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arXiv:1810.07894 · Physical Review A

Implementation of a generalized controlled-NOT gate between fixed-frequency transmons

Shavindra Premaratne, Jen-Hao Yeh, F. C. Wellstood, B. S. Palmer

Published Jan 11, 2019• 25 citations
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Abstract

We have embedded two fixed-frequency ${\mathrm{Al}/\mathrm{AlO}}_{x}$/Al transmons, with ground-to-excited transition frequencies at 6.0714 and 6.7543 GHz, in a single three-dimensional Al cavity with a fundamental mode at 7.7463 GHz. Strong coupling between the cavity and each transmon results in an effective qubit-qubit coupling strength of 26 MHz and a $\ensuremath{-}1$ MHz dispersive shift in each qubit's transition frequency, depending on the state of the other qubit. Using the all-microwave SWIPHT (speeding up wave forms by inducing phases to harmful transitions) technique [Economou and Barnes, Phys. Rev. B 91, 161405 (2015)], we demonstrate the operation of a generalized controlled-not gate between the two qubits, with a gate time of ${\ensuremath{\tau}}_{g}=907$ ns optimized for this device. Using quantum process tomography we find that the gate fidelity is 83--84%, somewhat less than the 87% fidelity expected from relaxation and dephasing in the transmons during the gate time.

DOI
10.1103/physreva.99.012317

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We have embedded two fixed-frequency Al/AlOx{\mathrm{Al}/\mathrm{AlO}}_{x}Al/AlOx​/Al transmons, with ground-to-excited transition frequencies at 6.0714 and 6.7543 GHz, in a single three-dimensional Al cavity with a fundamental mode at 7.7463 GHz. Strong coupling between the cavity and each transmon results in an effective qubit-qubit coupling strength of 26 MHz and a \ensuremath−1\ensuremath{-}1\ensuremath−1 MHz dispersive shift in each qubit's transition frequency, depending on the state of the other qubit. Using the all-microwave SWIPHT (speeding up wave forms by inducing phases to harmful transitions) technique [Economou and Barnes, Phys. Rev. B 91, 161405 (2015)], we demonstrate the operation of a generalized controlled-not gate between the two qubits, with a gate time of \ensuremathτg=907{\ensuremath{\tau}}_{g}=907\ensuremathτg​=907 ns optimized for this device. Using quantum process tomography we find that the gate fidelity is 83--84%, somewhat less than the 87% fidelity expected from relaxation and dephasing in the transmons during the gate time.
Superconducting transmon qubits comprise one of the most promising platforms for quantum information processing due to their long coherence times and to their scalability into larger qubit networks. However, their weakly anharmonic spectrum leads to spectral crowding in multiqubit systems, making it challenging to implement fast, high-fidelity gates while avoiding leakage errors. To address this challenge, we use a protocol for speeding up waveforms by inducing phases to harmful transitions (SWIPHT) [S. E. Economou and E. Barnes, Phys. Rev. B 91, 161405(R) (2015)], which yields smooth, simple microwave pulses designed to suppress leakage without sacrificing gate speed through spectral selectivity. Here, we determine the parameter regimes in which SWIPHT is effective and demonstrate that in these regimes, it systematically produces two-qubit gate fidelities for cavity-coupled transmons in the range 99.6%--99.9% with gate times as fast as 23 ns. Our results are obtained from full numerical simulations that include current experimental levels of relaxation and dephasing. These high fidelities persist over a wide range of system parameters that encompass many current experimental setups and are insensitive to small parameter variations and pulse imperfections.
We implemented all-microwave two qubit entanglement scheme via Stark shift-induced controlled phase gate, as suggested by J. Chow et al., [1]. Our system consists of two superconducting transmon qubits, one of which is a tunable-frequency qubit and the other is a fixed-frequency qubit, embedded in a three dimensional copper cavity. As we align higher quantum states outside the computational states, i.e., \\textbar 12\\textgreater and \\textbar 03\\textgreater , we could achieve controlled phase gate by applying a microwave tone which induces the Stark shift. The gate time can be controlled depending on how close we align the levels. We will present our results on the estimation of the fidelity of generated Bell states with tomographic reconstruction of the two-qubit states as a function of the gate time. [1] J. Chow et al., New J. Phys. 15, 115012 (2013).
Entangling gates between neighboring physical qubits are essential for quantum error correction. Implementing them in an all-microwave manner simplifies signal routing and control apparatus of superconducting quantum processors. We propose and experimentally demonstrate an all-microwave controlled-Z (CZ) gate that achieves high fidelity while suppressing residual ZZ interactions. Our approach utilizes a fixed-frequency transmon coupler and multi-path coupling, thereby sufficiently reducing the net transverse interaction between data transmons to suppress residual ZZ interactions. The controlled phase arises from the dispersive frequency shift of the ∣gf⟩|gf\rangle∣gf⟩$\unicode{x2013}$∣eg⟩|eg\rangle∣eg⟩ transition between the coupler and one of the data transmons conditioned on the state of the other data transmon. Driving the transitions at the midpoint of two dispersively shifted resonance frequencies induces state-dependent geometric phases to achieve the CZ gate. Crucially, with this scheme, we can maintain a small net transverse interaction between two data transmons while increasing the coupling between the data and coupler transmons to accelerate the CZ-gate speed. Additionally, we measure the coupler state after the gate to detect a subset of decoherence-induced failures that occur during the gate operation. These events constitute erasure errors with known locations, enabling erasure-aware quantum error-correcting codes to improve future logical qubit performance.
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.
All-microwave control of fixed-frequency superconducting quantum systems offers the potential to reduce control circuit complexity and increase system coherence. Nevertheless, due to the limited control flexibility in qubit parameters, one has to address several issues, such as quantum crosstalk and frequency crowding, for scaling up qubit architecture with nontunable elements. This paper proposes a microwave-activated two-qubit gate scheme for two fixed-frequency transmon qubits coupled via a fixed-frequency transmon coupler. The protocol relies on applying a microwave pulse exclusively to the coupler, enabling the implementation of a controlled-ZZZ gate. We show that the gate fidelity exceeding 0.999 can be achieved within 150 ns, excluding decoherence effects. Moreover, we also show that leakage from the computational subspace to noncomputational states can also be effectively suppressed.
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.