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Journal of Physics Communications

External current as a coupler between the spin-vortex-induced loop current qubits

Hikaru Wakaura, Hiroyasu Koizumi

Published Nov 8, 2017• 2 citations
Publisher

Abstract

The spin-vortex-induced loop current (SVILC) is a nano-sized loop current predicted to exist in the CuO 2 plane in the bulk of hole-doped cuprate superconductors. It is a persistent loop current protected by the topological winding number associated with the wave function. It exists around a spin-vortex created by the itinerant electrons with a doped hole at its center. The direction of each SVILC can be either clockwise (winding number −1) or counterclockwise (winding number +1); and the currentless winding number zero is forbidden by the single-valued requirement of the wave function with respect to the electron coordinates. Recently, it has been demonstrated, theoretically, that this degree-of-freedom can be used for qubits. The gate-operation time by the Rabi oscillation using an electromagnetic field with electric field intensity 10 5 V m –1 is estimated to be several nanoseconds. This is comparable or shorter than the existing superconducting qubits. Since SVILCs do not require Cooper pairs, the SVILC qubit is free from the relaxation caused by broken Cooper pair electrons that is speculated to limit the qubit coherence time in the existing superconducting qubits. Thus, the coherence time for the SVILC qubit may exceed the value achieved by the superconducting qubit (about 100 μ s). Further, since the stabilization temperature of SVILCs is expected to be the superconducting transition temperature of the cuprates, a much higher operation temperature may be possible for the SVILC qubits compared to the existing superconducting qubits, which requires the operation temperature of about 10 mK. In the present work, we show, theoretically, that coupling of two SVILC qubits can be achieved by external current feeding. This enables the construction of nano-sized qubit-couplers, and may provide a scalability that is needed in the construction of a fully fault-tolerant quantum computer.

DOI
10.1088/2399-6528/aa98ff

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Method for direct observation of coherent quantum oscillations in a superconducting phase qubit

