A hybrid quantum-classical algorithm that finds the minimum eigenvalue of a Hamiltonian — the workhorse for near-term quantum chemistry and material science applications, designed to be NISQ-friendly.
VQE uses a parameterized quantum circuit (the 'ansatz') to prepare a trial quantum state, measures the expectation value of the target Hamiltonian, then a classical optimizer adjusts the circuit parameters to minimize that expectation value. The minimum is the ground-state energy. VQE is hybrid (classical optimization, quantum measurement), tolerant of NISQ-era noise, and applicable to chemistry (molecular ground states), materials science, and certain optimization problems formulated as Hamiltonians.
Computing the H2 molecule's bond dissociation curve using VQE on a 4-qubit quantum simulator — within chemical accuracy of the exact answer.
VQE is the leading candidate for first commercially useful quantum advantage — quantum chemistry problems that classical methods scale poorly on, accessible to NISQ-era hardware.
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