Efficient verification of quantum processes

Abstract

Quantum processes, such as quantum circuits, quantum memories, and quantum channels, are essential ingredients in almost all quantum information processing tasks. However, the characterization of these processes remains as a daunting task due to the exponentially increasing amount of resources required by traditional methods. Here, by first proposing the concept of quantum process verification, we establish two efficient and practical protocols for verifying quantum processes which can provide an exponential improvement over the standard quantum process tomography and a quadratic improvement over the method of direct fidelity estimation. The efficacy of our protocols is illustrated with the verification of various quantum gates as well as the processes of well-known quantum circuits. Moreover, our protocols are readily applicable with current experimental techniques since only local measurements are required. In addition, we show that our protocols for verifying quantum processes can be easily adapted to verify quantum measurements.

Excluding false negative error in certification of quantum channels

“…Verification of quantum processes is often studied in the context of specific elements of quantum information processing tasks. Protocols for efficient certification of quantum processes, such as quantum gates and circuits, were recently studied in 6 – 8 .…”

Minimum number of experimental settings required to verify bipartite pure states and unitaries

“…In preparation for the later study, here we briefly review the basic frameworks of QSV [8][9][10] and QGV [27][28][29] (cf. Refs.…”

“…Then we verify whether the output state Λ(ρ j ) is sufficiently close to the target output state U(ρ j ) = U ρ j U † by virtue of QSV as described in Sec. II A, where ρ j = |ψ j ψ j | [27,28]. By construction, the target unitary transformation can always pass each test.…”

“…The sample complexity of QGV has been analyzed in Refs. [27][28][29] based on the idea of channel-state duality, but the details are not necessary to the current study. It turns out the verification of the unitary transformation U is closely tied to the verification of its Choi state, especially when the verification protocol is balanced, which means j p j ρ j = I/d [28].…”

“…Moreover, the efficiency of QSV has been demonstrated in a number of experiments [23][24][25][26]. Recently, the idea of QSV was generalized to quantum gate verification (QGV) [27][28][29] (cf. Refs.…”