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npj Quantum Information

Fast and high-fidelity dispersive readout of a spin qubit with squeezed microwave and resonator nonlinearity

Chon‐Fai Kam, Xuedong Hu

Published Dec 28, 2024• 8 citations
Publisher

Abstract

Abstract Fast and high-fidelity qubit measurement is crucial for achieving quantum error correction, a fundamental element in the development of universal quantum computing. For electron spin qubits, fast readout stands out as a major obstacle in the pursuit of error correction. In this work, we explore the dispersive measurement of an individual spin in a semiconductor double quantum dot coupled to a nonlinear microwave resonator. By utilizing displaced squeezed vacuum states, we achieve rapid and high-fidelity readout for semiconductor spin qubits. Our findings reveal that introducing modest squeezing and mild nonlinearity can significantly improve both the signal-to-noise ratio (SNR) and the fidelity of qubit-state readout. By properly marching the phases of squeezing, the nonlinear strength, and the local oscillator, the optimal readout time can be reduced to the sub-microsecond range. With current technology parameters ($\kappa\approx 2\chi_s$, $\chi_s/(2\pi)\approx 0.15 \:\mbox{MHz}$), utilizing a displaced squeezed vacuum state with $30$ photons and a modest squeezing parameter $r\approx 0.6$, along with a nonlinear microwave resonator charactered by a strength of $\lambda\approx -1.2 \chi_s$, a readout fidelity of $98\%$ can be attained within a readout time of around $0.6\:\mu\mbox{s}$. Intriguing, by using a positive nonlinear strength of $\lambda\approx 1.2\chi_s$, it is possible to achieve an SNR of approximately $6$ and a readout fidelity of $99.99\%$ at a slightly later time, around $0.9\:\mu\mbox{s}$, while maintaining all other parameters at the same settings.

