Efficient verification of bosonic quantum channels via benchmarking

Abstract

We aim to devise feasible, efficient verification schemes for bosonic channels. To this end, we construct an average-fidelity witness that yields a tight lower bound for average fidelity plus a general framework for verifying optimal quantum channels. For both multi-mode unitary Gaussian channels and single-mode amplification channels, we present experimentally feasible average-fidelity witnesses and reliable verification schemes, for which sample complexity scales polynomially with respect to all channel specification parameters. Our verification scheme provides an approach to benchmark the performance of bosonic channels on a set of Gaussian-distributed coherent states by employing only two-mode squeezed vacuum states and local homodyne detections. Our results demonstrate how to perform feasible tests of quantum components designed for continuous-variable quantum information processing.

On the optimal certification of von Neumann measurements

“…The validation of sources producing quantum states and measurement devices, which are involved in quantum computation workflows, is a necessary step of quantum technology [1][2][3] . The search for practical and reliable tools for validation of quantum architecture has attracted a lot of attention in recent years [4][5][6][7][8] . Rapid technology development and increasing interest in quantum computers paved the way towards creating more and more efficient validation methods of Noisy Intermediate-Scale Quantum devices (NISQ) 9,10 .…”

Efficient verification of continuous-variable quantum states and devices without assuming identical and independent operations

“…We begin with the observation that any test of quantum devices can be realized by preparing one entangled state on the input and an ancillary system, and then jointly measuring the output and the ancillary system [20]. The observable to be measured can then be chosen to be (average) fidelity witness as in a state verification task [13]. By adding a dimension test and rotational symmetry in the fidelity test, we get our quantum-device verification scheme.…”

“…While some efficient protocols exist [4,7], they require the tested systems to be identically and independently (i.i.d) prepared, an assumption that is hard to guarantee in realistic scenarios. Quantum device verification [13] is the problem of determining whether the outputs of a quantum device is close to associated target output states, averaged over all possible input states. CV quantum device verification in the non-i.i.d setting has so far been an open problem.…”

“…State verification under the i.i.d assumption can be performed by detecting a fidelity witness W , which is an observable whose expectation value with respect to any prepared state is a tight lower bound of its fidelity with the target state. This provides an efficient approach to verify both CV quantum states [4,7] and CV quantum channels [13]. The failure probabilities in both soundness and completeness are bounded by statistical inequalities like Hoeffding's inequality.…”

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

“…Refs. [30][31][32][33][34]), which enables efficient verification of various quantum gates and quantum circuits based on LOCC. Notably, all bipartite unitaries and Clifford unitaries can be verified with resources that are independent of the system size, while the resource required to verify the generalized controlled-NOT (CNOT) gate and generalized controlled-Z (CZ) gate grows only linearly with the system size.…”