Randomized benchmarking for qudit Clifford gates

Abstract

We introduce unitary-gate randomized benchmarking (URB) for qudit gates by extending singleand multi-qubit URB to single-and multi-qudit gates. Specifically, we develop a qudit URB procedure that exploits unitary 2-designs. Furthermore, we show that our URB procedure is not simply extracted from the multi-qubit case by equating qudit URB to URB of the symmetric multi-qubit subspace. Our qudit URB is elucidated by using pseudocode, which facilitates incorporating into benchmarking applications.Quantum computing and quantum communication typically focuse on quantum information encoded and processed with quantum bit (qubit) strings, but replacing qubits by higher-dimensional qudit strings [1,2] can be advantageous [3] for quantum simulation [4], quantum algorithms [5-7], quantum error correction [8-10], universal optics-based quantum computation [11], quantum communication [12, 13] and fault-tolerant quantum computation [14, 15]. Qudit quantum-information process could reduce space requirements and exploit natural properties such as orbital angular momentum for photons [16], superconductors [4] and neutral atoms [17]. Specifically, quantum computing on higher-dimensional systems can be more efficient than on qubits [7,14,18]. Ultimate success of quantum computing, both qubitand qudit-based, depends on being scalable, which, in turn, requires components meeting fault-tolerance conditions [19].Unitary-gate randomized benchmarking (URB) is the preferred technique to characterize unitary-gate performance due to its efficiency [20,21], which is robust against state-preparation-and-measurement (SPAM) errors and exponentially superior to the alternative of quantum process tomography (QPT) [22,23]. URB estimates average fidelity between real and ideal implementation of all 24 Clifford gates in C 2 , which normalizes the Pauli group

Characterization of Control in a Superconducting Qutrit Using Randomized Benchmarking

“…We now discuss the sources of error in the experiment. Comparing results from the RB and QPT experiment, the fidelity from RB being slightly higher than the fidelity from QPT is consistent with RB being less sensitive to state preparation and measurement error than QPT [21]. In the RB experiment, V i = 5.36 ± 0.03 mV matches Tr (V ρ th ) = 5.35 ± 0.07 mV and V f = 4.50 ± 0.07 mV matches Tr (V ρ dep ) = 4.59 ± 0.03 mV, where…”

“…, and d = 3 is the dimension of the qudit [21]. RB is used since it measures F faster than QPT, at the expense of not giving information about individual gates in C 3 [20].…”

Qudits and High-Dimensional Quantum Computing

“…Furthermore we show the advantages and the potential for qudit systems to outperform qubit counterparts. Of course these advantages can come with challenges such as possibly harder-to-implement universal gates, benchmarking [80,94,117]; characterization of qudit gate [68,136] and error correction connected with the complexity of the Clifford hierarchy for qudits [157].…”

A quantum number theory

“…represents a d-dimensional quantum information unit 9,15,32 . We will try to do this connection in the following.…”