Making the zeroth-order process fidelity independent of state preparation and measurement errors

TL;DR

The study addresses SPAM-induced biases in evaluating quantum processes by enhancing the zeroth-order zero-fidelity estimator. It first couples zero-fidelity with randomized benchmarking to achieve SPAM robustness up to three qubits, then employs zero-noise extrapolation to scale the approach to larger systems. Numerical results show that the decay rate of the zero-fidelity under RB is insensitive to SPAM and that ZNE can extend reliable estimation to five qubits with comparable fidelity proxies. The work thus offers scalable, resource-efficient methods for estimating process fidelity in realistic quantum devices.

Abstract

In this work, we demonstrate that the zero-fidelity, an approximation to the process fidelity, when combined with randomized benchmarking, becomes robust to state preparation and measurement (SPAM) errors. However, as randomized benchmarking requires randomly choosing an increasingly large number of Clifford elements from the Clifford group when the qubit number increases, this combination is also limited to quantum systems with up to three qubits. To make the zero-fidelity independent of SPAM errors and, at the same time, applicable to multi-qubit systems, we employ a channel noise scaling method similar to the method of global unitary folding, or identity scaling, used for quantum error mitigation.

Figures (6)

• Figure 1: An example three-qubit circuit. The first U gate on each qubit is for state preparation, where we rotate $|0\rangle$ to one of the SIC-states. The second U gate on each qubit is state preparation error. The actual target channel consists of a block of CZ gates. The gates behind the CZ gates are for performing measurement basis changes. We also add readout error on each measurement gate. The ideal target channel contains no SPAM or gate errors.
• Figure 2: Zero-fidelity for three-qubit circuit as in Fig. \ref{['fig CZ']}.
• Figure 3: A simple example a two-qubit circuit for zero-fidelity combined with interleaved randomized benchmarking. The first block of U gates is for preparation of SIC states, the second block of U gates is the state preparation error. Then, we have a Clifford gate represented by two operations, followed by the interleaved CZ channel, and the inverse of the Clifford gate. The gates directly before the measurements are used for basis change. For regular randomized benchmarking, we don't consider the interleaved CZ channel.
• Figure 4: Zero-fidelity with randomized benchmarking.
• Figure 5: Zero-fidelity with zero noise extrapolation.

Theorems & Definitions (3)

• Definition C.1
• Definition C.2
• Definition C.3