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Physical Review A

One-step generation of cluster states in superconducting charge qubits coupled with a nanomechanical resonator

Gang Chen, Zidong Chen, Lixian Yu, Jiu‐Qing Liang

Published Aug 6, 2007• 44 citations
Publisher

Abstract

We present a scalable solid-state system in which the superconducting charge qubits are coupled with a nanomechanical resonator (NAMR) to achieve highly entangled cluster states, which are responsible for one-way quantum computing via single-qubit measurements. Since the NAMR can play the essential role of the data bus, the long-range interactions among the qubits can occur. Therefore, without using the interacting picture we can directly obtain the long-range Ising-like unitary operator ${U}_{z}(\ensuremath{\lambda})=\mathrm{exp}[i\ensuremath{\lambda}{S}_{z}^{2}]$ with ${S}_{z}$ the collective spin operator in $z$ direction and $\ensuremath{\lambda}$ a parameter, which is insensitive to the thermal state of the NAMR. Based on this unitary operator, a set of highly entangled cluster states can be produced by efficient one-step generation. Moreover, the robustness of the highly entangled cluster states with respect to unavoidable parameter variations is also demonstrated.

DOI
10.1103/physreva.76.024301

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We present a scalable solid-state system in which the superconducting charge qubits are coupled with a nanomechanical resonator (NAMR) to achieve highly entangled cluster states, which are responsible for one-way quantum computing via single-qubit measurements. Since the NAMR can play the essential role of the data bus, the long-range interactions among the qubits can occur. Therefore, without using the interacting picture we can directly obtain the long-range Ising-like unitary operator Uz(\ensuremathλ)=exp[i\ensuremathλSz2]{U}_{z}(\ensuremath{\lambda})=\mathrm{exp}[i\ensuremath{\lambda}{S}_{z}^{2}]Uz​(\ensuremathλ)=exp[i\ensuremathλSz2​] with Sz{S}_{z}Sz​ the collective spin operator in zzz direction and \ensuremathλ\ensuremath{\lambda}\ensuremathλ a parameter, which is insensitive to the thermal state of the NAMR. Based on this unitary operator, a set of highly entangled cluster states can be produced by efficient one-step generation. Moreover, the robustness of the highly entangled cluster states with respect to unavoidable parameter variations is also demonstrated.
We propose theoretical schemes to generate highly entangled cluster state with superconducting qubits in a circuit QED architecture. Charge qubits are located inside a superconducting transmission line, which serves as a quantum data bus. We show that large clusters state can be efficiently generated in just one step with the long-range Ising-like unitary operators. The quantum operations which are generally realized by two coupling mechanisms: either voltage coupling or current coupling, depend only on global geometric features and are insensitive not only to the thermal state of the transmission line but also to certain random operation errors. Thus high-fidelity one-way quantum computation can be achieved.
Highly entangled states called cluster states are a universal resource for measurement-based quantum computing (QC). Here we propose an efficient method for producing large cluster states using superconducting quantum circuits. We show that a large cluster state can be efficiently generated in just one step by turning on the interqubit coupling for a short time. Because the interqubit coupling is only switched on during the time interval for generating the cluster state, our approach is also convenient for preparing the initial state for each qubit and for implementing one-way QC via single-qubit measurements. Moreover, the cluster state is robust against parameter variations.
Based on superconducting charge qubits (SCCQs) coupled to a single-mode microwave cavity, we propose a scheme for generating charge cluster states. For all SCCQs, the controlled gate voltages are all in their degeneracy points, the quantum information is encoded in two logic states of charge basis. The generation of the multi-qubit cluster state can be achieved step by step on a pair of nearest-neighbor qubits. Considering effective long-rang coupling, we provide an efficient way to one-step generating of a highly entangled cluster state, in which the qubit-qubit coupling is mediated by the cavity mode. Our quantum operations are insensitive to the initial state of the cavity mode by removing the influence of the cavity mode via the periodical evolution of the system. Thus, our operation may be against the decoherence from the cavity.
We propose a method to efficiently generate cluster states in charge qubits, both semiconducting and superconducting, as well as flux qubits. We show that highly entangled cluster states can be realized by a "one-touch" entanglement operation by tuning gate bias voltages for charge qubits. We also investigate the robustness of these cluster states for nonuniform qubits, which are unavoidable in solid-state systems. We find that quantum computation based on cluster states is a promising approach for solid-state qubits.
We propose a scheme for generating squeezed states of a nanomechanical resonator. The scheme is based on a hybrid system consisting of two NAMRs and a superconducting charge qubit (SCCQ). The nonlinear interaction between the two nanomechanical resonators (NAMRs) can be implemented by setting the external biased flux of the SCCQ at some certain values, which plays the role of “nonlinear media”. The noise in the SCCQ does not need to be considered, since we can adiabatically keep the SCCQ at the ground state. In addition, the squeezing parameters can also be adjusted by changing the external driving voltage.
We propose a simple unconventional geometric scenario to achieve a kind of nontrivial multiqubit operation with superconducting charge qubits placed in a microwave cavity. The proposed quantum operations are insensitive not only to the thermal state of the cavity mode but also to certain random operation errors, and thus may lead to high-fidelity quantum-information processing. By executing the designated quantum operations, a class of highly entangled cluster states may be generated efficiently in the present scalable solid-state system, enabling one to achieve one-way quantum computation.