DOI
10.1038/s41534-024-00924-8

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Abstract Fast and high-fidelity qubit measurement is crucial for achieving quantum error correction, a fundamental element in the development of universal quantum computing. For electron spin qubits, fast readout stands out as a major obstacle in the pursuit of error correction. In this work, we explore the dispersive measurement of an individual spin in a semiconductor double quantum dot coupled to a nonlinear microwave resonator. By utilizing displaced squeezed vacuum states, we achieve rapid and high-fidelity readout for semiconductor spin qubits. Our findings reveal that introducing modest squeezing and mild nonlinearity can significantly improve both the signal-to-noise ratio (SNR) and the fidelity of qubit-state readout. By properly marching the phases of squeezing, the nonlinear strength, and the local oscillator, the optimal readout time can be reduced to the sub-microsecond range. With current technology parameters (κ≈2χs\kappa\approx 2\chi_sκ≈2χs​, χs/(2π)≈0.15 \mboxMHz\chi_s/(2\pi)\approx 0.15 \:\mbox{MHz}χs​/(2π)≈0.15\mboxMHz), utilizing a displaced squeezed vacuum state with 303030 photons and a modest squeezing parameter r≈0.6r\approx 0.6r≈0.6, along with a nonlinear microwave resonator charactered by a strength of λ≈−1.2χs\lambda\approx -1.2 \chi_sλ≈−1.2χs​, a readout fidelity of 98%98\%98% can be attained within a readout time of around 0.6 μ\mboxs0.6\:\mu\mbox{s}0.6μ\mboxs. Intriguing, by using a positive nonlinear strength of λ≈1.2χs\lambda\approx 1.2\chi_sλ≈1.2χs​, it is possible to achieve an SNR of approximately 666 and a readout fidelity of 99.99%99.99\%99.99% at a slightly later time, around 0.9 μ\mboxs0.9\:\mu\mbox{s}0.9μ\mboxs, while maintaining all other parameters at the same settings.
Fast and high-fidelity qubit measurement is crucial for achieving quantum error correction, a fundamental element in the development of universal quantum computing. For electron spin qubits, fast readout stands out as a major obstacle in the pursuit of error correction. In this work, we explore the dispersive measurement of an individual spin in a semiconductor double quantum dot coupled to a nonlinear microwave resonator. By utilizing displaced squeezed vacuum states, we achieve rapid and high-fidelity readout for semiconductor spin qubits. Our findings reveal that introducing modest squeezing and mild nonlinearity can significantly improve both the signal-to-noise ratio (SNR) and the fidelity of qubit-state readout. By properly marching the phases of squeezing, the nonlinear strength, and the local oscillator, the optimal readout time can be reduced to the sub-microsecond range. With current technology parameters (κ≈2χsκ\approx 2χ_sκ≈2χs​, $χ_s\approx 2π\times 0.15 \:\mbox{MHz}$), utilizing a displaced squeezed vacuum state with 303030 photons and a modest squeezing parameter r≈0.6r\approx 0.6r≈0.6, along with a nonlinear microwave resonator charactered by a strength of λ≈−1.2χsλ\approx -1.2 χ_sλ≈−1.2χs​, a readout fidelity of 98%98\%98% can be attained within a readout time of around $0.6\:μ\mbox{s}$. Intriguing, by using a positive nonlinear strength of λ≈1.2χsλ\approx 1.2χ_sλ≈1.2χs​, it is possible to achieve an SNR of approximately 666 and a readout fidelity of 99.99%99.99\%99.99% at a slightly later time, around $0.9\:μ\mbox{s}$, while maintaining all other parameters at the same settings.
Fast and high-fidelity qubit measurement is essential for realizing quantum error correction, which is in turn a key ingredient to universal quantum computing. For electron spin qubits, fast readout is one of the significant road blocks toward error correction. Here we examine the dispersive readout of a single spin in a semiconductor double quantum dot coupled to a microwave resonator. We show that using displaced squeezed vacuum states for the probing photons can improve the qubit readout fidelity and speed. Under condition of proper phase matching, we find that a moderate, and only moderate, squeezing can enhance both the signal-to-noise ratio and the fidelity of the qubit-state readout, and the optimal readout time can be shortened to the sub-microsecond range with above 99%99\%99% fidelity. These enhancements are achieved at low probing microwave intensity, ensuring non-demolition qubit measurement.
Strong coupling of semiconductor spin qubits to superconducting microwave resonators was recently demonstrated [X. Mi et al., Nature 555, 599 (2018); A. J. Landig et al., Nature 560, 179 (2018); N. Samkharadze et al., Science 359, 1123 (2018); T. Cubaynes et al., NPJ Quant. Inf. 5, 47 (2019)]. These breakthroughs pave the way for quantum information processing that combines the long coherence times of solid-state spin qubits with the long-distance connectivity, fast control, and fast high-fidelity quantum-non-demolition readout of existing superconducting qubit implementations. Here we theoretically analyze and optimize the dispersive readout of a single spin in a semiconductor double quantum dot (DQD) coupled to a microwave resonator via its electric dipole moment. The strong spin-photon coupling arises from the motion of the electron spin in a local magnetic field gradient. We calculate the signal-to-noise ratio (SNR) of the readout accounting for both Purcell spin relaxation and spin relaxation arising from intrinsic electric noise within the semiconductor. We express the maximum achievable SNR in terms of the cooperativity associated with these two dissipation processes. We find that while the cooperativity increases with the strength of the dipole coupling between the DQD and the resonator, it does not depend on the strength of the magnetic field gradient. We then optimize the SNR as a function of experimentally tunable DQD parameters. We identify wide regions of parameter space where the unwanted backaction of the resonator photons on the qubit is small. Moreover, we find that the coupling of the resonator to other DQD transitions can enhance the SNR by at least a factor of two, a ``straddling'' effect [J. Koch et al., Phys. Rev. A 76, 042319 (2007)] that occurs only at nonzero energy detuning of the DQD double-well potential. We estimate that with current technology, single-shot readout fidelities in the range 82--95% can be achieved within a few $\ensuremath{\mu}\mathrm{s}$ of readout time without requiring the use of Purcell filters.
Realizing fault-tolerant quantum computing relies on efficient quantum error correction. Bosonic cat-state qubits offer a highly promising, hardware-efficient approach by intrinsically suppressing bit-flip errors. However, fully unlocking their potential demands fast and high-fidelity quantum nondemolition (QND) measurements. Here, we propose a high-fidelity QND readout protocol for cat-state qubits in a Kerr-nonlinear resonator utilizing an effective longitudinal interaction. By deriving analytical expressions and performing numerical simulations, we demonstrate that longitudinal readout achieves faster signal-to-noise ratio (SNR) growth and shorter measurement times than conventional dispersive readout. Furthermore, we show that injecting squeezed input states can exponentially enhance the SNR, while time-dependent coupling further reduces the measurement time. This scheme provides a robust pathway toward rapid and nondestructive measurement of cat qubits in near-term quantum processors. Reliable quantum computers require error-resistant components like cat-state qubits, along with fast, non-destructive ways to readout them. Here, the authors propose a longitudinal readout protocol for these qubits that achieves faster and higher-fidelity measurements than conventional methods.
It has been a long-standing goal to improve dispersive qubit readout with squeezed light. However, injected external squeezing (IES) cannot enable a practically interesting increase in the signal-to-noise ratio (SNR), and simultaneously, the increase of the SNR due to the use of intracavity squeezing (ICS) is even negligible. Here, we counterintuitively demonstrate that using IES and ICS together can lead to an exponential improvement of the SNR for any measurement time, corresponding to a measurement error reduced typically by many orders of magnitude. More remarkably, we find that in a short-time measurement, the SNR is even improved exponentially with twice the squeezing parameter. As a result, we predict a fast and high-fidelity readout. This work offers a promising path toward exploring squeezed light for dispersive qubit readout, with immediate applications in quantum error correction and fault-tolerant quantum computation.