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Investigation of Two Qubit Gates between Remote Spin Qubits using a Superconducting Coupler

Harry Hanlim Kang

Published Feb 1, 2025• 0 citations
OpenAlex

Abstract

Circuit QED elements can facilitate entanglement generation between distant spin qubits, acting as a quantum bus to connect different parts of future spin-based quantum processors. Here, microwave-activated phase gates between two remote, gate-defined spin qubits, where an offset-charge-sensitive (OCS) transmon coupler is driven, are proposed. The spin qubits, specifically resonant-exchange (RX) qubits, are longitudinally coupled to the coupler such that the coupler’s frequency depends on the logical states of the qubits. The capacitance network model is used to describe the coupling between the quantum dots and the coupler, using first-quantized charge operators instead of second quantized field operators. Two pulse sequences are investigated: a faster, off-resonant drive pulse with constant amplitude, and a pulse with envelope engineering that incorporates dynamical decoupling to mitigate charge noise. The main source of decoherence for the system is the 1/f ᵝ charge noise, with β ∼ 1. The non-Markovian time-domain simulations in the presence of charge noise are employed to accurately predict the gate performance. Simulation results suggest that a CZ gate fidelity exceeding 90% is possible with realistic parameters and noise models.

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Tunable couplers have recently become one of the most powerful tools for implementing two-qubit gates between superconducting qubits.A tunable coupler typically includes a nonlinear element, such as a superconducting quantum interference device, which is used to tune the resonance frequency of an LC circuit connecting two qubits.Here we propose a complimentary approach where instead of tuning the resonance frequency of the tunable coupler by applying a quasistatic control signal, we excite by microwave the degree of freedom associated with the coupler itself.Because of strong effective longitudinal coupling between the coupler and the qubits, the frequency of this transition strongly depends on the computational state, leading to different phase accumulations in different states.Using this method, we experimentally demonstrate a controlled-Z gate of 44-ns duration on a fluxonium-based quantum processor, obtaining a fidelity of 97.6% ± 0.4% characterized by cross-entropy benchmarking.

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Circuit QED elements can facilitate entanglement generation between distant spin qubits, acting as a quantum bus to connect different parts of future spin-based quantum processors. Here, microwave-activated phase gates between two remote, gate-defined spin qubits, where an offset-charge-sensitive (OCS) transmon coupler is driven, are proposed. The spin qubits, specifically resonant-exchange (RX) qubits, are longitudinally coupled to the coupler such that the coupler’s frequency depends on the logical states of the qubits. The capacitance network model is used to describe the coupling between the quantum dots and the coupler, using first-quantized charge operators instead of second quantized field operators. Two pulse sequences are investigated: a faster, off-resonant drive pulse with constant amplitude, and a pulse with envelope engineering that incorporates dynamical decoupling to mitigate charge noise. The main source of decoherence for the system is the 1/f ᵝ charge noise, with β ∼ 1. The non-Markovian time-domain simulations in the presence of charge noise are employed to accurately predict the gate performance. Simulation results suggest that a CZ gate fidelity exceeding 90% is possible with realistic parameters and noise models.
We propose a method to realize microwave-activated cz gates between two remote spin qubits in quantum dots using a charge-sensitive superconducting coupler. The qubits are longitudinally coupled to the coupler, such that the transition frequency of the coupler depends on the logical qubit states; a capacitive network model using first-quantized charge operators is developed to illustrate this. Driving the coupler transition then implements a conditional phase shift on the qubits. Two pulsing schemes are investigated: a rapid, off-resonant pulse with constant amplitude, and a pulse with envelope engineering that incorporates dynamical decoupling to mitigate charge noise. We develop non-Markovian time-domain simulations to accurately model gate performance in the presence of $1/{f}^{\ensuremath{\beta}}$ charge noise. Simulation results indicate that a cz gate fidelity exceeding 90% is possible with realistic parameters and noise models.
Two qubit gates constitute fundamental building blocks in the realization of large-scale quantum devices. Using superconducting circuits, two-qubit gates have previously been implemented in different ways with each method aiming to maximize gate fidelity. Another important goal of a new gate scheme is to minimize the complexity of gate calibration. In this work, we demonstrate a high-fidelity two-qubit gate between two fluxonium qubits enabled by an intermediate capacitively coupled transmon. The coupling strengths between the qubits and the coupler are designed to minimize residual crosstalk while still allowing for fast gate operations. The gate is based on frequency selectively exciting the coupler using a microwave drive to complete a 2πππ rotation, conditional on the state of the fluxonium qubits. When successful, this drive scheme implements a conditional phase gate. Using analytically derived pulse shapes, we minimize unwanted excitations of the coupler and obtain gate errors of 10−210^{-2}10−2 for gate times below 60~ns. At longer durations, our gate is limited by relaxation of the coupler. Our results show how carefully designed control pulses can speed up frequency selective entangling gates.
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.
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.
Tunable couplers have recently become one of the most powerful tools for implementing two-qubit gates between superconducting qubits.A tunable coupler typically includes a nonlinear element, such as a superconducting quantum interference device, which is used to tune the resonance frequency of an LC circuit connecting two qubits.Here we propose a complimentary approach where instead of tuning the resonance frequency of the tunable coupler by applying a quasistatic control signal, we excite by microwave the degree of freedom associated with the coupler itself.Because of strong effective longitudinal coupling between the coupler and the qubits, the frequency of this transition strongly depends on the computational state, leading to different phase accumulations in different states.Using this method, we experimentally demonstrate a controlled-Z gate of 44-ns duration on a fluxonium-based quantum processor, obtaining a fidelity of 97.6% ± 0.4% characterized by cross-entropy benchmarking.