Imaginary time evolution with quantum nondemolition measurements: multi-qubit interactions via measurement nonlinearities

Abstract

We show that quantum nondemolition (QND) measurements can be used to realize measurement-based imaginary time evolution. In our proposed scheme, repeated weak QND measurements are used to estimate the energy of a given Hamiltonian. Based on this estimated energy, adaptive unitary operations are applied such that only the targeted energy eigenstates are fixed points of the evolution. In this way, the system is deterministically driven towards the desired state. The nonlinear nature of the QND measurement, which allows for producing interactions between systems, is explicitly derived in terms of measurement operators. We show that for suitable interaction times, single qubit QND Hamiltonians can be converted to effective multi-qubit imaginary time operations. We illustrate our techniques with the example of preparing a four qubit cluster state, which is prepared using only collective single qubit QND measurements and single qubit adaptive operations.

12 pages, 4 figures

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Cited by in corpus (4)

• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Quantum nondemolition measurement operator with spontaneous emission
• Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
• Quantum teleportation of cat states with binary-outcome measurements