Feedback-based quantum algorithms.

Alicia B Magann

Alicia B Magann, Kenneth Rudinger, Matthew Grace +4 more

Vicente Peña Pérez, Matthew D. Grace, Christian Arenz +1 more

Feedback-based quantum algorithms (FQAs) operate by iteratively growing a quantum circuit to optimize a given task. At each step, feedback from qubit measurements is used to inform the next quantum circuit update. In practice, the sampling cost associated with these measurements can be significant. Here, we ask whether FQA parameter sequences can be predicted using classical machine learning, obviating the need for qubit measurements altogether. To this end, we train a teacher-student model to map problem instances to associated FQA parameter curves in a single classical inference step. We first study weighted MaxCut problem instances, where numerical experiments show that this machine learning model can accurately predict FQA parameter curves across a range of problem sizes, including sizes not seen during model training. We then extend the analysis to transverse-field Ising models on graphs, and analyze how this learning strategy performs and generalizes beyond the original MaxCut setting. To evaluate performance, we compare the predicted parameter curves in simulation against FQA reference curves and linear quantum annealing schedules. We observe similar results to the former and performance improvements over the latter. These results suggest that machine learning can offer a heuristic, practical path to reducing sampling costs and resource overheads in quantum algorithms.

L. A. M. Rattighieri, G. E. L. Pexe, Bertúlio de Lima Bernardo +1 more

This work investigates the impact of time rescaling on the performance of Feedback-Based Quantum Algorithms (FQAs) and their variant for optimization tasks, Feedback-Based Algorithm for Quantum Optimization (FALQON). We introduce the Time-Rescaled Feedback-Based Quantum Algorithm (TR-FQA) and Time-Rescaled Feedback-Based Algorithm for Quantum Optimization (TR-FALQON), time-rescaled versions of FQA and FALQON, respectively. The method is applied to two representative problems: the MaxCut combinatorial optimization problem and ground-state preparation in the axial next-nearest neighbor Ising (ANNNI) model. The results show that TR-FALQON accelerates convergence toward the optimal solution in the circuit's early layers and outperforms the standard version in low-depth regimes. In the context of state preparation, TR-FQA requires fewer layers than the original algorithm. These findings suggest that time rescaling can reduce the number of layers needed to reach a high-quality solution, even if the exact ground state is not obtained.

Alicia B Magann, Kenneth Rudinger, Matthew Grace +1 more

Salahuddin Abdul Rahman, Özkan Karabacak, Rafał Wiśniewski

Recently, feedback-based quantum algorithms have been introduced to calculate the ground states of Hamiltonians, inspired by quantum Lyapunov control theory. This paper 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 layer wise 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.