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Physical Review A

Fast quantum phase gate in a small-detuning circuit QED model

Chun-Wang Wu, Han Yang, Hongyi Li, Zhi-Jiao Deng, Ping‐Xing Chen, Cheng-Zu Li

Published Jul 23, 2010• 19 citations
Publisher

Abstract

We propose a theoretical protocol for a quantum phase gate between two transmon qubits capacitively coupled to a superconducting transmission line resonator driven by a strong microwave field. Compared with previous protocols involving a dispersive regime, our protocol works at a small detuning, $\ensuremath{\Delta}~g$, and the nontrivial two-qubit gates can be realized in a short time, $~$$1/g$, where $g$ is the qubit-resonator coupling strength. Our analysis shows that the protocol is robust against the main decoherence sources and unavoidable parameter variations. Moreover, our protocol can be implemented using the current experimental design of circuit QED.

DOI
10.1103/physreva.82.014303

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We propose a theoretical protocol for a quantum phase gate between two transmon qubits capacitively coupled to a superconducting transmission line resonator driven by a strong microwave field. Compared with previous protocols involving a dispersive regime, our protocol works at a small detuning, \ensuremathΔ g\ensuremath{\Delta}~g\ensuremathΔ g, and the nontrivial two-qubit gates can be realized in a short time, ~$$1/g, where ggg is the qubit-resonator coupling strength. Our analysis shows that the protocol is robust against the main decoherence sources and unavoidable parameter variations. Moreover, our protocol can be implemented using the current experimental design of circuit QED.
Stark shift on a superconducting qubit in circuit quantum electrodynamics (QED) has been used to construct universal quantum entangling gates on superconducting resonators in previous works. It is a second-order coupling effect between the resonator and the qubit in the dispersive regime, which leads to a slow state-selective rotation on the qubit. Here, we present two proposals to construct the fast universal quantum gates on superconducting resonators in a microwave-photon quantum processor composed of multiple superconducting resonators coupled to a superconducting transmon qutrit, that is, the controlled-phase (c-phase) gate on two microwave-photon resonators and the controlled-controlled phase (cc-phase) gates on three resonators, resorting to quantum resonance operations, without any drive field. Compared with previous works, our universal quantum gates have the higher fidelities and shorter operation times in theory. The numerical simulation shows that the fidelity of our c-phase gate is 99.57% within about 38.1 ns and that of our cc-phase gate is 99.25% within about 73.3 ns.
We propose a method for realizing a quantum phase gate of one qubit simultaneously controlling [Formula: see text] target qubits based on the qubit–qubit interaction. We show how to implement the proposed gate with one transmon qubit simultaneously controlling [Formula: see text] transmon qubits in a circuit QED driven by a strong microwave field. In our scheme, the operation time of this phase gate is independent of the number [Formula: see text] of qubits. On the other hand, this gate can be realized in a time of nanosecond-scale much smaller than the decoherence time and dephasing time both being the time of microsecond-scale. Numerical simulation of the occupation probabilities of the second excited lever shows that the scheme could be achieved efficiently within current technology.
The latest technological progress of achieving the ultrastrong-coupling regime in circuit quantum electrodynamics (QED) systems has greatly promoted the developments of quantum physics, where novel quantum optics phenomena and potential computational benefits have been predicted. Here, we propose a scheme to accelerate the nontrivial two-qubit phase gate in a circuit QED system, where superconducting flux qubits are ultrastrongly coupled to a transmission line resonator (TLR), and two more TLRs are coupled to the ultrastrongly-coupled system for assistant. The nontrivial unconventional geometric phase gate between the two flux qubits is achieved based on close-loop displacements of the three-mode intracavity fields. Moreover, as there are three resonators contributing to the phase accumulation, the requirement of the coupling strength to realize the two-qubit gate can be reduced. Further reduction in the coupling strength to achieve a specific controlled-phase gate can be realized by adding more auxiliary resonators to the ultrastrongly-coupled system through superconducting quantum interference devices. We also present a study of our scheme with realistic parameters considering imperfect controls and noisy environment. Our scheme possesses the merits of ultrafastness and noise-tolerance due to the advantages of geometric phases.
We theoretically study single and two-qubit dynamics in the circuit QED architecture. We focus on the current experimental design [Wallraff et al., Nature (London) 431, 162 (2004); Schuster et al., Nature (London) 445, 515 (2007)] in which superconducting charge qubits are capacitively coupled to a single high-QQQ superconducting coplanar resonator. In this system, logical gates are realized by driving the resonator with microwave fields. Advantages of this architecture are that it allows for multiqubit gates between non-nearest qubits and for the realization of gates in parallel, opening the possibility of fault-tolerant quantum computation with superconduting circuits. In this paper, we focus on one- and two-qubit gates that do not require moving away from the charge-degeneracy ``sweet spot.'' This is advantageous as it helps to increase the qubit dephasing time and does not require modification of the original circuit QED. However, these gates can, in some cases, be slower than those that do not use this constraint. Five types of two-qubit gates are discussed, these include gates based on virtual photons, real excitation of the resonator, and a gate based on the geometric phase. We also point out the importance of selection rules when working at the charge degeneracy point.
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.
We propose a theoretical scheme for realizing the general conditional phase shift gate of charge qubits situated in a high-Q superconducting transmission line resonator. The phase shifting angle can be tuned from 0 to 2π by simply adjusting the qubit-resonator detuning and the interaction time. Based on this gate proposal, we give a detailed procedure to implement the three-qubit quantum Fourier transform with circuit quantum electrodynamics (QED). A careful analysis of the decoherence sources shows that the algorithm can be achieved with a high fidelity using current circuit QED techniques.