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Physical Review B

Mobile qubits in quantum Josephson circuits

Toshiyuki Fujii, Munehiro Nishida, Noriyuki Hatakenaka

Published Jan 10, 2008• 14 citations
Publisher

Abstract

A massive mobile qubit is proposed that uses quantum-mechanical aspects of a mobile bound excitation pair consisting of a fluxon and an antifluxon, called a breather, in a long Josephson junction with small capacitance per unit length. This massive mobile qubit acts as a quantum data bus that transfers quantum information from one node to another. Moreover, it performs calculations during communication without the support of stationary qubits. In addition, the proposed qubits are elementary excitations that are regarded as macroscopic artificial two-level atoms. This means they can be introduced anytime and anywhere on demand in contrast to built-in solid-state qubits. They provide a platform for testing fundamental problems in quantum mechanics on a macroscopic scale.

DOI
10.1103/physrevb.77.024505

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In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling \namplitude between the two macroscopic states. The latter can be controlled via the height and form of \nthe potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest \ncircuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. \nThe tunneling amplitude between two macroscopically different states can be essentially increased, by \nengineering of the qubit circuit, if tunnel junction is replaced by a ScS contact. However, only Josephson \ntunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with preset- \nday technology. To overcome this difficulty we consider here the flux qubit with high-level energy separation \nbetween «ground» and «excited» states, which consists of a superconducting loop with two lowcapacitance \nJosephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition \nbetween the two macroscopic states the tunneling amplitude can reach values greater than 1 K. Analytical \nresults for the tunneling amplitude obtained within semiclassical approximation by instanton technique \nshow good correlation with a numerical solution.

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A massive mobile qubit is proposed that uses quantum-mechanical aspects of a mobile bound excitation pair consisting of a fluxon and an antifluxon, called a breather, in a long Josephson junction with small capacitance per unit length. This massive mobile qubit acts as a quantum data bus that transfers quantum information from one node to another. Moreover, it performs calculations during communication without the support of stationary qubits. In addition, the proposed qubits are elementary excitations that are regarded as macroscopic artificial two-level atoms. This means they can be introduced anytime and anywhere on demand in contrast to built-in solid-state qubits. They provide a platform for testing fundamental problems in quantum mechanics on a macroscopic scale.
Breather is an elementary excitation regarded as a bound state of a fluxon and an antifluxon in a long Josephson junction. In quantum-mechanical regime, the breather energy is quantized so that the breather can be considered as an artificial moving atom. We propose a new type of fluxon qubit that is constructed by quantum-mechanical superposition of the breather's states. We describe quantum logic gates of breather qubit required for constructing quantum computer. In addition, our qubit can move in the system so that transfer of quntum information is possible between mobile qubits as well as stationary qubits. Our talking qubits support the global information sharing in quantum information networks.
We propose a new type of mobile qubit that utilizes a bound pair of half fluxons in a long superconductor-ferromagnet-superconductor (SFS) Josephson junction. The qubit states are composed of the lowest two levels of the quantized nonlinear internal oscillation of the bound pair. The energy levels are estimated by the numerical quantization based on a collective coordinate method. The qubit operation scheme is discussed, showing an estimate of the interaction strength between a bound pair and a microcircuit.
This work concerns the study of Josephson junction circuits in the context of their usability for quantum computing. The zero-voltage state of a current-biased Josephson junction has a set of metastable quantum energy levels. If a junction is well isolated from its environment, it will be possible to use the two lowest states as a qubit in a quantum computer. I first examine the meaning of isolation theoretically. Using a master equation, I analyzed the effect of dissipation on escape rates and suggested a simple method, population depletion technique, to measure the relaxation time. Using a stochastic Bloch equation to analyze microwave resonance shapes, I found a relation between current noise induced decoherence and the noise spectrum. I then analyze and test a few qubit isolation schemes, including resistive isolation, inductor-capacitor (LC) isolation, and inductor-junction (LJ) isolation. I found the resistive isolation scheme has a severe heating problem. Macroscopic quantum tunneling and energy level quantization were observed in the LC isolated junction qubits at 25 mK. Relaxation times of 4-12 ns and spectroscopic coherence times of 1-3 ns were obtained for these LC isolated qubits. I measured a relaxation time of 50 ns and a spectroscopic coherence time of 5-8 ns for the LJ isolated junction qubit. Both times are much longer than those of the LC isolated qubits. Rabi oscillations were also observed on this sample with a decay time of around 10 ns. Using microwave spectroscopy techniques, I probed quantum phenomena in a coupled macroscopic three-qubit system that is comprised of two Nb/AlOx/Nb Josephson junctions and an LC resonator. The measured spectrum at 25 mK in the frequency range 4-15 GHz agrees well with quantum mechanical calculations, consistent with the existence of entangled states between the three degrees of freedom. These entangled states and a first-order strong coupling between two junction qubits open the possibility of using a resonator as a data bus for information storage and manipulation in a multi-qubit system. The measurements also demonstrate spectroscopy is a powerful tool and can be used to study a composite system with many qubits.
In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling amplitude between the two macroscopic states. The latter can be controlled via the height and form of the potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest circuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. The tunneling amplitude between two macroscopically different states can be increased substantially by engineering of the qubit circuit if the tunnel junction is replaced by a ScS contact. However, only Josephson tunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with present-day technology. To overcome this difficulty we consider here a flux qubit with high energy-level separation between the “ground” and “excited” states, consisting of a superconducting loop with two low-capacitance Josephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition between the two macroscopic states the tunneling amplitude can reach values greater than 1K. Analytical results for the tunneling amplitude obtained within the semiclassical approximation by the instanton technique show good correlation with a numerical solution.
Long-lived fluxon excitations can be trapped inside a superinductor ring, which is divided into an array of loops by a periodic sequence of Josephson junctions in the quantum regime, thereby allowing fluxons to tunnel between neighboring sites. By tuning the Josephson couplings and, implicitly, the fluxon tunneling probability amplitudes, a wide class of one-dimensional tight-binding lattice models may be implemented and populated with a stable number of fluxons. We illustrate the use of this quantum simulation platform by discussing the Su-Schrieffer-Heeger model in the one-fluxon subspace, which hosts a symmetry-protected topological phase with fractionally charged bound states at the edges. This pair of localized edge states could be used to implement a superconducting qubit increasingly decoupled from decoherence mechanisms.
In this paper we discuss solid-state nanoelectronic realizations of Josephson flux qubits with large tunneling \namplitude between the two macroscopic states. The latter can be controlled via the height and form of \nthe potential barrier, which is determined by quantum-state engineering of the flux qubit circuit. The simplest \ncircuit of the flux qubit is a superconducting loop interrupted by a Josephson nanoscale tunnel junction. \nThe tunneling amplitude between two macroscopically different states can be essentially increased, by \nengineering of the qubit circuit, if tunnel junction is replaced by a ScS contact. However, only Josephson \ntunnel junctions are particularly suitable for large-scale integration circuits and quantum detectors with preset- \nday technology. To overcome this difficulty we consider here the flux qubit with high-level energy separation \nbetween «ground» and «excited» states, which consists of a superconducting loop with two lowcapacitance \nJosephson tunnel junctions in series. We demonstrate that for real parameters of resonant superposition \nbetween the two macroscopic states the tunneling amplitude can reach values greater than 1 K. Analytical \nresults for the tunneling amplitude obtained within semiclassical approximation by instanton technique \nshow good correlation with a numerical solution.