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arXiv:cond-mat/0101454

Spin Environment Engineering for a Persistent Current Qubit

Jacek Dziarmaga

Published Jan 30, 2001• 0 citations
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Abstract

A persistent current qubit has two quantum states with opposite currents flowing in a superconducting loop. Their magnetic field couple to nuclear spins. The qubit state is not only perturbed by the spins but it also gets entangled with the spins' state on a very short timescale. However, when the same spins are exposed to a strong but less than critical external magnetic field, then the qubit field is just a small perturbation on top of the external field and the entanglement with each spin is negligible. For a qubit which is more microscopic than certain threshold this partial entanglement results in negligible partial decoherence.

DOI
10.48550/arxiv.cond-mat/0101454

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A persistent current qubit has two quantum states with opposite currents flowing in a superconducting loop. Their magnetic field couple to nuclear spins. The qubit state is not only perturbed by the spins but it also gets entangled with the spins' state on a very short timescale. However, when the same spins are exposed to a strong but less than critical external magnetic field, then the qubit field is just a small perturbation on top of the external field and the entanglement with each spin is negligible. For a qubit which is more microscopic than certain threshold this partial entanglement results in negligible partial decoherence.
We present the design of a superconducting qubit that has circulating currents of opposite sign as its two states. The circuit consists of three nanoscale aluminum Josephson junctions connected in a superconducting loop and controlled by magnetic fields. The advantages of this qubit are that it can be made insensitive to background charges in the substrate, the flux in the two states can be detected with a superconducting quantum interference device, and the states can be manipulated with magnetic fields. Coupled systems of qubits are also discussed as well as sources of decoherence.
The superconducting flux qubit has two quantum states with opposite currents which generate different magnetic fields. Environment of nuclear spins can find out the magnetic field after a decoherence time ${\ensuremath{\tau}}_{0}$ inversely proportional to the magnetic field and the square root of the number of spins. When the Hamiltonian of the qubit drives fast coherent Rabi oscillations between the states with opposite current, then the magnetic field is flipped at a constant rate $\ensuremath{\omega}$ and the decoherence time $\ensuremath{\tau}=\ensuremath{\omega}{\ensuremath{\tau}}_{0}^{2}$ is much longer than ${\ensuremath{\tau}}_{0}$. However, on closer inspection decoherence actually takes place on two time scales. The long time $\ensuremath{\tau}$ is a time of full decoherence but a part of quantum coherence is lost already after the much shorter time $\ensuremath{\pi}∕\ensuremath{\omega}$. This fast partial decoherence biases coherent flux oscillations towards the initial flux direction and it can affect performance of the superconducting devices as qubits.
We consider a superconducting persistent-current qubit consisting of a three-junction superconducting loop in an applied magnetic field. We show that by choosing the field, Josephson couplings, and offset charges suitably, we can perfectly suppress the tunneling between the two oppositely directed states of circulating current, leading to a vanishing of the splitting between the two qubit states. This suppression arises from interference between tunneling along different paths and is analogous to that predicted previously for magnetic particles with half-integer spin.
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A qubit was designed that can be fabricated with conventional electron beam lithography and is suited for integration into a large quantum computer. The qubit consists of a micrometer-sized loop with three or four Josephson junctions; the two qubit states have persistent currents of opposite direction. Quantum superpositions of these states are obtained by pulsed microwave modulation of the enclosed magnetic flux by currents in control lines. A superconducting flux transporter allows for controlled transfer between qubits of the flux that is generated by the persistent currents, leading to entanglement of qubit information.
A qubit was designed that can be fabricated with conventional electron beam lithography and is suited for integration into a large quantum computer. The qubit consists of a micrometer-sized loop with three or four Josephson junctions; the two qubit states have persistent currents of opposite direction. Quantum superpositions of these states are obtained by pulsed microwave modulation of the enclosed magnetic flux by currents in control lines. A superconducting flux transporter allows for controlled transfer between qubits of the flux that is generated by the persistent currents, leading to entanglement of qubit information.