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The spin-vortex-induced loop current (SVILC) is a nano-sized loop current predicted to exist in the CuO 2 plane in the bulk of hole-doped cuprate superconductors. It is a persistent loop current protected by the topological winding number associated with the wave function. It exists around a spin-vortex created by the itinerant electrons with a doped hole at its center. The direction of each SVILC can be either clockwise (winding number −1) or counterclockwise (winding number +1); and the currentless winding number zero is forbidden by the single-valued requirement of the wave function with respect to the electron coordinates. Recently, it has been demonstrated, theoretically, that this degree-of-freedom can be used for qubits. The gate-operation time by the Rabi oscillation using an electromagnetic field with electric field intensity 10 5 V m –1 is estimated to be several nanoseconds. This is comparable or shorter than the existing superconducting qubits. Since SVILCs do not require Cooper pairs, the SVILC qubit is free from the relaxation caused by broken Cooper pair electrons that is speculated to limit the qubit coherence time in the existing superconducting qubits. Thus, the coherence time for the SVILC qubit may exceed the value achieved by the superconducting qubit (about 100 μ s). Further, since the stabilization temperature of SVILCs is expected to be the superconducting transition temperature of the cuprates, a much higher operation temperature may be possible for the SVILC qubits compared to the existing superconducting qubits, which requires the operation temperature of about 10 mK. In the present work, we show, theoretically, that coupling of two SVILC qubits can be achieved by external current feeding. This enables the construction of nano-sized qubit-couplers, and may provide a scalability that is needed in the construction of a fully fault-tolerant quantum computer.
Toward the Detection of Spin-Vortex-Induced Loop Currents in a Single Bilayer Bi2_22​Sr2_22​CaCu2_22​O8+δ_{8+\delta }8+δ​ Thin Film and Their Possible Use as Qubits: Model Calculations for Three Nano-island Architecture
Abstract A theory for cuprate superconductivity predicts the existence of nano-sized loop currents called “spin-vortex-induced loop currents (SVILCs).” In this work, we first calculate magnetic fields produced by them in a single bilayer Bi 2_22​ 2 Sr 2_22​ 2 CaCu 2_22​ 2 O 8+δ_{8+\delta }8+δ​ 8 + δ (Bi-2212) thin film for the purpose of detecting the SVILCs. The estimated magnitude of the magnetic field at the point 10a (a is the lattice constant of the CuO 2_22​ 2 plane) above the surface could be in the order of 100 mT; thus, they may be detectable by currently available detection methods. Next, we investigate the use of them as qubits (the “SVILC qubits”) in an architecture composed of three nano-islands of the thin film and consider the use of the detection of the magnetic field generated by the SVILCs as the qubit readout. We show there are a number of energy levels suitable for qubit states that can be manipulated by external current feeding, and the magnetic field generated by the SVILCs is large enough to be used for the readout.
Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop induce the voltage oscillations across the coil of a high quality resonant tank circuit, inductively coupled to the phase qubit. It is the presence of these voltage oscillations in the detected signal which reveals the existence of Rabi oscillations in the qubit. A detailed calculation for zero and nonzero temperatures are made for the case of persistent current qubit. According to the estimates for decoherence and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi frequency in the MHz range.
In this thesis measurements on single and coupled Josephson persistent current qubits are presented. The Josephson persistent current qubit consists of a superconducting loop intersected by three Josephson junctions. When half a flux quantum is applied to the loop this system acts as a quantum two state system. The two states are associated with a clock or anti clockwise current flowing in the loop and can be measured using a SQUID magnetometer. The research presented in this thesis aimed at achieving coupling between two Josephson persistent current qubits and to show conditional gate operations in such a coupled qubit system. Also it was tried to improve the coherence properties of a single qubit by using a gradiometer type configuration to minimize influence from fluxnoise which would cause a disturbance of the energy bias of the qubit system. The basic principles of the Josephson persistent current qubit are discussed, as well as design criteria to minimize decoherence due to the environment seen by the squid or microwave lines. Spectroscopy measurements have been performed on coupled qubit systems mapping out the energy level structure of these systems. For two coupled qubits the origin and magnitude of the coupling J is derived for coupling via the geometrical inductance between the qubits. Also it is shown that coupling via a shared junction or a shared line acts the same as the geometrical coupling. Spectroscopy measurements show coupling for qubits which are mainly geometrical coupled and spectroscopy measurements on an other sample show a coupling for qubits coupled via a large shared Josephson junction. Using such a shared junction allows for the coupling to be designed within a large range. For the coupled qubit system with coupling via a large junction spectroscopy measurements from both the ground state to higher states as well as from the partially populated first excited state to higher states have been performed and the level structure of this system is mapped out. The energy level structure is in good agreement with the 4 level approximation for two coupled qubits. Coherent Rabi oscillations between two states flipping either qubit of this system have been performed with an oscillation decay time of up to 70ns. Also conditional spectroscopy has been performed by first going coherently from the ground state to a higher state and then incoherently pumping the system to other states. Spectroscopy measurements on a gradiometer type Josephson persistent current qubit show trapped fluxoid biasing can be used to create a phase bias of pi over the qubit junctions. The results of this thesis show that coupling between Josephson persistent current qubits can be achieved and designed within the wanted range. Superpositions between the ground state and higher states in such a coupled qubit system have been created by performing Rabi oscillations. Also conditional spectroscopy has been performed.
