Qubit-efficient entanglement spectroscopy using qubit resets

The utility of NISQ devices can be increased by algorithms that fit larger problem sizes on smaller devices. In this talk I will describe qubit-efficient quantum algorithms for entanglement spectroscopy that exploit the ability to measure and reinitialize subsets of qubits in the course of the computation. These algorithms compute the trace of the n-th power of the density operator of a quantum system, i.e. Tr[ρⁿ ]. They use fewer qubits (independent of n) than any previous efficient algorithm while achieving similar performance in the presence of noise. I will introduce the notion of effective circuit depth as a generalization of standard circuit depth suitable for circuits with qubit resets. This tool helps explain the noise-resilience of our qubit-efficient algorithms and should aid in designing future algorithms. Finally, I will report results of experiments on the Honeywell System Model H0, estimating Tr[ρⁿ ] for larger n than would have been possible with previous algorithms.