Universal Nonadiabatic Control of Small-Gap Superconducting Qubits

Open Access

Universal Nonadiabatic Control of Small-Gap Superconducting Qubits

Daniel L. Campbell, Yun-Pil Shim, Bharath Kannan, Roni Winik, David K. Kim, Alexander Melville, Bethany M. Niedzielski, Jonilyn L. Yoder, Charles Tahan, Simon Gustavsson, and William D. Oliver

Phys. Rev. X 10, 041051 – Published 14 December 2020

Abstract

Resonant transverse driving of a two-level system as viewed in the rotating frame couples two degenerate states at the Rabi frequency, an equivalence that emerges in quantum mechanics. While successful at controlling natural and artificial quantum systems, certain limitations may arise (e.g., the achievable gate speed) due to nonidealities like the counterrotating term. We introduce a superconducting composite qubit (CQB), formed from two capacitively coupled transmon qubits, which features a small avoided crossing—smaller than the environmental temperature—between two energy levels. We control this low-frequency CQB using solely baseband pulses, nonadiabatic transitions, and coherent Landau-Zener interference to achieve fast, high-fidelity, single-qubit operations with Clifford fidelities exceeding 99.7%. We also perform coupled qubit operations between two low-frequency CQBs. This work demonstrates that universal nonadiabatic control of low-frequency qubits is feasible using solely baseband pulses.

Received 31 March 2020
Revised 5 October 2020
Accepted 7 October 2020

DOI:https://doi.org/10.1103/PhysRevX.10.041051

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum benchmarking Quantum computation Quantum control Quantum gates

Quantum Information, Science & Technology

Authors & Affiliations

Daniel L. Campbell^1,†,‡, Yun-Pil Shim ^2,3,§, Bharath Kannan ^1,4, Roni Winik¹, David K. Kim⁵, Alexander Melville⁵, Bethany M. Niedzielski⁵, Jonilyn L. Yoder⁵, Charles Tahan², Simon Gustavsson¹, and William D. Oliver ^1,4,5,6,*

¹Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Laboratory for Physical Sciences, College Park, Maryland 20740, USA
³Department of Physics, University of Maryland, College Park, Maryland 20740, USA
⁴Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁵MIT Lincoln Laboratory, 244 Wood Street, Lexington, Massachusetts 02420, USA
⁶Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*Corresponding author. william.oliver@mit.edu
^†Corresponding author. daniel.campbell.22@us.af.mil
^‡Present address: Air Force Research Laboratory, Information Directorate. 585 Brooks Rd. Rome, New York, 13441 USA.
^§Present address: Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA

Popular Summary

The promise of quantum computation is contingent upon the ability to perform operations with low error rates. While there has been tremendous progress toward achieving low error rates with superconducting qubits, much work remains to be done in improving how long the quantum states remain coherent. One approach to mitigating decoherence is to reduce the qubit coupling to the environment by using a low frequency, or “small-gap,” qubit. However, the speed of conventional methods for controlling such a qubit would be correspondingly reduced, thus negating any benefits from improved coherence. In this work, we have demonstrated a new, robust, method for controlling small-gap qubits that maintains fast operation.

We construct a “composite qubit” by coupling together two transmon qubits, a type of superconducting qubit. The composite qubit not only features a small gap for improved coherence times but also is intrinsically immune to many common forms of noise. To operate this small-gap qubit, we develop a method based on nonresonant “baseband” control of the underlying transmons. We then use this control method to demonstrate fast single- and two-qubit operations with the composite qubits.

With further device optimization, the protection from decoherence offered by our architecture can enable quantum gates that outperform those of the current standard architectures. Our control techniques are broadly applicable to small-gapped states, as they appear in certain “protected” superconducting qubits and many other systems.

