Robust photon-mediated entangling gates between quantum dot spin qubits

Ada Warren, Utkan Güngördü, J. P. Kestner, Edwin Barnes, and Sophia E. Economou

Phys. Rev. B 104, 115308 – Published 28 September 2021

Abstract

Significant experimental advances in single-electron silicon spin qubits have opened the possibility of realizing long-range entangling gates mediated by microwave photons. Recently proposed imaginary swap (iswap) gates, however, require tuning qubit energies into resonance and have limited fidelity due to charge noise. We present a photon-mediated cross-resonance gate that is consistent with realistic experimental capabilities and requires no resonant tuning. Furthermore, we propose gate sequences capable of suppressing errors due to quasistatic noise for both the cross-resonance and iswap gates.

Received 4 March 2021
Revised 19 July 2021
Accepted 13 September 2021

DOI:https://doi.org/10.1103/PhysRevB.104.115308

Physics Subject Headings (PhySH)

Quantum control Quantum gates Quantum information with solid state qubits

Quantum dots

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & Technology

Authors & Affiliations

Ada Warren ¹, Utkan Güngördü^2,*, J. P. Kestner², Edwin Barnes¹, and Sophia E. Economou¹

¹Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
²Department of Physics, University of Maryland Baltimore County, Baltimore, Maryland 21250, USA

^*Current address: Laboratory for Physical Sciences, College Park, Maryland 20740, USA.

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Vol. 104, Iss. 11 — 15 September 2021

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Figure 1
Average fidelity of the cross-resonance cnot gate, maximized at each time step over local rotations. Here, we have chosen $ω_{r} = 6 GHz, ω_{1}^{z} = 5.96 GHz, ω_{2}^{z} = 5.94 GHz, ε_{1} = ε_{2} = 0, 2 t_{c 1} = 2 t_{c 2} = 7 GHz, g_{1}^{A C} = g_{2}^{A C} = 40 MHz$ , and $g_{1}^{x} = g_{2}^{x} = 200 MHz$ corresponding to a transverse magnetic field difference between the two QDs in each DQD of approximately $30 mT$ . Starting at time $t = 0$ , qubit 1 is subject to a microwave drive with ${\tilde{Ω}}_{1}$ chosen so that $Ω_{1}^{x} = 15 MHz$ and with drive frequency $ω_{1}^{d} = 5.9059 GHz$ . At time $t = 590 ns$ , the microwave drive is stopped. The final gate fidelity is between 98 and $99 %$ , with remaining infidelity primarily due to leakage to excited resonator states.
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Figure 2
The first-order charge noise sensitivities $(\partial x = \sum_{i} | \frac{\partial x}{\partial t_{c i}} |)$ of various system parameters at the charge degeneracy sweet spot $(ε_{1} = ε_{2} = 0)$ [20] with $ω_{r} = 6 GHz, t_{c 1} = t_{c 2} = t_{c}, g_{1}^{A C} = g_{2}^{A C} = 40 MHz$ , and $g_{1}^{x} = g_{2}^{x} = 200 MHz$ . (a) For a cross-resonance cnot with $ω_{1} = 5.96 GHz, ω_{2} = 5.94 GHz$ , and $Ω_{1}^{x} = 20 MHz$ . (b) For a resonant iswap with $ω_{1} = ω_{2} = 5.95 GHz$ . Leading-order sensitivities to DQD detunings are given in Appendix pp2.
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Figure 3
(a) Diagram for the different drive schemes used to generate a cross-resonance cnot. In either case, we have two qubits coupled via a microwave resonator with coupling strength $J$ . For the gate $U_{ϕ}^{(12)}$ , which is used in 2Qecho, both the control and target qubit are driven at the target qubit transition frequency. For the gate $U_{ϕ}^{(1)}$ , which is used in 1Qpartial and 1Qfull, only the control qubit is driven. (b) Circuit diagram for the 2Qecho corrected cnot. (c) Circuit diagram for the 1Qpartial corrected cnot or iswap, which corrects only the noncommuting errors. (d) Circuit diagram for the 1Qfull corrected cnot or iswap, which corrects both the commuting and noncommuting errors.
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Figure 4
Average gate infidelities for various amplitudes of quasistatic charge noise, starting from the noisy doubly rotating frame Hamiltonian. Here, we set $2 σ_{t} = σ_{ε} / 100$ and have again chosen $ω_{r} = 6 GHz, ε_{1} = ε_{2} = 0, 2 t_{c 1} = 2 t_{c 2} = 7 GHz, g_{1}^{A C} = g_{2}^{A C} = 40 MHz$ , and $g_{1}^{x} = g_{2}^{x} = 200 MHz$ . (a) For the iswap, we choose $ω_{1} = ω_{2} = 5.95 GHz$ and plot infidelity of the uncorrected gate $U_{π}$ as well as the corrected 1Qfull. (b) For the cross-resonance cnot, we present gate fidelities both with ( $σ_{μ} = 0.01$ ) (upper frame) and without control field amplitude noise (lower frame). We choose $ω_{1} = 5.96 GHz, ω_{2} = 5.94 GHz$ , and $Ω_{1}^{x} = 28.5 MHz$ , which tunes us to the $δ η = 0$ sweet spot. Here, in addition to the uncorrected gate $U_{π / 2}^{(1)}$ and 1Qfull, we also plot the infidelity of 1Qpartial, as well as the infidelity of 2Qecho with $Ω_{2}^{x} = 15 MHz$ .
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Figure 5
Second-order sensitivity to DQD detunings $(\partial^{2} x = \frac{1}{2} \sum_{i} | \frac{\partial^{2} x}{\partial ε_{i}^{2}} |)$ of various system parameters at the charge degeneracy sweet spot $(ε_{1} = ε_{2} = 0)$ with $ω_{r} = 6 GHz, t_{c 1} = t_{c 2} = t_{c}, g_{1}^{A C} = g_{2}^{A C} = 40 MHz$ , and $g_{1}^{x} = g_{2}^{x} = 200 MHz$ . (a) For a cross-resonance cnot with $ω_{1} = 5.96 GHz, ω_{2} = 5.94 GHz$ , and $Ω_{1}^{x} = 20 MHz$ . (b) For a resonant iswap with $ω_{1} = ω_{2} = 5.95 GHz$ .
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