Bell-Pair Clifford Memory for Pauli-Channel Spectroscopy on a Noisy QPU: A Hardware Channel-Use Crossover

Introduction

Quantum memory can fundamentally change the statistical cost of learning quantum processes. In Pauli spectroscopy, entangling a system with an ancillary memory before probing an unknown channel allows information about many Pauli components to be extracted from the same set of channel uses. In contrast, memoryless strategies that estimate different observables through independent channel interrogations can require substantially more uses of the channel for the same simultaneous accuracy target. This separation is particularly appealing because the memory-assisted protocol can be implemented with a restricted and experimentally favorable gate set: Bell-pair preparation followed by Clifford operations and computational-basis measurements.

The theoretical distinction, however, does not by itself establish a useful hardware advantage. On a noisy quantum processor, the memory-assisted branch introduces additional physical structure that is absent from an idealized oracle-counting model. Bell pairs must be prepared and preserved, additional qubits must remain available throughout the experiment, Bell measurements must be decomposed into native Clifford-compatible operations, and state-preparation-and-measurement errors must be calibrated. Moreover, calibration drift can invalidate otherwise precise estimates, while routing, finite-shot uncertainty, and device-specific noise can erase an apparent reduction in channel uses. The relevant experimental question is therefore not merely whether quantum memory reduces an asymptotic sample complexity, but whether that reduction survives an end-to-end implementation on real hardware.

We address this question experimentally for Pauli-channel spectroscopy using a Bell-pair Clifford memory protocol executed on a noisy superconducting QPU. For each $n$-qubit instance, the protocol prepares $n$ Bell pairs, applies the channel under study to one half of each pair, and performs Bell-basis readout using only Clifford operations and measurements. The resulting data are used to reconstruct multiple Pauli expectation values simultaneously. The memory-assisted protocol is compared with an explicitly executed nonadaptive memoryless strategy based on independent Pauli queries, so that the comparison is made between two hardware-executed procedures rather than between an experiment and an asymptotic theoretical bound.

Our certification framework is designed to preserve this distinction at the level of the final claim. Each Pauli estimate is assigned a finite-shot confidence interval and a SPAM-corrected uncertainty radius. Position-resolved pre- and post-experiment calibrations are used to determine whether the hardware calibration relevant to that estimate remained sufficiently stable during the acquisition window. The primary memory criterion requires at least $480$ of $504$ preregistered estimates to satisfy a total uncertainty radius not exceeding $0.30$ together with the corresponding calibration-validity conditions. The memoryless comparator is evaluated independently on $72$ matched estimates under the same accuracy target.

In the completed hardware campaign reported here, 498 of 504 primary memory-assisted Pauli estimates satisfy the certification criterion, exceeding the required threshold of $480$. All 72 of 72 executed memoryless comparator estimates satisfy their matched accuracy criterion. At $n=8$, the memory-assisted and memoryless branches achieve the required task accuracy with a 24-fold difference in channel uses in favor of the Bell-memory protocol. The experiment therefore exhibits a hardware channel-use crossover for the executed spectroscopy task while explicitly incorporating finite-shot uncertainty, SPAM correction, position-resolved calibration, Bell-memory resources, and the physical Clifford measurement circuit into the experimental procedure.

The result should be interpreted in the metric in which it is established. The certified advantage is an advantage in number of channel uses, not a claim of shorter wall-clock runtime or lower total gate count. Likewise, the experimental comparator is the preregistered nonadaptive independent-query memoryless protocol implemented in this work; the result is not a finite-size experimental lower bound against every possible adaptive ancilla-free strategy. Within this scope, however, the experiment provides direct evidence that a remarkably restricted form of quantum memory—Bell pairs combined with Clifford measurements—can retain a substantial channel-use advantage after being instantiated on noisy hardware.

More broadly, these results suggest that quantum memory can be treated as an experimentally testable resource rather than only as an element of asymptotic query-complexity theory. Pauli spectroscopy offers an especially transparent setting because the memory resource, the measurement structure, the comparator, and the certification metric can all be specified explicitly. This makes it possible to ask a concrete hardware question: can entanglement-assisted memory reduce the number of times an unknown quantum process must actually be invoked, after the operations required to realize and certify that memory are included in the experiment? The campaign reported here answers that question positively for the executed $n=8$ Bell-pair Clifford protocol and its matched memoryless comparator.