Exploring the Fidelity of Flux Qubit Measurement in Different Bases via Quantum Flux Parametron

TL;DR

The paper tackles high-fidelity readout of flux qubits using a quantum flux parametron (QFP)–mediated dispersive scheme. It develops a theoretical and numerical framework to compare measurement bases (flux, energy, bare, dressed) in single-qubit and coupled two-qubit systems, and to contrast sequential versus simultaneous QFP annealing strategies. The main findings show that the energy basis generally yields higher fidelity than the flux basis, and that sequential measurements in a dressed basis over longer times often provide the most robust readouts, whereas simultaneous measurements in a bare basis can achieve high fidelity over shorter durations. These results offer concrete guidance for optimizing readout protocols in multi-qubit superconducting architectures and contribute to the development of scalable, high-fidelity quantum measurement strategies.

Abstract

High-fidelity qubit readout is a fundamental requirement for practical quantum computing systems. In this work, we investigate methods to enhance the measurement fidelity of flux qubits via a quantum flux parametron-mediated readout scheme. Through theoretical modeling and numerical simulations, we analyze the impact of different measurement bases on fidelity in single-qubit and coupled two-qubit systems. For single-qubit systems, we show that energy bases consistently outperform flux bases in achieving higher fidelity. In coupled two-qubit systems, we explore two measurement models: sequential and simultaneous measurements, both aimed at reading out a single target qubit. Our results indicate that the highest fidelity can be achieved either by performing sequential measurement in a dressed basis over a longer duration or by conducting simultaneous measurement in a bare basis over a shorter duration. Importantly, the sequential measurement model consistently yields more robust and higher fidelity readouts compared to the simultaneous approach. These findings quantify achievable fidelities and provide valuable guidance for optimizing measurement protocols in emerging quantum computing architectures.

Figures (11)

• Figure 1: Quantum flux parametron (QFP)-mediated scheme for measuring a single flux qubit. The flux qubit is coupled to a QFP. After QFP annealing, the qubit state is latched into the QFP, which is then read out using a resonator.
• Figure 2: QFP annealing fidelity as a function of (a) normalized annealing time $t/t_{\mathrm{qfp}}$ for $\beta_{\mathrm{max}}=1.5$ and (b) maximal screening parameter $\beta_{\mathrm{max}}$ at the total annealing time $t_{\mathrm{qfp}}$. Fidelity is evaluated in both flux and energy bases for $\Delta_{q}/\epsilon_{q}=4$ and $\xi=0.4$.
• Figure 3: Fidelity calculated using the Hamiltonian expressed in both flux and energy bases for $\eta=1.25$ and $\eta=2.5$, with $N=27$, $\Delta_{q}/\epsilon_{q}=4$, and $\delta/g=8$. Fidelity as a function of (a) $\chi t$ for $\alpha=1$ and (b) $\alpha$ at the measurement time $t = t_d$.
• Figure 4: Sequential measurement model. Two flux qubits $q_1$ and $q_2$ are coupled. QFP2 undergoes adiabatic annealing to latch the state of $q_2$. Subsequently, the state of QFP2 is read out using a resonator.
• Figure 5: Fidelity calculated using the Hamiltonian expressed in the flux basis, $q_2$ energy basis, and $q_1$-$q_2$ energy basis with $N=27$, $\eta=1.25$, $\Delta_{2}/\epsilon_2 = 1$, and $\delta/g=8$. Fidelity as a function of (a) $\chi t$ for $J/(\omega_{2}-\omega_{1})=0.05$ and $\alpha=1$; (b) $\alpha$ for $J/(\omega_{2}-\omega_{1})=0.05$ and $t = t_d$; and (c) $J/(\omega_{2}-\omega_{1})$ for $t = t_d$ and $\alpha=1$.