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Superlattices and Microstructures

Josephson-junction qubits: entanglement and coherence

J. R. Anderson, A. J. Berkley, Alex J. Dragt, M. A. Gubrud, P.R. Johnson, Christopher J. Lobb, Roberto Ramos, Frederick W. Strauch, F. C. Wellstood, Huizhong Xu

Published Oct 1, 2002• 1 citation
Publisher
DOI
10.1016/s0749-6036(03)00023-5

Related papers

Josephson vortex quantum bits: Decoherence and entanglement

Ramesh P. Dhungana

In this dissertation work, I investigate the decoherence time of a Josephson vortex qubit (JVQ) and the level of entanglement between two JVQs. A JVQ may be fabricated by embedding two closely spaced microresistors in the insulating layer of a long Josephson junction (LJJ). The phase dynamics of the JVQ may be described by using the perturbed sine-Gordon equation. This sine-Gordon equation is transformed to describe the motion of fluxons in the double-well potential. An oscillation of a fluxon in this double-well potential is mapped onto a quantum two-state system. The coherent oscillation of fluxons in the two-state system decays due to dissipation and noises in the LJJ. To estimate the decoherence time, the two-state system in a noisy environment is described by using the spin-boson Hamiltonian. The time evolution of the system is studied by using the generalized master equation. Finally, I use the experimental parameters for Nb-AlOx-Nb Josephson junction to estimate the decoherence time. The result shows that JVQ has a very long decoherence time (several tens of microseconds) compared to other Josephson qubits. Entanglement between two coupled JVQs is estimated by computing the concurrence. The concurrence depends on the ground-state energy splitting due to the one-fluxon and two-fluxon tunneling between the potential minima of the two coupled JVQs. The tunneling amplitude between the potential minima depends on the junction parameters such as magnetic induction effect S, the separation distance ℓ, and the pinning strength of the microresistors ϵ. The estimation of the concurrence shows that a near perfect entanglement may be achieved by using the experimentally accessible values of the parameters. Also the study shows that the tunneling amplitude of the fluxon between the potential minima of the JVQs may be increased by coupling the junction with a resonant cavity. This characteristic of the junction-cavity coupling may be exploited to control the entanglement between two JVQs.

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Engineering entanglement in Josephson qubit

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Mechanical quantum resonators

Andrew N. Cleland

We describe the design for a solid‐state quantum computational architecture based on the integration of GHz‐frequency mechanical resonators with Josephson phase qubits, which have the potential for demonstrating a variety of single‐ and multi‐qubit operations critical to quantum computation. The computational qubits are eigenstates of large‐area, current‐biased Josephson junctions. Two or more qubits are capacitively coupled to a piezoelectric nanoelectromechanical disk resonator, which enables coherent coupling of the qubits. The integrated system is analogous to one or more few‐level atoms (the Josephson junction qubits) in an electromagnetic cavity (the nanomechanical resonator). However, here we can individually tune the level spacing of the “atoms” and control their “electromagnetic” interaction strength. We show that quantum states prepared in a Josephson junction can be passed to the nanomechanical resonator and stored there, and then can be passed back to the original junction or transferred to another with high fidelity. The resonator can also be used to produce maximally entangled Bell states between a pair of Josephson junctions.

AIP conference proceedings•Jan 1, 2005•2 citations

A Josephson junction qubit

A. J. Berkley

I studied the Josephson junction system in the context of its usability for quan-tum computation. The zero-voltage state of a Josephson junction biased with constant current has a set of metastable quantum energy levels. In principle, it should be possible to use the two lowest states as a qubit for a quantum computer, provided both the dissipation time and coherence time of this qubit can be made long enough. I describe two methods for isolating a Josephson junction to increase its dissipation time. The rst is a resistive isolation scheme, for which I fabricated and measured a prototype system. I discuss the results of these measurements and show that the constraints of heating in conjunction with high-frequency design require-ments make it unlikely that this isolation method will lead to the coherence times required for quantum computation. I then discuss a resonant isolation method that I used to successfully increase the dissipation time of a Josephson junction qubit. I performed spectroscopic mea-surements at low temperatures to nd the coherence time of resonantly isolated 100 m2 Al/AlOx/Al and Nb/AlOx/Nb junctions with critical currents of roughly 10 A. The results of these measurements reveal two mechanisms beyond spontaneous emission for decoherence: low-frequency current noise and tunneling to the voltage state. To explain these results on decoherence, I present a model based on the Bloch equations. Going beyond a single qubit, I designed a capacitively coupled two-qubit system. Using spectroscopy, I showed that the energy level spacings between the ground state and the excited entangled states of the system agree with those calculated from the Schrodinger equation.

