Interferometric Measurement of Hamiltonian Expectation Values in Variational Quantum Algorithms

Estimating expectation values of large Hamiltonians is a central bottleneck in variational quantum algorithms such as the Variational Quantum Eigensolver. The standard approaches require decomposing the Hamiltonian into a sum of Pauli operators and estimating each term through separate measurement bases. This strategy relies on grouping commuting terms whose optimization is NP-hard. In this work, we propose and analyze a modification of variational algorithms by introducing an interferometric dynamics that enables the extraction of the expectation value ⟨H⟩ from a parametrized quantum circuit through repeated measurements of a single auxiliary qubit. Our scheme bypasses the need for Pauli term grouping by encoding the Hamiltonian information in interference fringes, enabling the direct estimation of global contributions. This interferometric approach is fully compatible with parametrized quantum circuits and integrates naturally with Variational Quantum Eigensolver.