Complete Physical Characterization of Quantum Nondemolition Measurements via Tomography

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.

Efficient characterization of quantum nondemolition qubit readout

“…Theoretical and experimental quantifications of the QND property are essential in the diagnosis and improvement of a measurement apparatus [33,34]. The commonly used experimental scheme for the characterization of the QND-ness of a measurement is constructed of two consecutive measurements [11], and the QND-ness is quantified by the probability of obtaining the same outcomes from these two measurements [11,17,32,35].…”

“…The commonly used experimental scheme for the characterization of the QND-ness of a measurement is constructed of two consecutive measurements [11], and the QND-ness is quantified by the probability of obtaining the same outcomes from these two measurements [11,17,32,35]. However, the QND-ness defined in this way actually qualifies its projectivity or ideality, i.e., the overlap with an ideal projective measurement, rather than the QND character of the measurement [33]. It should be noted that non-ideal QND measurements are important in quantum information tasks that require precise evaluations of expectation values [33], such as variational quantum eigensolver algorithms [36][37][38] and quantum sensing [39].…”

“…However, the QND-ness defined in this way actually qualifies its projectivity or ideality, i.e., the overlap with an ideal projective measurement, rather than the QND character of the measurement [33]. It should be noted that non-ideal QND measurements are important in quantum information tasks that require precise evaluations of expectation values [33], such as variational quantum eigensolver algorithms [36][37][38] and quantum sensing [39].…”

“…To characterize the physical nature of a QND measurement, L. Pereira et al have introduced a self-consistent tomography for detectors, which consists of two consecutive applications of a detector, in between an unitary operation from a universal set of gates is interleaved [33]. There they apply quantum process tomography to reconstruct all the Choi matrices of the measurement process and accordingly provide a quantification of the measurement destructiveness by solving a series of optimization problems.…”

Directional Josephson traveling-wave parametric amplifier via non-Hermitian topology

“…Low-noise amplification enables high-sensitivity applications ranging from astronomic instrumentation [1] to nanomechanical sensing [2]. In superconducting quantum technology [3,4], in particular, microwave signals carrying quantum information are so weak that near quantum-limited amplification is indispensable to detect them in a single-shot measurement [5][6][7][8]. In this respect, the most advanced amplifiers currently available are Josephson traveling-wave parametric amplifiers (JTWPAs) which are built of a carefully engineered array of Josephson junctions (JJs) [9][10][11][12].…”