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arXiv:2109.06616 · Physical Review Letters

Complete Physical Characterization of Quantum Nondemolition Measurements via Tomography

Luciano Pereira, Juan José García‐Ripoll, Tomás Ramos

Published Jun 29, 2022• 7 citations
arXivHTMLPDF

Abstract

We introduce a self-consistent tomography for arbitrary quantum nondemolition (QND) detectors. Based on this, we build a complete physical characterization of the detector, including the measurement processes and a quantification of the fidelity, ideality, and backaction of the measurement. This framework is a diagnostic tool for the dynamics of QND detectors, allowing us to identify errors, and to improve their calibration and design. We illustrate this on a realistic Jaynes-Cummings simulation of a superconducting qubit readout. We characterize nondispersive errors, quantify the backaction introduced by the readout cavity, and calibrate the optimal measurement point.

DOI
10.1103/physrevlett.129.010402

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Abstract An efficient characterization of QND measurements is an important ingredient toward certifying and improving the performance and scalability of quantum processors. In this work, we introduce a parallel tomography of QND measurements that addresses single- and two-qubit readout on a multi-qubit quantum processor. We provide an experimental demonstration of the tomographic protocol on a 7-qubit IBM-Q device, characterizing the quality of conventional qubit readout as well as generalized measurements such as parity or measurement-and-reset schemes. Our protocol reconstructs the Choi matrices of the measurement processes, extracts relevant quantifiers—fidelity, QNDness, destructiveness—and identifies sources of errors that limit the performance of the device for repeated QND measurements. We also show how to quantify measurement crosstalk and use it to certify the quality of simultaneous readout on multiple qubits.
As progress is made towards the first generation of error-corrected quantum computers, robust characterization and validation protocols are required to assess the noise environments of physical quantum processors. While standard coherence metrics and characterization protocols such as T1{T}_{1}T1​ and T2{T}_{2}T2​, process tomography, and randomized benchmarking are now ubiquitous, these techniques provide only partial information about the dynamic multiqubit loss channels responsible for processor errors, which can be described more fully by a Lindblad operator in the master equation formalism. Here, we introduce and experimentally demonstrate Lindblad tomography, a hardware-agnostic characterization protocol for tomographically reconstructing the Hamiltonian and Lindblad operators of a quantum noise environment from an ensemble of time-domain measurements. Performing Lindblad tomography on a small superconducting quantum processor, we show that this technique naturally builds on standard process tomography and T1/T2{T}_{1}/{T}_{2}T1​/T2​ measurement protocols, characterizes and accounts for state-preparation and measurement errors, and allows one to place bounds on the fit to a Markovian model. Comparing the results of single- and two-qubit measurements on a superconducting quantum processor, we demonstrate that Lindblad tomography can also be used to identify and quantify sources of crosstalk on quantum processors, such as the presence of always-on qubit-qubit interactions.
We use quantum detector tomography to characterize the qubit readout in terms of measurement positive operator-valued measures (POVMs) on IBM quantum computers IBM Q 5 Tenerife and IBM Q 5 Yorktown. Our results suggest that the characterized detector model deviates from the ideal projectors, ranging from 10 to 40%. This is mostly dominated by classical errors, evident from the shrinkage of arrows from the poles in the corresponding Bloch-vector representations. There are also small deviations that are not ``classical,'' of order 3% or less, represented by the tilt of the arrows from the zzz axis. Further improvement on this characterization can be made by adopting two- or more-qubit detector models instead of independent single-qubit detectors for all the qubits in one device. We also find evidence indicating correlations in the detector behavior, i.e., the detector characterization is slightly altered (to a few percent) when other qubits and their detectors are in operation. Such peculiar behavior is consistent with characterization from the more sophisticated approach of the gate set tomography. We also discuss how the characterized detectors' POVMs, despite deviation from the ideal projectors, can be used to estimate the ideal detection distribution.