We present experiments that address the issue of measurement of superconducting qubits. A quantum non‐demolition (QND) type of readout is used to implement a projective measurement, which is an important component of many protocols in quantum information. The state of a persistent current qubit is measured using a driven non‐linear resonator, based on DC‐SQUID whose Josephson inductance is qubit‐state dependent. When properly optimized, the readout is efficient and projective. We discuss the relation between the concept of QND detection and the observed projective character of the measurement.
We present experiments that address the issue of measurement of superconducting qubits. A quantum non‐demolition (QND) type of readout is used to implement a projective measurement, which is an important component of many protocols in quantum information. The state of a persistent current qubit is measured using a driven non‐linear resonator, based on DC‐SQUID whose Josephson inductance is qubit‐state dependent. When properly optimized, the readout is efficient and projective. We discuss the relation between the concept of QND detection and the observed projective character of the measurement.
We present a readout method for superconducting flux qubits. The qubit quantum flux state can be measured by determining the Josephson inductance of an inductively coupled dc superconducting quantum interference device (dc-SQUID). We determine the response function of the dc-SQUID and its back-action on the qubit during measurement. Due to driving, the qubit energy relaxation rate depends on the spectral density of the measurement circuit noise at sum and difference frequencies of the qubit Larmor frequency and SQUID driving frequency. The qubit dephasing rate is proportional to the spectral density of circuit noise at the SQUID driving frequency. These features of the back-action are qualitatively different from the case when the SQUID is used in the usual switching mode. For a particular type of readout circuit with feasible parameters we find that single shot readout of a superconducting flux qubit is possible.
Fast, precise, and quantum-non-demolition (QND) readout of superconducting qubits is a fundamental component of high-fidelity quantum sensing and computation. Conventional approaches typically operate in the dispersive regime, where the qubit-resonator coupling g is weak compared to the detuning Δ. While exhibiting good QND properties, the readout rate is limited to ∼g2N/Δ≪g, where N is the number of photons in the resonator. QND readout in the nondispersive regime, where the readout rate reaches its full potential ∼g, relies on parameter sweeps that may encounter resonances, leading to measurement-induced state transitions (MIST). In this work, we study a nondispersive readout protocol that replaces these sweeps by sudden quenches of the coupling constant, using a resonator that is preloaded with photons. We call this protocol bang-bang readout, and show that it realizes single-shot projective measurements. The fidelity and QNDness of the qubit post-measurement are remarkably high, with an error that decreases like 1/N. We show that the protocol can also be implemented without preloading the resonator by instead strongly driving the qubit, e.g., with a classical flux drive.
Quantum state detectors based on switching of hysteretic Josephson junctions biased close to their critical current are simple to use but have strong backaction. We show that the backaction of a dc-switching detector can be considerably reduced by limiting the switching voltage and using a fast cryogenic amplifier, such that a single readout can be completed within 25 ns at a repetition rate of 1 MHz without loss of contrast. Based on a sequence of two successive readouts we show that the measurement has a clear quantum nondemolition character, with a QND fidelity of 75%.
Repeated quantum non-demolition measurement is a cornerstone of quantum error correction protocols. In superconducting qubits, the speed of dispersive state readout can be enhanced by increasing the power of the readout tone. However, such an increase has been found to result in additional qubit state transitions that violate the desired quantum non-demolition character of the measurement. Recently, the readout of a transmon superconducting qubit was improved by using a tone with frequency much larger than the qubit frequency. Here, we experimentally identify the mechanisms of readout-induced transitions in this regime. In the dominant mechanism, the energy of an incoming readout photon is partially absorbed by the transmon and partially returned to the transmission line as a photon with lower frequency. Other mechanisms involve the excitation of unwanted package modes, decay via material defects, and, at higher qubit frequencies, the activation of undesired resonances in the transmon spectrum. Our work provides a comprehensive characterization of superconducting qubit state transitions caused by a strong drive.
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.
While relatively easy to engineer, static transverse coupling between a qubit and a cavity mode satisfies the criteria for a quantum non-demolition (QND) measurement only if the coupling between the qubit and cavity is much less than their mutual detuning. This can put significant limits on the speed of the measurement, requiring trade-offs in the circuit design between coupling, detuning, and decoherence introduced by the cavity mode. Here, we study a circuit in which the qubit-cavity and the cavity-feedline coupling can be turned on and off, which helps to isolate the qubit. We do not rely on the rotating-wave or dispersive approximations, but solve the full transverse interaction between the qubit and the cavity mode. We show that by carefully choosing the detuning and interaction time, we can exploit a recurrence in the qubit-cavity dynamics in a way that makes it possible to perform very fast, high fidelity, QND measurements. Here, the qubit measurement is performed more like a gate operation between the qubit and the cavity, where the cavity state can be amplified, squeezed, and released in a time-sequenced fashion. In addition, we also show that the non-demolition property of the off-resonant approximation breaks down much faster than its dispersive property, suggesting that many of the dispersive measurements to date have been implemented outside the QND regime.