Joint Seminar on Quantum Information and Technologies

It is imperative to minimize resources needed to implement quantum operations on existing near-term quantum devices. With this in mind, we propose a scheme to implement an arbitrary general quantum measurement (POVM) in dimension d using only classical resources and a single ancillary qubit. The proposed method is based on probabilistic implementation of d-outcome measurements which is followed by postselection on some of the received outcomes. This is an extension of an earlier work (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.012351) which required dichotomic measurements, no additional ancillary qubits, and whose success probability scaled like 1/d. The success probability of our scheme depends on the operator norms of the coarse grained POVM effects. For Haar random POVMs in dimension d, these properties are related to operator norms of truncations of Haar-random unitaries. Significantly, we show that for typical Haar random rank-one POVMs with at most d^2 outcomes, the success probability of our simulation scheme does not go to zero with the dimension of the system. We conjecture that this is true for all quantum measurements in dimension d. This is supported by numerical computations showing constant success probability for SIC-POVMs in dimension up to 323. Additionally, for the gate noise model used in the recent demonstration of quantum computational advantage (https://www.nature.com/articles/s41586-019-1666-5), we prove that for typical Haar random POVMs noise compounding in circuits required by our scheme is substantially lower than in the scheme that directly uses Naimark’s dilation theorem.

ZOOM link: https://zoom.us/j/6526721604?pwd=Y0pPdE9vT1hNWWNiZVBMaEVOeHN2dz09