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Physical review. B, Condensed matter

Design aspects of superconducting-phase quantum bits

G. Blatter, V. B. Geshkenbeǐn, L. B. Ioffe

Published Apr 11, 2001• 181 citations
Publisher

Abstract

A superconducting-phase quantum bit (qubit) involves three or more Josephson junctions combined into a superconducting loop and defines one of the promising solid-state device implementations for quantum computing. Recently, so called $\ensuremath{\pi}$ junctions, Josephson junctions with a ground state characterized by a \ensuremath{\pi}-phase shift across, have attracted much attention. We show how to make use of such $\ensuremath{\pi}$ junctions in the construction of superconducting phase qubits and discuss the advantage over conventional designs based on magnetically frustrated loops. Starting from a basic five-junction loop with one $\ensuremath{\pi}$ junction, we show how to construct effective junctions with degenerate minima characterized by phase shifts 0 and $\ensuremath{\pi}$ and superconducting-phase switches. These elements are then combined into a superconducting-phase qubit which operates exclusively with switches, thus avoiding permanent contact with the environment through external biasing. The resulting superconducting-phase qubits can be understood as the macroscopic analog of the ``quiet'' s-wave--d-wave--s-wave Josephson-junction qubits introduced by Ioffe et al. [Nature (London) 398, 679 (1999)].

DOI
10.1103/physrevb.63.174511

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A superconducting-phase quantum bit (qubit) involves three or more Josephson junctions combined into a superconducting loop and defines one of the promising solid-state device implementations for quantum computing. Recently, so called \ensuremathπ\ensuremath{\pi}\ensuremathπ junctions, Josephson junctions with a ground state characterized by a \ensuremath{\pi}-phase shift across, have attracted much attention. We show how to make use of such \ensuremathπ\ensuremath{\pi}\ensuremathπ junctions in the construction of superconducting phase qubits and discuss the advantage over conventional designs based on magnetically frustrated loops. Starting from a basic five-junction loop with one \ensuremathπ\ensuremath{\pi}\ensuremathπ junction, we show how to construct effective junctions with degenerate minima characterized by phase shifts 0 and \ensuremathπ\ensuremath{\pi}\ensuremathπ and superconducting-phase switches. These elements are then combined into a superconducting-phase qubit which operates exclusively with switches, thus avoiding permanent contact with the environment through external biasing. The resulting superconducting-phase qubits can be understood as the macroscopic analog of the ``quiet'' s-wave--d-wave--s-wave Josephson-junction qubits introduced by Ioffe et al. [Nature (London) 398, 679 (1999)].
The superconducting phase qubit combines Josephson junctions into superconducting loops and defines one of the promising solid state device implementations for quantum computing. While conventional designs are based on magnetically frustrated superconducting loops, here we discuss the advantages offered by πππ-junctions in obtaining naturally degenerate two-level systems. Starting from a basic five-junction loop, we show how to construct degenerate two-level junctions and superconducting phase switches. These elements are then effectively engineered into a superconducting phase qubit which operates exclusively with switches, thus avoiding permanent contact with the environment through external biasing. The resulting superconducting phase qubits can be understood as the macroscopic analogue of the `quiet' s-wave-d-wave-s-wave Josephson junction qubits introduced by Ioffe {\it et al.} [Nature {\bf 398}, 679 (1999)].
Superconducting flux qubits are a promising candidate for solid-state quantum computation. One of the reasons is that implementing a controlled coupling between the qubits appears to be relatively easy, if one uses tunable Josephson junctions. We evaluate possible coupling strengths and show how much extra decoherence is induced by the subgap conductance of a tunable junction. In light of these results, we evaluate several options of using intrinsically shunted junctions and show that based on available technology, Josephson field effect transistors and high-Tc junctions used as π shifters would be a good option, whereas the use of magnetic junctions as π shifters severely limits quantum coherence.
We propose a qubit consisting of a superconducting ring with two zero junctions and one ferromagnetic π junction. In the system, degenerate states appear in the phase space without an external magnetic field because of a competition between the zero and π states. Quantum tunneling between the degenerate states leads to a formation of bonding and antibonding states which are used as a bit. For manipulating the states, only a small magnetic field around zero is required. This feature leads to a large-scale integration and a construction of the smaller-sized qubit which is robust to the decoherence by external noises.
The theory of superconducting phase qubits---also known as current-biased Josephson junctions---is presented. In the first part of this thesis, I introduce quantum computation, quantum simulation, and their deep connection with symplectic integration. I then consider the fundamental many-body theory of superconductivity and Josephson junctions and show how the quantum dynamics of a single macroscopic degree of freedom, the gauge invariant phase difference, emerges. A complete study of the Hilbert space structure of such a variable is performed for the current-biased junction. The resulting resonance structure is studied in detail, using various formalisms including the WKB approximation, instanton methods, the complex scaling transformation, basis set stabilization, numerical integration, and dynamical simulation using Lie algebraic wave-packet propagation. The second part of this thesis explores how the current-biased junction can be used as an element of a quantum computer---a quantum bit (qubit). Single qubit operations are studied, followed by the presentation of the theory of coupled qubit devices. My key result is the design and optimization of quantum logic gates with high fidelity (F ~ 0.9999) for capacitively coupled phase qubits with short gate times (~ 10 ns). Finally, I examine an advanced qubit-coupling scheme, a resonant coupling method utilizing a harmonic oscillator as the auxiliary degree of freedom. The models and methods presented here have been developed in direct collaboration with an experimental program. These experiments are the first to show spectroscopic evidence for entanglement between two and three macroscopic degrees of freedom in a superconducting circuit.
Solid-state qubits have the potential for the large-scale integration and for the flexibility of layout for quantum computing. However, their short decoherence time due to the coupling to the environment remains an important problem to be overcome. We propose a new superconducting qubit which incorporates a spin-electronic device: the qubit consists of a superconducting ring with a ferromagnetic pi junction which has a metallic contact and a normal Josephson junction with an insulating barrier. Thus, a quantum coherent two-level state is formed without an external magnetic field. This feature and the simple structure of the qubit make it possible to reduce its size leading to a long decoherence time.
The presence of spontaneous currents in unconventional Josephson junctions gives rise to the possibility of using zero magnetic field magnetization states in an unconventional loop as qubit states in a Josephson quantum computing device. However, the advantage of zero field may be insufficient to overcome the problems arising in the design and fabrication of low-noise, low-dissipation, reproducible devices. On the other hand, low-T/sub c/ "flux" devices suffer the same problems though their perspectives are more promising. The solution could be an increase in the device complexity, but with the gain of an effective advantage on the external noise rejection of the system during quantum evolution. Using advanced fabrication techniques it is now possible to build Josephson junction arrays made of superconducting unconventional loops. On this basis, a new qubit device can be designed as a ring array of unconventional loops. From a theoretical point of view this device is analogous to an annular Josephson junction, but with a "built in" natural degeneracy. For their topological and energetical properties, such arrays could be excellent devices for the qubit circuitry usable as the basic building blocks for quantum computing devices. In this work, we show how some of the principles of qubit design could be implemented in such devices.