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arXiv:1506.05339 · Physical Review Applied

Unitary-Feedback-Improved Qubit Initialization in the Dispersive Regime

Luke C. G. Govia, Frank K. Wilhelm

Published Nov 3, 2015• 21 citations
arXivHTMLPDF

Abstract

In quantum information processing one strives for quantum nondemolition (QND) measurements, which are least likely to perturb the subsequent evolution of the system. The authors show, however, that common superconducting-qubit readout schemes are in fact not QND. They identify a mechanism that induces an effective coherent rotation of the qubit, which means that such a scheme is QND only in the limit of infinite measurement time. This affects any protocol where measurement is used during computation, and therefore is of immediate importance to contemporary experiments. Thankfully, the authors also explain how to fix the problem.

DOI
10.1103/physrevapplied.4.054001

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In quantum information processing one strives for quantum nondemolition (QND) measurements, which are least likely to perturb the subsequent evolution of the system. The authors show, however, that common superconducting-qubit readout schemes are in fact not QND. They identify a mechanism that induces an effective coherent rotation of the qubit, which means that such a scheme is QND only in the limit of infinite measurement time. This affects any protocol where measurement is used during computation, and therefore is of immediate importance to contemporary experiments. Thankfully, the authors also explain how to fix the problem.
Fast nondemolition measurement of superconducting qubits is important for the operation of quantum computers, but readout is constrained by measurement-induced state transitions that shift the qubit population outside of its computational subspace. This work experimentally characterizes the phenomenon and provides an intuitive model to explain its physical process. Surprisingly, the offset charge of the transmon qubit, which is usually ignored, is important in explaining the experiments. These results inform engineering and physics-based solutions to this problem by providing performance limits for the dispersive readout of superconducting qubits.
Dispersive readout, the current standard for measuring superconducting qubits, relies on relatively easy to engineer, static transverse coupling between a qubit and a detuned cavity mode. However, this method requires circuit design trade-offs between qubit-cavity coupling, cavity-feedline coupling, detuning, and the resultant decoherence introduced by the cavity mode. Additionally, the criteria for performing quantum nondemolition measurements, including reduced cavity photon numbers, further limits speed and fidelity. In this work, we introduce a circuit with pulse-tunable qubit-cavity and cavity-feedline couplings so that the entire qubit-measurement process can be fully optimized. Here, the core measurement process resembles a quantum gate operation between the qubit and the cavity, with the cavity acting like an ancilla, storing the qubit-state information. To fully explore time-dependent effects of the full qubit-cavity dynamics, we go beyond the rotating-wave, Jaynes-Cummings, or dispersive approximations, to develop a pulsed-measurement protocol. In addition, we propose a realistic circuit architecture that can provide a very fast, high-fidelity, QND measurement with near-unit efficiency.
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 ggg is weak compared to the detuning ΔΔΔ. While exhibiting good QND properties, the readout rate is limited to ∼g2N/Δ≪g\sim g^2\sqrt{N}/Δ\ll g∼g2N​/Δ≪g, where NNN is the number of photons in the resonator. QND readout in the nondispersive regime, where the readout rate reaches its full potential ∼g\sim g∼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/N1/N1/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.
The ability to perform high-fidelity quantum nondemolition qubit readout is pivotal for the realization of large and powerful quantum computers. Such readout of superconducting qubits is generally enabled by amplifying the weak dispersive measurement signals using phase-preserving quantum-limited Josephson amplifiers with sufficient gain to dilute the contribution of the added noise by the output chain. Here, we further enhance the qubit readout fidelity by (1) simultaneously measuring the two-mode squeezed states of the amplified readout signals at the signal and idler frequencies of the nondegenerate amplifier and (2) coherently combining them at the classical processing stage following a relative rotation that maximizes the signal to noise ratio of the qubit-encoded readout quadrature. Such readout scheme exhibits enhancement in the readout fidelity for all practical values of amplifier gain and noise added by the output chain and is fully compatible with frequency multiplexed setups used in large quantum processors.
The dispersive-readout scheme enables quantum nondemolition measurement of superconducting qubits. An increased readout power can shorten the readout time and reduce the state-discrimination error but can promote qubit transitions into higher noncomputational states. The ability to predict the onset of these measurement-induced state transitions can aid the optimization of qubit circuits and provide means for comparing the readout performance of different qubit types. Building upon the concept of dressed coherent states, we consider two straightforward metrics for determining the maximum number of photons that can be used for dispersive readout without causing state transitions. We focus on the fluxonium readout to demonstrate the independence of the metrics from any qubit-type-specific approximations. The dispersive readout of transmons and other superconducting qubits can be treated universally in the same fashion.