•Jan 1, 2003•2 citations

Coherent-state qubits: entanglement and decoherence

János K. Asbóth, Петер Адам, Mátyás Koniorczyk +1 more

The European Physical Journal D•Aug 9, 2004•20 citations
In this dissertation work, I investigate the decoherence time of a Josephson vortex qubit (JVQ) and the level of entanglement between two JVQs. A JVQ may be fabricated by embedding two closely spaced microresistors in the insulating layer of a long Josephson junction (LJJ). The phase dynamics of the JVQ may be described by using the perturbed sine-Gordon equation. This sine-Gordon equation is transformed to describe the motion of fluxons in the double-well potential. An oscillation of a fluxon in this double-well potential is mapped onto a quantum two-state system. The coherent oscillation of fluxons in the two-state system decays due to dissipation and noises in the LJJ. To estimate the decoherence time, the two-state system in a noisy environment is described by using the spin-boson Hamiltonian. The time evolution of the system is studied by using the generalized master equation. Finally, I use the experimental parameters for Nb-AlOx-Nb Josephson junction to estimate the decoherence time. The result shows that JVQ has a very long decoherence time (several tens of microseconds) compared to other Josephson qubits. Entanglement between two coupled JVQs is estimated by computing the concurrence. The concurrence depends on the ground-state energy splitting due to the one-fluxon and two-fluxon tunneling between the potential minima of the two coupled JVQs. The tunneling amplitude between the potential minima depends on the junction parameters such as magnetic induction effect S, the separation distance ℓ, and the pinning strength of the microresistors ϵ. The estimation of the concurrence shows that a near perfect entanglement may be achieved by using the experimentally accessible values of the parameters. Also the study shows that the tunneling amplitude of the fluxon between the potential minima of the JVQs may be increased by coupling the junction with a resonant cavity. This characteristic of the junction-cavity coupling may be exploited to control the entanglement between two JVQs.
We describe the design for a solid‐state quantum computational architecture based on the integration of GHz‐frequency mechanical resonators with Josephson phase qubits, which have the potential for demonstrating a variety of single‐ and multi‐qubit operations critical to quantum computation. The computational qubits are eigenstates of large‐area, current‐biased Josephson junctions. Two or more qubits are capacitively coupled to a piezoelectric nanoelectromechanical disk resonator, which enables coherent coupling of the qubits. The integrated system is analogous to one or more few‐level atoms (the Josephson junction qubits) in an electromagnetic cavity (the nanomechanical resonator). However, here we can individually tune the level spacing of the “atoms” and control their “electromagnetic” interaction strength. We show that quantum states prepared in a Josephson junction can be passed to the nanomechanical resonator and stored there, and then can be passed back to the original junction or transferred to another with high fidelity. The resonator can also be used to produce maximally entangled Bell states between a pair of Josephson junctions.
I studied the Josephson junction system in the context of its usability for quan-tum computation. The zero-voltage state of a Josephson junction biased with constant current has a set of metastable quantum energy levels. In principle, it should be possible to use the two lowest states as a qubit for a quantum computer, provided both the dissipation time and coherence time of this qubit can be made long enough. I describe two methods for isolating a Josephson junction to increase its dissipation time. The rst is a resistive isolation scheme, for which I fabricated and measured a prototype system. I discuss the results of these measurements and show that the constraints of heating in conjunction with high-frequency design require-ments make it unlikely that this isolation method will lead to the coherence times required for quantum computation. I then discuss a resonant isolation method that I used to successfully increase the dissipation time of a Josephson junction qubit. I performed spectroscopic mea-surements at low temperatures to nd the coherence time of resonantly isolated 100 m2 Al/AlOx/Al and Nb/AlOx/Nb junctions with critical currents of roughly 10 A. The results of these measurements reveal two mechanisms beyond spontaneous emission for decoherence: low-frequency current noise and tunneling to the voltage state. To explain these results on decoherence, I present a model based on the Bloch equations. Going beyond a single qubit, I designed a capacitively coupled two-qubit system. Using spectroscopy, I showed that the energy level spacings between the ground state and the excited entangled states of the system agree with those calculated from the Schrodinger equation.