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Issue

Vol. 10, Iss. 4 — October - December 2020

Subject Areas

Quantum Information

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Images

Figure 1
Device and control. (a) Optical micrograph of two composite qubits (CQB-A and CQB-B) comprising four transmon qubits (1, 2, 3, and 4) with nearest-neighbor capacitive coupling. A microwave feedline allows frequency multiplexed readout and state preparation via the microwave driving fields $Ω_{r}$ and $Ω_{QB}$ , respectively. (b) Eigenenergies of individual (dashed lines) and coupled (solid lines) asymmetric-junction transmons 1 and 2 (CQB-A). An avoided level crossing occurs when the coupled transmons are resonantly biased at $φ_{1, 2} = \pm φ_{A}^{*}$ . (c) Upper panel: corresponding measured excited-state spectroscopy centered at zero frequency (offset in frequency) to form a two-level system model with parameters $Δ$ and $ϵ (δ f)$ . Near the avoided crossing region, $ϵ$ is proportional to the flux detuning $δ f$ , realized by simultaneously biasing $φ_{1}$ and $φ_{2}$ . Lower panel: nonadiabatic control implemented by applying a single period of a nonresonant ( $ω_{p} \neq Δ$ ) sinusoidal excursion about the avoided crossing.
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Figure 2
Single-CQB gates. (a) Pulses for $X$ , $Y$ , and $Z$ gates. For $X (\pm π / 2)$ and $Y (\pm π / 2)$ gates, the sinusoidal pulse is applied within a time window with a relative shift $t_{x y} = t_{Δ} / 4 = 2 π / 4 Δ$ , which establishes the $x$ and $y$ axes. The $X (\pm π / 2)$ and $Y (\pm π / 2)$ gates require an additional $Z$ rotation of duration $t_{c}$ that corrects for small parasitic $Z$ evolution during the gate. The $Z$ gates are realized by idling at the avoided crossing for the appropriate fraction of the precession period $1 / t_{Δ}$ . (b) Table of parameters $ϵ_{p}$ , $t_{xy}$ , $t_{Δ}$ , and $t_{c}$ for the various $X$ , $Y$ , and $Z$ gates, and the calibrated values for CQB-A and CQB-B. (c) Examples of concatenated gates and simulations of the resulting Bloch vector projections on $⟨ σ_{x} ⟩$ , $⟨ σ_{y} ⟩$ , and $⟨ σ_{z} ⟩$ . (d) Simultaneous randomized benchmarking traces corresponding to Clifford fidelity (errors within the computational subspace) and leakage Clifford fidelity (errors that leave the computational subspace).
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Figure 3
Photon shot-noise characterization. (a) Ramsey decoherence rate. The CQB is protected by design against photon shot noise, exhibiting a much lower decay rate (see text). In panel (b), we show how this protection extends to operations applied to the encoded qubit, as indicated by the slow falloff of the randomized benchmarking Clifford fidelity with the number of photons in the resonator.
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Figure 4
Two-CQB gates. (a) Controlled- $Z$ (CZ) gate between CQB-A and CQB-B (upper panel), performed by adiabatically ramping the CQB diabatic frequencies (at the transmon energy degeneracies) $ω_{A}^{*}$ and $ω_{B}^{*}$ [31], to the avoided level crossing between $| 11 ⟩$ and the hybridized second excited states $(| g_{1}, g_{2}, f_{3}, g_{4} ⟩ - | g_{1}, g_{2}, g_{3}, f_{4} ⟩) / \sqrt{2}$ of CQB-B’s bare transmons. The CQB CZ avoided level crossing occurs when $ω_{B}^{*} \approx ω_{A}^{*} + (Δ_{A} + Δ_{B}) / 2 + E_{C} / h$ . Lower panel: effective $σ_{z} σ_{z}$ coupling as a function of detuning from the avoided level crossing. (b) Syncing single-CQB gates after a CZ gate, achieved by applying a compensatory $Z$ gate, which takes into account the time of the last single-CQB gate, and phase evolution rate $η_{A, B}$ during the CZ. (c) Two-CQB randomized benchmarking within and out of the CQB manifold.
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