Quantum Two-Level Systems in Josephson Junctions as Naturally Formed Qubits

The two-level systems (TLSs) naturally occurring in Josephson junctions constitute a major obstacle for the operation of superconducting phase qubits. Since these TLSs can possess remarkably long decoherence times, we show that such TLSs can themselves be used as qubits, allowing for a well controlled initialization, universal sets of quantum gates, and readout. Thus, a single current-biased Josephson junction can be considered as a multiqubit register. It can be coupled to other junctions to allow the application of quantum gates to an arbitrary pair of qubits in the system. Our results indicate an alternative way to realize superconducting quantum information processing.

Figure 1

Fidelity of the ISWAP gate on two TLS qubits in a CBJJ as a function of the relative difference between the TLS energy splittings (${\Delta }_1$ and ${\Delta }_2$, respectively). The solid line corresponds to no decoherence; the dashed and dotted lines correspond to CBJJ decoherence rates ${\Gamma }_1=\lambda /20\pi$ and ${\Gamma }_1=\lambda /2\pi$, respectively, where in both cases ${\Gamma }_2=2{\Gamma }_1$. The much slower decoherence of the TLSs have been neglected. $\lambda =0.005{\Delta }_1$. Inset: Schematic depiction of the quantum beats between the CBJJ and the ${\mathrm{TLS}}_1$ in resonance; ${\mathrm{TLS}}_2$ is effectively decoupled from the CBJJ.

Figure 2

Scalability of the structure: Two-qubit operations between the TLSs on different CBJJs ($j=1,\dots ,N$) are enabled by the common LC circuit, which is capacitively coupled to the CBJJs. The Josephson energy, capacitance, and bias current of the $j$th CBJJ are $E_j$, $C_j$, and $I_j$, respectively.