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arXiv:cond-mat/0407667 · Physical Review B

Quantum computation with Josephson qubits using a current-biased information bus

L. F. Wei, Yu-xi Liu, Franco Nori

Published Apr 13, 2005• 56 citations
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Abstract

We propose an effective scheme for manipulating quantum information stored in a superconducting nanocircuit. The Josephson qubits are coupled via their separate interactions with an information bus, a large current-biased Josephson junction treated as an oscillator with adjustable frequency. The bus is sequentially coupled to only one qubit at a time. Distant Josephson qubits without any direct interaction can be indirectly coupled with each other by independently interacting with the bus sequentially, via exciting/deexciting vibrational quanta in the bus. This is a superconducting analog of the successful ion trap experiments on quantum computing. Our approach differs from previous schemes that simultaneously coupled two qubits to the bus, as opposed to their sequential coupling considered here. The significant quantum logic gates can be realized by using these tunable and selective couplings. The decoherence properties of the proposed quantum system are analyzed within the Bloch-Redfield formalism. Numerical estimations of certain important experimental parameters are provided.

DOI
10.1103/physrevb.71.134506

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We propose an effective scheme for manipulating quantum information stored in a superconducting nanocircuit. The Josephson qubits are coupled via their separate interactions with an information bus, a large current-biased Josephson junction treated as an oscillator with adjustable frequency. The bus is sequentially coupled to only one qubit at a time. Distant Josephson qubits without any direct interaction can be indirectly coupled with each other by independently interacting with the bus sequentially, via exciting/deexciting vibrational quanta in the bus. This is a superconducting analog of the successful ion trap experiments on quantum computing. Our approach differs from previous schemes that simultaneously coupled two qubits to the bus, as opposed to their sequential coupling considered here. The significant quantum logic gates can be realized by using these tunable and selective couplings. The decoherence properties of the proposed quantum system are analyzed within the Bloch-Redfield formalism. Numerical estimations of certain important experimental parameters are provided.
Josephson qubits without direct interaction can be effectively coupled by sequentially connecting them to an information bus: a current-biased large Josephson junction treated as an oscillator with adjustable frequency. The coupling between any qubit and the bus can be controlled by modulating the magnetic flux applied to that qubit. This tunable and selective coupling provides two-qubit entangled states for implementing elementary quantum logic operations, and for experimentally testing Bell's inequality.
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.
Exploiting the intrinsic nonlinearity of superconducting Josephson junctions, we propose a scalable circuit with superconducting qubits (SCQs) which is very similar to the successful one now being used for trapped ions. The SCQs are coupled to the ``vibrational'' mode provided by a superconducting LCLCLC circuit or its equivalent (e.g., a superconducting quantum interference device). Both single-qubit rotations and qubit-LCLCLC-circuit couplings and/or decouplings can be controlled by the frequencies of the time-dependent magnetic fluxes. The circuit is scalable since the qubit-qubit interactions, mediated by the LCLCLC circuit, can be selectively performed, and the information transfer can be realized in a controllable way.
Josephson junction-based qubits have been shown to be promising components for a future quantum computer. A network of these superconducting qubits will require quantum information to be stored in and transferred among them. Resonators made of superconducting metal strips are useful elements for this purpose because they have long coherence times and can dispersively couple qubits. We explore the use of multiple resonators with different resonant frequencies to couple qubits. We find that an array of resonators with different frequencies can be individually addressed to store and retrieve information, while coupling qubits dispersively. We show that a control qubit can be used to effectively isolate an active qubit from an array of resonators so that it can function within the same frequency range used by the resonators.
We present a quantum computing scheme with atomic Josephson junction arrays. The system consists of a small number of atoms with three internal states and trapped in a far-off-resonant optical lattice. Raman lasers provide the ``Josephson'' tunneling, and the collision interaction between atoms represent the ``capacitive'' couplings between the modes. The qubit states are collective states of the atoms with opposite persistent currents. This system is closely analogous to the superconducting flux qubit. Single-qubit quantum logic gates are performed by modulating the Raman couplings, while two-qubit gates result from a tunnel coupling between neighboring wells. Readout is achieved by tuning the Raman coupling adiabatically between the Josephson regime to the Rabi regime, followed by a detection of atoms in internal electronic states. Decoherence mechanisms are studied in detail promising a high ratio between the decoherence time and the gate operation time.