Efficient verification of quantum gates with local operations

Abstract

Efficient verification of the functioning of quantum devices is a key to the development of quantum technologies, but is a daunting task as the system size increases. Here we propose a simple and general framework for verifying unitary transformations that can be applied to both individual quantum gates and gate sets, including quantum circuits. This framework enables efficient verification of many important unitary transformations, including but not limited to all bipartite unitaries, Clifford unitaries, generalized controlled-Z gates, generalized CNOT gates, and CSWAP gate. The sampling complexity increases at most linearly with the system size and is often independent of the system size. Moreover, little overhead is incurred even if one can only prepare Pauli eigenstates and perform local measurements. Our approach is applicable in many scenarios in which randomized benchmarking (RB) does not apply and is thus instrumental to quantum computation and many other applications in quantum information processing.

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.…”

“…Suppose the test state |ψ j is chosen with probability p j > 0; denote the verification operator for the output state U(ρ j ) by Ω j . Then the average probability that the process Λ can pass each test reads [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.…”