Section: Numerical Resultsmentioning

confidence: 99%

Quantum Orbital Minimization Method for Excited States Calculation on a Quantum Computer

Bierman

2022

J. Chem. Theory Comput.

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We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parametrized ansatz circuits representing eigenstates, qOMM implements quantum circuits to represent the objective function in the orbital minimization method and adopts a classical optimizer to minimize the objective function with respect to the parameters in ansatz circuits. The objective function has an orthogonality constraint implicitly embedded, which allows qOMM to apply a different ansatz circuit to each input reference state. We carry out numerical simulations that seek to find excited states of H2, LiH, and a toy model consisting of four hydrogen atoms arranged in a square lattice in the STO-3G basis with UCCSD ansatz circuits. Comparing the numerical results with existing excited states methods, qOMM is less prone to getting stuck in local minima and can achieve convergence with more shallow ansatz circuits.

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Section: Numerical Resultsmentioning

confidence: 99%