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Advances in Condensed Matter Physics

Geometric Phase in a Quantum Computa-tion with Josephson Qubits Using a Current-Biased Information Bus

元新 乔

Published Jan 1, 2018• 0 citations
Publisher

Abstract

量子计算是一种遵循量子力学规律调控量子信息单元进行计算的新型计算模式。本文利用电流偏置信息总线的Josephson量子位,计算了几何相位。发现该几何相位与大电流约瑟夫逊结、量子振荡器频率、对称约瑟夫逊能量耦合器的偏置电流无关,与施加到第k个量子位的栅极电容、磁通量子、外部电流和栅极电压无关。本文结果对利用约瑟夫森量子比特计算具有一定的理论意义。 Quantum computation is a new computational model which follows the rules of quantum mechanics to control the quantum information unit. This paper calculates the geometric phase by using the Josephson qubits of current-biased information bus. The geometric phase has nothing to do with the bias current of the large current-biased Josephson junction, the quantum oscillator frequency, the coupler with symmetric Josephson energies, and also the gate capacitance, flux quantum, external flux, and gate voltage applied to the kth qubit. The results of this paper have a certain theoretical significance to the calculation of the quantum bit of Josephson.

DOI
10.12677/cmp.2018.71002

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量子计算是一种遵循量子力学规律调控量子信息单元进行计算的新型计算模式。本文利用电流偏置信息总线的Josephson量子位,计算了几何相位。发现该几何相位与大电流约瑟夫逊结、量子振荡器频率、对称约瑟夫逊能量耦合器的偏置电流无关,与施加到第k个量子位的栅极电容、磁通量子、外部电流和栅极电压无关。本文结果对利用约瑟夫森量子比特计算具有一定的理论意义。 Quantum computation is a new computational model which follows the rules of quantum mechanics to control the quantum information unit. This paper calculates the geometric phase by using the Josephson qubits of current-biased information bus. The geometric phase has nothing to do with the bias current of the large current-biased Josephson junction, the quantum oscillator frequency, the coupler with symmetric Josephson energies, and also the gate capacitance, flux quantum, external flux, and gate voltage applied to the kth qubit. The results of this paper have a certain theoretical significance to the calculation of the quantum bit of Josephson.
通过使用Lewis-Riesenfeld不变量理论,我们研究了大约瑟夫逊结量子比特中拉比振荡的几何相位。发现几何相位与偏置电流的直流和微波脉冲无关,也与微波的转换频率无关。 By using the Lewis–Riesenfeld invariant theory, we have studied the geometric phase of Rabi oscillations in a large Josephson-junction qubit. The geometric phase has nothing to do with the dc and microwave pulses of bias current, and is independent of the transitions frequencies of microwaves.
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.
Josephson junction is one of the promising devices to be used as a quantum bit or known as qubit in a quantum computer. The dynamics of current-bias Josephson junction can be described by using the Resistively and Capacitively Shunted Junction (RCSJ) model which is analogous to the classical motion of a particle in a tilted washboard potential. In this work, quantum theory and approximation methods are used to calculate and explain quantum properties of the Josepson junction. We found that the energy levels in the washboard potential can be quantum mechanically quantized, and thus used as a qubit in quantum computation. The tunneling rate from the n[superscript th] energy level exponentially increases with bias current and the first excited state is three orders of magnitude more than the ground state. The wave function of the state in the potential well is relatively similar to the harmonic oscillator wave function because of the shape of the washboard potential. The transition rate between the energy levels due to an electromagnetic radiation depends on the amplitude and the frequency of microwave current. The period of the oscillation is in the order of nanoseconds. Finally the decoherence time in Josephson junction can be observed by considering the Rabi's oscillation in the presence of current noise. The decoherence time depends on the magnitude of the current noise. This result can be used to determine the feasibility of using Josephson Junction as a qubit
Berry's phase often appears in quantum two-level systems with a degeneracy. An example of such a system is a spin-1/2 particle in a magnetic field. As the magnetic field is slowly evolved through a closed path, the particle has been shown to acquire an additional phase called Berry's phase, in addition to the usual dynamical phase. This phase has been found in two-level quantum systems intrinsic to many superconducting qubits and has particularly been calculated for the charge, flux and Josephson phase qubit. Here, we present an alternative derivation of the Berry's phase in a current-biased Josephson junction qubit. We also calculate the complete Berry's phase evaluated over a closed loop in a frequency parameter space and compare this with the geometric phase. From this comparison, we examine the possibility of using a single phase qubit for topological quantum computing.
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.