Measurement-driven analog of adiabatic quantum computation for frustration-free Hamiltonians

The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realized in systems which support Hamiltonian evolution rather than discrete gates. We explore an alternative approach in which slowly varying measurements are used to mimic adiabatic evolution. We show that, for certain Hamiltonians, which remain frustration free all along the adiabatic path, the necessary measurements can be implemented through the measurement of random terms from the Hamiltonian. This offers a potentially more viable method of realizing adiabatic evolution in gate-based quantum computer architectures.