Qubit readout enabled by qubit cloaking

Manuel H. Muñoz-Arias, Cristóbal Lledó, and Alexandre Blais

Phys. Rev. Applied 20, 054013 – Published 6 November 2023

Abstract

Time-dependent drives play a crucial role in quantum computing efforts with circuit quantum electrodynamics. They enable single-qubit control and entangling logical operations, as well as qubit readout. However, their presence can lead to deleterious effects such as large ac-Stark shifts and unwanted qubit transitions ultimately reflected into reduced control or readout fidelities. Qubit cloaking was introduced by Lledó et al. [C. Lledó, R. Dassonneville, A. Moulinas et al., Nat. Commun. 14, 6313 (2023)] to temporarily decouple the qubit from the coherent photon population of a driven cavity, allowing for the application of arbitrary displacements to the cavity field while avoiding the deleterious effects on the qubit. For qubit readout, cloaking permits us to prearm the cavity with an, in principle, arbitrarily large number of photons, in anticipation of the qubit-state-dependent evolution of the cavity field, allowing for improved readout strategies. Here, we take a closer look at two such strategies: first, arm-and-release readout, introduced together with qubit cloaking, where after arming the cavity, the cloaking mechanism is released and the cavity field evolves under the application of a constant drive amplitude; and, second, an arm-and-longitudinal readout scheme, where the cavity drive amplitude is slowly modulated after the release. We show that the two schemes complement each other, offering an improvement over standard dispersive readout for any values of the dispersive interaction and the cavity decay rate, as well as any target measurement integration time. Our results provide a recommendation for improving qubit readout without changes to the standard circuit-QED architecture.

Received 11 May 2023
Revised 3 August 2023
Accepted 12 October 2023

DOI:https://doi.org/10.1103/PhysRevApplied.20.054013

Physics Subject Headings (PhySH)

Circuit quantum electrodynamics Quantum control Quantum nondemolition measurement

Superconducting qubits

Quantum Information, Science & Technology

Authors & Affiliations

Manuel H. Muñoz-Arias ^1,*, Cristóbal Lledó ^1,†, and Alexandre Blais^1,2

¹Institut Quantique and Département de Physique, Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada
²Canadian Institute for Advanced Research, Toronto, Ontario M5G1M1, Canada

^*munm2002@usherbrooke.ca
^†cristobal.lledo.veloso@usherbrooke.ca

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Vol. 20, Iss. 5 — November 2023

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Images

Figure 1
The path in phase space of the cavity amplitude when the qubit is in the ground (blue) or excited (red) state for the three different schemes: dispersive readout (dashed line), arm-and-release (A&R, dashed-dotted), and arm-and-longitudinal (A&L, full line). The colored dots indicate different times in the evolution, $κ かっぱ t = 0$ , 1, 2, 4, 10, and 20. The parameters are as follows: $| χ かい | / κ かっぱ = 1$ and ${ε いぷしろん}_{1} / 2 π ぱい = 19.85 MHz$ and $18.49 MHz$ as well as ${α あるふぁ}_{arm} / \sqrt{n_{max}} \approx 0.8$ and $1 / \sqrt{2}$ for arm-and-release and arm-and-longitudinal, respectively.
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Figure 2
(a) The signal-to-noise ratio (SNR) as a function of the measurement integration time for dispersive (dashed) and arm-and-release (solid) readout, for the corresponding pairs of trajectories shown in Fig. 1. (b),(c) The normalized SNR versus $| χ かい | / κ かっぱ$ for (b) dispersive and (c) arm-and-release readout. The different curves correspond to different measurement integration times in units of $1 / κ かっぱ$ .
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Figure 3
(a)–(c) The path in phase space of the cavity amplitude ${α あるふぁ}_{g} (t)$ for the three different schemes: (a) $| χ かい | / κ かっぱ = 1 / 3$ ; (b) $| χ かい | / κ かっぱ = 1$ ; (c) $| χ かい | / κ かっぱ = 3$ . Key to lines: black dashed line, standard dispersive readout; full lines, arm-and-release; red dashed line, arm-and-longitudinal. The different colors for the arm-and-release trajectories indicate different initial amplitudes ${α あるふぁ}_{arm}$ , while the colored dots indicate different times in the evolution, $κ かっぱ t = 0$ , 1, 2, 4, 10, and 20. All trajectories, in all three panels, visit the same maximum mean photon number $n_{max} = 2.44$ . (d)–(f) The assignment error as a function of the measurement integration time for the corresponding trajectories depicted in (a)–(c). From left to right, the parameters are as follows: $| χ かい | / κ かっぱ = 1 / 3$ , $1$ , and $3$ and, for arm-and-longitudinal, ${α あるふぁ}_{arm} / \sqrt{n_{max}} = \sqrt{9} / \sqrt{10}$ , $1 / \sqrt{2}$ , and $1 / \sqrt{10}$ . For dispersive readout, ${ε いぷしろん}_{1} / 2 π ぱい = 15.77 MHz$ , $19.85 MHz$ , and $34.38 MHz$ . For arm-and-release, ${α あるふぁ}_{arm} \in (0, \sqrt{n_{max}}]$ and ${ε いぷしろん}_{1}$ is obtained, after fixing ${α あるふぁ}_{arm}$ , from the constraint of having less than the maximum mean photon number.
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Figure 4
(a) The SNR relative gain between arm-and-release and dispersive readout [see Eq. (20)], as a function of $| χ かい | / κ かっぱ$ and the measurement integration time. (b) The optimal value of the (normalized) amplitude ${\tilde{α あるふぁ}}_{arm}$ associated with the best SNR in (a). (c) The SNR relative gain between arm-and-longitudinal and dispersive readout [see Eq. (21)], as a function of $| χ かい | / κ かっぱ$ and the measurement integration time. (d) The ratio between the relative gains of arm-and-longitudinal and arm-and-release [see Eq. (22)]. The black stars correspond to the parameters of the experiment in Ref. [9] and the red dot to those of Ref. [7] (in which arm-and-release was used; see the text). In (a), (c), and (d), the gray contours indicate the separation between the regions with different optimal-readout strategies. In all panels, for a given $| χ かい | / κ かっぱ$ , all other parameters are fixed by the choice of $n_{max}$ .
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Figure 5
Numerically obtained paths of the cavity-pointer states in phase space using a transmon multilevel Hamiltonian, no RWA, and no dispersive approximation for arm-and-longitudinal (full lines) and standard dispersive readout (dashed lines). In (a) [(b)], we use $κ かっぱ / 2 π ぱい = 1 MHz (10.1 MHz)$ , and for arm-and-longitudinal readout we choose $n_{tar} = 2$ ( $1$ ), which is in between zero photons and the maximum number attained ${\bar{n}}_{max} = 4$ ( $2$ ). This results in $| {χ かい}_{n_{tar}} | / κ かっぱ = 3.286$ in (a) and 0.326 in (b). For the standard-dispersive-readout case, we use ${ω おめが}_{1} / 2 π ぱい = 7.665 GHz$ ( $7.666 GHz$ ) and ${ε いぷしろん}_{1} / 2 π ぱい = 4.876 MHz$ ( $15 MHz$ ) for (a) [(b)]. All the other system parameters read as follows: $E_{J} / 2 π ぱい = 16.93 GHz$ , $E_{C} / 2 π ぱい = 200.4 MHz$ , $g / 2 π ぱい = 159.1 MHz$ , and ${ω おめが}_{r} / 2 π ぱい = 7.655 GHz$ .
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