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Feedback-Based Quantum Algorithm for Excited States Calculation
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DOI：10.1109/TQE.2026.3654528.png)
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Abstract
En 中文
Recently, feedback-based quantum algorithms have been introduced to calculate the ground states of Hamiltonians, inspired by quantum Lyapunov control theory. This article aims to generalize these algorithms to the problem of calculating an eigenstate of a given Hamiltonian, assuming that the lower energy eigenstates are known. To this aim, we propose a new design methodology that combines the layerwise construction of the quantum circuit in feedback-based quantum algorithms with a new feedback law based on a new Lyapunov function to assign the quantum circuit parameters. We present two approaches for evaluating the circuit parameters: one based on the expectation and overlap estimation of the terms in the feedback law and another based on the gradient of the Lyapunov function. We demonstrate the algorithm through an illustrative example and through an application in quantum chemistry. To assess its performance, we conduct numerical simulations and execution on IBM's superconducting quantum computer.
Keywords:
Quantum algorithm
Quantum circuit
Optimization
Stationary state
Quantum computing
Quantum chemistry
Lyapunov methods
Convergence
Approximation algorithms
Qubit
Excited states
feedback-based quantum algorithms (FQAs)
noisy intermediate-scale quantum (NISQ) devices
quantum Lyapunov control (QLC)
variational quantum algorithms (VQAs)
Journal
I
IF:
4.6
Papers:
52
Citations:
0