Parity-protected superconducting qubits offer intrinsically long coherence, but many current implementations require magnetic-flux biasing, which introduces flux noise, control overhead, and limited scalability. Here we propose a parity-protected qubit based on a gate-tunable superconductor-altermagnet-superconductor Josephson junction. Altermagnets are compensated magnets with momentum-dependent spin splitting and zero net magnetization, providing spin-dependent functionality without external magnetic fields. In the proposed junction, the two spin sectors acquire opposite phase shifts, generating two Josephson channels whose interference is controlled electrically by the chemical potential. At the tuned 000-πππ transition, the first Josephson harmonic is strongly suppressed while the second harmonic dominates, yielding a double-well potential with two nearly degenerate states of opposite Cooper-pair parity. For realistic gatemon-compatible parameters, we estimate coherence times of up to tens of milliseconds while maintaining fully gate-controlled qubit operations. These results establish altermagnetic Josephson junctions as a promising route toward protected superconducting qubits with local, scalable, and all-electrical control.
During this grant, we have invented, designed and successfully operated a new type of readout for charge-phase superconducting qubits. This new readout is based on the bifurcation of an RF-driven Josephson junction inserted in the loop of a split Cooper pair box. When the amplitude of the RF drive is in the vicinity of the bifurcation points a small change in the effective critical current of the junction is amplified into a large phase change in the reflected signal. The performance reached by the device is in agreement with theoretical predictions. The speed of this readout is unprecedented: we measure in 20ns the critical current increment corresponding to the transition between the 2 states of the qubit. The repetition rate is 10Mz. We have performed a series of experiments showing that the amplification mechanism behaves as expected. No quasiparticles are produced during the readout and the back-action on the qubit when the readout is OFF is minimal. We have performed decoherence measurements at dilution refrigerator temperatures on the quantronium qubit integrated with RF readout. These measurements involve all possible 1-qubit gate operations. Compared with the DC readout method we have gained in repetition rate (factor of 100), signal-to-noise ration on all coherence signals (factor of 10) but most importantly, on readout fidelity which now attains more than 60% (compared to 15%). This last improvement is very important for showing the entanglement produced by two-bit gate operations. The T1 has also been improved by 250%. We still have comparable T2 as before but we suspect this is due to insufficient filtering on the listening lines of our measurement apparatus and this problem is technically solvable. In parallel with this work on readout and decoherence of the quantronium qubit, we have designed a new 2-bit gate based on capacitive coupling between qubits and worked out the complete protocol of pulses.
Recently, fault tolerant quantum computation such as surface coding and topological quantum computation has been paid attention to due to high threshold against computational errors compared with that of conventional gate-model quantum computation.These schemes use a two or three-dimensional cluster state as universal resources for quantum computation.We can generate a cluster state by performing controlled-phase gates on an initial state prepared in |+⟩ state, where the control-phase gates are realized by nearest neighbor Ising type interactions.There are many proposal to realize Ising type interaction such as ultracold atoms in an optical lattice, superconducting charge qubits, superconducting spin qubits, resonator wave guides, nitrogen-vacancy centers, and quantum dots.Among many candidates, we especially discuss superconducting flux qubits.Superconducting flux qubits have a strong anharmonicity, so that we can perform high-speed single-qubit rotation with excellent fidelity.Usually, implementation of high-fidelity two-qubit gates is the hardest part for the realization of quantum computation.Two qubit gates require in-situ turn on/off the interaction between qubits by the external control apparatus.Since imperfection of the interaction control tends to induce spatially correlated errors between qubits, sophisticated technology is required to suppress such error rate below the threshold of fault tolerant quantum computation.Up to now, the generation of a large cluster state using solid-state qubit has not been demonstrated in a scalable manner yet.One of the main obstacles is the requirement for independent control of two-qubit gates that are necessary for the scalable quantum information processing.For a superconducting flux qubit, existing method uses applied magnetic field to control the interaction.It is known that the application of magnetic field to local area is difficult.Thus, it is hard to implement local control of the interaction without cross-talk problem where unwanted errors occurs between qubits.Firstly, we propose a novel way to control a number of two-qubit gates independently without using the on/off switching of locally applied magnetic field.Specifically, we assume the superconducting flux qubits that are inductively coupled with each other via always-on Ising interaction.Unlike the previous method to change the interaction strength with unitary operations, we fully make use of non-unitary properties of projective measurements so that we can effectively turn on/off the interaction via quantum feedforward.Also, we show how to generate a two or three-dimensional cluster state that are universal resource for fault tolerant quantum computation with constant stepsize operations.The on/off switching of locally applied magnetic field is not necessary to First of all, I would like to thank my adviser Professor Hiroshi Imai for his valuable comments and continuous support during the last five years.