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Laser Physics Letters

Gaussian soft control for controlled- Z gate on superconducting qubits with unilateral external driving

Qianyu Zhu, Cheng Lü, Jin‐Lei Wu, Yan Li

Published Aug 4, 2022• 5 citations
Publisher

Abstract

Abstract Soft quantum control is a valid technique for highly selective interactions recently illustrated in Haase et al (2018 Phys. Rev. Lett. 121 050402), holding efficient resonant couplings among target levels while largely suppressing unwanted off-resonant contributions. Here we present a model for implementing a controlled- Z (CZ) gate in superconducting circuit quantum electrodynamics (QED) with two qubits being coupled to a microwave cavity. An external classical field that drives only one qubit, combined with the strong single-mode quantized cavity field dressing both qubits, is employed to induce the CZ gate between two qubits, and is also further tailored as a Gaussian soft control (GSC) to improve gate performances in various aspects. By contrast, we show that, with the same gate time, the CZ gate based on GSC can hold a higher fidelity, greater resilience to parameter errors, and stronger robustness against decoherence of system than that based on a rectangular pulse.

DOI
10.1088/1612-202x/ac83c2

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Abstract Soft quantum control is a valid technique for highly selective interactions recently illustrated in Haase et al (2018 Phys. Rev. Lett. 121 050402), holding efficient resonant couplings among target levels while largely suppressing unwanted off-resonant contributions. Here we present a model for implementing a controlled- Z (CZ) gate in superconducting circuit quantum electrodynamics (QED) with two qubits being coupled to a microwave cavity. An external classical field that drives only one qubit, combined with the strong single-mode quantized cavity field dressing both qubits, is employed to induce the CZ gate between two qubits, and is also further tailored as a Gaussian soft control (GSC) to improve gate performances in various aspects. By contrast, we show that, with the same gate time, the CZ gate based on GSC can hold a higher fidelity, greater resilience to parameter errors, and stronger robustness against decoherence of system than that based on a rectangular pulse.
Hybrid atom-photon gates play an important role for the realization of a quantum interface capable of mapping atomic states to photons for communication across quantum networks. Here, we propose a feasible theoretical scheme for implementing a hybrid atom-photon controlled-Z gate between an atom and a microwave photon in a superconducting coplanar waveguide resonator based on the Gaussian soft control technique. The gate protocol employs a classical auxiliary field that induces an atomic transition between one state of the atomic qubit and Rydberg states for obtaining strong coupling of the atom and microwave resonator. By tailoring the amplitude of this field with Gaussian temporal modulation, the gate performances are improved in various aspects. Numerical simulations demonstrate that the controlled-Z gate based on Gaussian soft control is resilient to the variation of the atom-photon coupling strength and deviation in the gate time, and it is less sensitive to the Rydberg level shifts caused by stray electric fields.
Hybrid atom-photon gates play an important role for the realization of a quantum interface capable of mapping atomic states to photons for communication across quantum networks. Here, we propose a feasible theoretical scheme for implementing a hybrid atom-photon controlled-Z gate between an atom and a microwave photon in a superconducting coplanar waveguide resonator based on the Gaussian soft control technique. The gate protocol employs a classical auxiliary field that induces an atomic transition between one state of the atomic qubit and Rydberg states for obtaining strong coupling of the atom and microwave resonator. By tailoring the amplitude of this field with Gaussian temporal modulation, the gate performances are improved in various aspects. Numerical simulations demonstrate that the controlled-Z gate based on Gaussian soft control is resilient to the variation of the atom-photon coupling strength, deviation in the gate time, and less sensitive to the Rydberg level shifts caused by stray electric fields.
A possible building block for a scalable quantum computer has recently been demonstrated [Mariantoni et al., Science 334, 61 (2011)]. This architecture consists of superconducting qubits capacitively coupled both to individual memory resonators as well as a common bus. In this work we study a natural primitive entangling gate for this and related resonator-based architectures, which consists of a controlled-${\ensuremath{\sigma}}^{z}$ (cz) operation between a qubit and the bus. The cz gate is implemented with the aid of the noncomputational qubit $|2\ensuremath{\rangle}$ state [Strauch et al., Phys. Rev. Lett. 91, 167005 (2003)]. Assuming phase or transmon qubits with 300 MHz anharmonicity, we show that by using only low frequency qubit-bias control it is possible to implement the qubit-bus cz gate with 99.9% (99.99%) fidelity in about 17ns17\phantom{\rule{0.16em}{0ex}}\mathrm{ns}17ns (23ns23\phantom{\rule{0.16em}{0ex}}\mathrm{ns}23ns) with a realistic two-parameter pulse profile, plus two auxiliary zzz rotations. The fidelity measure we refer to here is a state-averaged intrinsic process fidelity, which does not include any effects of noise or decoherence. These results apply to a multiqubit device that includes strongly coupled memory resonators. We investigate the performance of the qubit-bus cz gate as a function of qubit anharmonicity, identify the dominant intrinsic error mechanism and derive an associated fidelity estimator, quantify the pulse shape sensitivity and precision requirements, simulate qubit-qubit cz gates that are mediated by the bus resonator, and also attempt a global optimization of system parameters including resonator frequencies and couplings. Our results are relevant for a wide range of superconducting hardware designs that incorporate resonators and suggest that it should be possible to demonstrate a 99.999.9%99.9 cz gate with existing transmon qubits, which would constitute an important step towards the development of an error-corrected superconducting quantum computer.
Construction of optimal gate operations is significant for quantum computation. Here an efficient scheme is proposed for performing shortcut-based quantum gates on superconducting qubits in circuit quantum electrodynamics (QED). Two four-level artificial atoms of Cooper-pair box circuits, having sufficient level anharmonicity, are placed in a common quantized field of circuit QED and are driven by individual classical microwaves. Without the effect of cross resonance, one-qubit NOT gate and phase gate in a decoupled atom can be implemented using the invariant-based shortcuts to adiabaticity. With the assistance of cavity bus, a one-step SWAP gate can be obtained within a composite qubit-photon-qubit system by inversely engineering the classical drivings. We further consider the gate realizations by adjusting the microwave fields. With the accessible decoherence rates, the shortcut-based gates have high fidelities. The present strategy could offer a promising route towards fast and robust quantum computation with superconducting circuits experimentally.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZZZZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off-resonantly. We show tunable coupling over one order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave crosstalk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)%99.43(1)\%99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.
Generating high-fidelity, tunable entanglement between qubits is crucial for realizing gate-based quantum computation. In superconducting circuits, tunable interactions are often implemented using flux-tunable qubits or coupling elements, adding control complexity and noise sources. Here, we realize a tunable ZZ interaction between two transmon qubits with fixed frequencies and fixed coupling, induced by driving both transmons off resonantly. We show tunable coupling over 1 order of magnitude larger than the static coupling, and change the sign of the interaction, enabling cancellation of the idle coupling. Further, this interaction is amenable to large quantum processors: the drive frequency can be flexibly chosen to avoid spurious transitions, and because both transmons are driven, it is resilient to microwave cross talk. We apply this interaction to implement a controlled phase (CZ) gate with a gate fidelity of 99.43(1)% as measured by cycle benchmarking, and we find the fidelity is limited by incoherent errors.