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Physical Review A

Microwave-driven i swap-like gate for fixed-frequency superconducting transmon qutrits

Peng Xu, Qingli Jing, Peng Zhao, Yang Yu

Published Sep 26, 2023• 10 citations
Publisher

Abstract

High-fidelity two-qubit gates are crucial for the scalability of superconducting quantum processors. While quantum information processing is typically based on qubits, qutrits (or qudits) provide a larger state space for quantum information storage and processing. In this study, we analyze a high-fidelity two-qutrit gate using microwave pulses on fixed-frequency superconducting transmon qutrits and show that a high-fidelity imaginary swap-like ($i$swap-like) gate can be achieved. Perturbation theory is employed to derive an effective interaction Hamiltonian, allowing us to estimate the gate time for the two-qutrit system. Moreover, by employing a microwave-activation scheme, we can realize a high-fidelity $i$swap-like gate on different excited states of the two qutrits. Our numerical results indicate that the proposed scheme can be readily extended to multiqutrit scenarios. Additionally, we investigate the impact of microwave pulse ramp time and qutrit relaxation on gate fidelity. The results demonstrate that, with a longer ramp time and the currently accessible qutrit relaxation time, the gate error remains sufficiently small. This proposed gate scheme enables the implementation of qutrit-qutrit entangling gates, providing a promising approach to realizing superconducting quantum computation.

DOI
10.1103/physreva.108.032615

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High-fidelity two-qubit gates are crucial for the scalability of superconducting quantum processors. While quantum information processing is typically based on qubits, qutrits (or qudits) provide a larger state space for quantum information storage and processing. In this study, we analyze a high-fidelity two-qutrit gate using microwave pulses on fixed-frequency superconducting transmon qutrits and show that a high-fidelity imaginary swap-like (iiiswap-like) gate can be achieved. Perturbation theory is employed to derive an effective interaction Hamiltonian, allowing us to estimate the gate time for the two-qutrit system. Moreover, by employing a microwave-activation scheme, we can realize a high-fidelity iiiswap-like gate on different excited states of the two qutrits. Our numerical results indicate that the proposed scheme can be readily extended to multiqutrit scenarios. Additionally, we investigate the impact of microwave pulse ramp time and qutrit relaxation on gate fidelity. The results demonstrate that, with a longer ramp time and the currently accessible qutrit relaxation time, the gate error remains sufficiently small. This proposed gate scheme enables the implementation of qutrit-qutrit entangling gates, providing a promising approach to realizing superconducting quantum computation.
High-dimensional quantum systems, such as qutrits (quantum three-level systems), have multiple accessible energy levels beyond the two-level qubits. Therefore, qutrits can offer a larger state space to improve the efficiency of quantum computation. Here, we demonstrate a high-fidelity iSWAP-like gate operation on a frequency-tunable superconducting qutrits system. The superconducting quantum system consists of two qutrits that are coupled via a resonator with fixed qutrit-resonator coupling strengths. Through designing the frequency pulse profile and optimizing the parameter values, the gate error can be suppressed below 1.5 × 10−3. To bear out the feasibility of the proposal, we have conducted our study with experimentally accessible parameters. As the resonator can mediate the interaction between the irrelevant qutrits, the presented approach can also be used to couple multiple qutrits together, providing a good platform for quantum information processing.
High-fidelity iSWAP\sqrt{i\text{SWAP}}iSWAP​ gates using a fixed coupler driven by two microwave pulses
Attaining high-fidelity two-qubit gates represents a pivotal quantum operation for the realization of large-scale quantum computation and simulation. In this study, we propose a microwave-control protocol for the implementation of a two-qubit gate employing two transmon qubits coupled via a fixed-frequency transmon coupler. This protocol entails applying two microwave pulses exclusively to the coupler, thereby inducing interaction between the fixed-frequency transmon qubits. This interaction facilitates the realization of iSWAP\sqrt{i\text{SWAP}}iSWAP​ gates. Additionally, we explore the implementation of the gate scheme in two distinct qubit architectures. Demonstrating with experimentally accessible parameters, we show that high-fidelity iSWAP\sqrt{i\text{SWAP}}iSWAP​ gates can be achieved
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.
Achieving high-fidelity two-qubit gates is a key requirement for the realization of large-scale quantum computation and simulation. In this paper, we propose a microwave-control protocol for the implementation of a two-qubit gate employing two transmon qubits coupled via a fixed-frequency transmon coupler. This protocol entails applying two microwave pulses exclusively to the coupler, thereby inducing interaction between fixed-frequency transmon qubits. This interaction facilitates the realization of iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​ gates. Additionally, we explore the implementation of the gate scheme in two distinct qubit architectures (ABA and ABC). Without considering decoherence, the ABA architecture iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​ gate has a fidelity of 94.60% in 346 ns, while the ABC architecture achieves 99.63% in 378 ns. When considering the implementation of the iSWAP\sqrt{i\mathrm{SWAP}}iSWAP​-like gate, we show that gate fidelity can exceed 99.9% in both architectures.
A current bottleneck for quantum computation is the realization of high-fidelity two-qubit quantum operations between two or more quantum bits in arrays of coupled qubits. Gates based on parametrically driven tunable couplers offer a convenient method to entangle multiple qubits by selectively activating different interaction terms in the effective Hamiltonian. Here, we theoretically and experimentally study a superconducting qubit setup with two transmon qubits connected via a capacitively coupled tunable bus. We develop a time-dependent Schrieffer-Wolff transformation and derive analytic expressions for exchange-interaction gates swapping excitations between the qubits (iswap) and for two-photon gates creating and annihilating simultaneous two-qubit excitations (bswap). We find that the bswap gate is generally slower than the more commonly used iswap gate, but features favorable scalability properties with less severe frequency-crowding effects, which typically degrade the fidelity in multiqubit setups. Our theoretical results are backed by experimental measurements as well as exact numerical simulations including the effects of higher transmon levels and dissipation.
Abstract Ternary quantum information processing in superconducting devices poses a promising alternative to its more popular binary counterpart through larger, more connected computational spaces and proposed advantages in quantum simulation and error correction. Although generally operated as qubits, transmons have readily addressable higher levels, making them natural candidates for operation as quantum three-level systems (qutrits). Recent works in transmon devices have realized high fidelity single qutrit operation. Nonetheless, effectively engineering a high-fidelity two-qutrit entanglement remains a central challenge for realizing qutrit processing in a transmon device. In this work, we apply the differential AC Stark shift to implement a flexible, microwave-activated, and dynamic cross-Kerr entanglement between two fixed-frequency transmon qutrits, expanding on work performed for the Z Z interaction with transmon qubits. We then use this interaction to engineer efficient, high-fidelity qutrit CZ † and CZ gates, with estimated process fidelities of 97.3(1)% and 95.2(3)% respectively, a significant step forward for operating qutrits on a multi-transmon device.