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arXiv:2208.02893 · Quantum Information Processing

Swap Test-based characterization of decoherence in universal quantum computers

Pedro Ripper, Gustavo Castro do Amaral, Guilherme P. Temporão

Published May 17, 2023• 9 citations
arXivHTMLPDF
DOI
10.1007/s11128-023-03961-y

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Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning approach for discovering such algorithms. We apply our method to a ubiquitous primitive: computing the overlap between two quantum states ρ and σ . The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines, and, when specialized to ρ = σ , quantifies the Renyi entanglement. Here, we find algorithms that have shorter depths than the Swap Test, including one that has a constant depth (independent of problem size). Furthermore, we apply our approach to the hardware-specific connectivity and gate sets used by Rigetti's and IBM's quantum computers and demonstrate that the shorter algorithms that we derive significantly reduce the error—compared to the Swap Test—on these computers.
We present an optical scheme for a SWAP test (controlled swap operation) that can determine whether the difference between two unknown states (photons) using cross-Kerr nonlinearities (XKNLs). The SWAP test, based on quantum fingerprinting, has been widely applied to various quantum information processing (QIP) schemes. Thus, for a reliable QIP scheme, it is important to implement a scheme for a SWAP test that is experimentally feasible. Here, we utilize linearly and nonlinearly optical (XKNLs) gates to design a scheme for a SWAP test. We also analyze the efficiency and the performance of nonlinearly optical gates in our scheme under the decoherence effect and exhibit a technique employing quantum bus beams and photon-number-resolving measurements to reduce the effect of photon loss and dephasing caused by the decoherence effect. Consequently, our scheme, which is designed using linearly optical devices and XKNLs (nonlinear optics), can feasibly operate the nearly deterministic SWAP test with high efficiency, in practice.