Local robust shadows on a trapped ion computer -- a case study

Abstract

We experimentally demonstrate local robust shadows on a trapped-ion device, a protocol developed to counteract measurement errors. We alternate between a calibration stage and the shadow estimation stage and also introduce Pauli-X-twirling before measurements in both stages to symmetrize error rates. We then demonstrate the protocol on a trapped-ion quantum computer with artificially shortened measurement pulse duration. This yields faster experiments at the cost of increased error rates which are subsequently mitigated by the robust shadow protocol. We benchmark this approach on three exemplary quantum states: a local Haar random state, as well as standard and Pauli-correlation encoded QAOA states. In all three cases, the local robust shadow protocol succeeds at mitigating the increased error rates hailing from shorter measurement pulse durations.

Figures (2)

• Figure 1: Local robust shadows with X-twirling. Here, circuit diagrams go from left to right. Step I (left): characterize the read-out noise via twirling the zero state with a random bit flip layer before read-out. Use the acquired data to estimate the noisy single-qubit expansion coefficients $\tilde{f}_j$. Step II (center): execute a sequential local shadow protocol with random single-qubit measurements and add an additional layer of random bit flips before reading out to symmetrize the read-out error. Use the estimated noisy expansion coefficients to create a robust snapshot for the following classical post-processing. The plot on the right displays results for estimating the single qubit fidelities of a local Haar-random $12$-qubit state on a trapped-ion computer with an intentionally shortened measurement pulse length of 150µs. This reduces measurement time duration at the cost of increased readout noise which is then mitigated by our protocol.
• Figure 2: Experimental data evaluation. Error bars denote 95% confidence intervals obtained from 20 parametric bootstrap samples. (a) Estimated local readout error probabilities $p_{\mathrm{flip}}$ for different measurement pulse lengths, (b.1) Estimated two-qubit subsystem purities $p^{(2)}$ for the QAOA state across qubit pairs (150µs) . (c.1) Estimated Pauli correlators $c^{(2)} = \langle P_i P_j \rangle$ for the Pauli-correlation encoding (PCE) solution states (150µs). Panels (d), (b.2), (c.2), and (c.3) show the corresponding absolute deviations $\Delta q = |q - q_{\mathrm{true}}|$ for fidelity, subsystem purity, and Pauli correlators, respectively, comparing non-robust (NR) and robust (R) post-processing. Left (right) violin plots correspond to a measurement pulse length of 300µs (150µs).