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Communications in Theoretical Physics

Effect of Multiphoton Processes on Geometric Quantum Computation in Superconducting Circuit QED

Changyong Chen

Published Nov 1, 2012• 0 citations
Publisher

Abstract

We study the influence of multi-photon processes on the geometric quantum computation in the systems of superconducting qubits based on the displacement-like and the general squeezed operator methods. As an example, we focus on the question about how to implement a two-qubit geometric phase gate using superconducting circuit quantum electrodynamics with both single- and two-photon interaction between the qubits and the cavity modes. We find that the multiphoton processes are not only controllable but also improve the gating speed. The comparison with other physical systems and experimental feasibility are discussed in detail.

DOI
10.1088/0253-6102/58/5/06

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We study the influence of multi-photon processes on the geometric quantum computation in the systems of superconducting qubits based on the displacement-like and the general squeezed operator methods. As an example, we focus on the question about how to implement a two-qubit geometric phase gate using superconducting circuit quantum electrodynamics with both single- and two-photon interaction between the qubits and the cavity modes. We find that the multiphoton processes are not only controllable but also improve the gating speed. The comparison with other physical systems and experimental feasibility are discussed in detail.
We give the brief review on the related definition of the geometric phase independent of specific physical system based on the displacement opreator and the sqeezed operator, then show how the displacement operator and the squeezed operator can induce the general geometric phase. By means of the displacement operator and the squeezed operator concerning the circuit cavity mode state along a closed path in the phase space, we discuss specifically how to implement a two-qubit geometric phase gate in circuit quantum electrodynamics with both single photon interaction and two-photon interaction between the superconducting qubits and the circuit cavity modes. The experimental feasibility is discussed in detail.
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.
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.
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.
We introduce the general definition of the unconventional geometric phase independent of the specific physical system and show how a highly squeezed operator can approximately induce the general unconventional geometric phase, which goes beyond the original unconventional one by displacement operators (Zhu and Wang 2003 Phys. Rev. Lett. 91 187902). By means of the squeezed operator concerning the cavity mode state along a closed path in the phase space, we discuss specifically how to implement approximately a two-qubit geometric phase gate in a cavity QED system with two-photon interaction between the atoms and the cavity mode, assisted by a classical field. Discussions regarding the implementation time of the gating, the possible decaying sources and the experimental feasibility are given in detail.