Flux Qubit Research Articles

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

The spin-vortex-induced loop current (SVILC) is a nano-sized loop current predicted to exist in the CuO2 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 105 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 μs). 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.

Efficient single-photon frequency conversion in the microwave domain using superconducting quantum circuits

We present an approach to achieve efficient single-photon frequency conversion in the microwave domain based on coherent control in superconducting quantum circuits, which consist of a driven artificial atom coupled to a semi-infinite transmission line. Using the full quantum-mechanical method, we analyze the single-photon scattering process in this system and find that single-photon frequency up- or down-conversion with efficiency close to unity can be achieved by adjusting the parameters of the control field applied to the artificial atom. We further show that our approach is experimentally feasible in currently available superconducting flux qubit circuits.

Emulating Majorana fermions and their braiding by Ising spin chains

We analyze the control of Majorana zero-energy states by mapping the fermionic system onto a chain of Ising spins. Although the topological protection is lost for the Ising system, the mapping provides additional insight into the nature of the quantum states. By controlling the local magnetic field, one can separate the Ising chain into ferromagnetic and paramagnetic phases, corresponding to topological and nontopological sections of the fermionic system. In this paper we propose (topologically nonprotected) protocols performing the braiding operation, and in fact also more general rotations. We first consider a $T$-junction geometry, but we also propose a protocol for a purely one-dimensional (1D) system. Both setups rely on an extra spin-$\frac{1}{2}$ coupler. By including the extra spin in the $T$-junction geometry, we overcome limitations due to the 1D character of the Jordan--Wigner transformation. In the 1D geometry the coupler, which controls one of the Ising links, should be manipulated once the ferromagnetic (topological) section of the chain is moved far away. We also propose experimental implementations of our scheme. One is based on a chain of flux qubits which allows for all needed control fields. We also describe how to translate our scheme for the 1D setup to a chain of superconducting wires hosting each a pair of Majorana edge states.

Development of a Superconducting Differential Double Contour Interferometer.

We study operation of a new device, the superconducting differential double contour interferometer (DDCI), in the application for the ultrasensitive detection of magnetic flux and for digital read out of the state of the superconducting flux qubit. DDCI consists of two superconducting contours weakly coupled by Josephson junctions. In such a device a change of the critical current, caused by an external magnetic flux or a nearby electric current, happens in a step-like manner when the angular momentum quantum number changes by one in one of the two contours. With a choice of parameters, the DDCI may outperform traditional superconducting quantum interference devices.

3D integrated superconducting qubits

As the field of quantum computing advances from the few-qubit stage to larger-scale processors, qubit addressability and extensibility will necessitate the use of 3D integration and packaging. While 3D integration is well-developed for commercial electronics, relatively little work has been performed to determine its compatibility with high-coherence solid-state qubits. Of particular concern, qubit coherence times can be suppressed by the requisite processing steps and close proximity of another chip. In this work, we use a flip-chip process to bond a chip with superconducting flux qubits to another chip containing structures for qubit readout and control. We demonstrate that high qubit coherence (T1, T2,echo > 20 μs) is maintained in a flip-chip geometry in the presence of galvanic, capacitive, and inductive coupling between the chips.

The road to long coherence time superconducting quantum bits

Superconducting quantum computing is a solid state quantum computing technology based on Josephson junction circuits. It becomes one of the most promising candidates for realizing practical quantum computer/simulator, because of its scalability, easy to coupling and control, compatibility to semiconductor technologies, etc. As the complicated electromagnetic environment in solid state metal and insulator, superconducting quantum bits (qubits) suffered from shot coherence time since its early development. In this review, we described some recently developed superconducting qubit structures, including Transmon/Xmon, Fluxonium and C-shunt flux qubit. Although these new qubit structures have very different circuit parameters and energy scales, they all find their way to effectively suppress environmental noises. As a result, their coherence time were improved significantly. Transmon, a transmission-line shunted plasma oscillation qubit, was now among the most popular structures for building a multi-qubit superconducting quantum circuit. It introduced a relatively large shunt capacitor to remarkably reduce the charge dispersion. Although the non-linearity is also decreased, by operating in a properly chosen E J / E c , transmon can greatly reduce the charge noise while only sacrificing a small amount of non-linearity. Xmon can be considered as a modified version of transmon. It is designed and optimized for multi-qubit operation and measurement with separate X / Y and Z control lines for each qubit, and a readout bus (a transmission line or a low- Q bandpass filter) for simultaneous readout of all the qubits. Fluxonium provide another solution for suppressing the charge noise in Cooper-pair box (CPB). It introduces a large shunt inductance to filter low-frequency offset charge in the small capacitor of the phase-slip junction (the small junction). To keep the qubit operating in the charge region, the shunt inductor should be large enough to keep the impedance larger than the superconducting impedance quantum R Q ~1 kΩ. As a result, the inductance can only be provided by a large series of Josephson junctions. Fluxonium keeps the advantage of high anharmonicity of CPB. In addition, it introduces another degree of freedom: external flux Φext. Quasiparticles (electrons or holes) tunneling at the small junction add coherently to produce a ″1+cos φ ″ term. As a result, when Φext= Φ0/2, dissipation caused by quasiparticle tunneling is suppressed and the energy relaxation time ( T 1) increases drastically. C-shunt flux qubit (CSFQ) decreases α and E J to suppress flux noise in the qubit. While the charge noise becomes the dominant noise source, a large shunt capacitor is added to suppress the charge noise, similar to that in a transmon qubit. It is worth to notice that in CSFQ, the α decreases to below but near 1/2. As a result, the double-well potential no longer exists. The energy structure become similar to transmon, with the anharmonicity be opposite. CSFQ can get a much improved coherence time, while its anharmonicity can be larger than that of transmon. Those new superconducting qubit structures provide different solutions to improve the coherence time. Although it looks much different in circuit models and parameters, they have ideas in common, and may act as guides to other novel designs with longer coherence time. We can summarize as below. (1) The qubit circuit should be free of small superconducting islands. Charge fluctuation in small islands is a major source of decoherence. As a result, increase the area of the islands, that is, increase the capacitance becomes a straight forward way to suppress the charge noise. In Fluxonium, the small junction is connected with a large series of large junctions that there is also no small islands in the whole loop. (2) Remove superconducting loops in the qubit circuit, or minimize the loop size and loop current to suppress flux noise. (3) Bias the phase difference of the small junction to π, where dissipation caused by quasiparticle tunneling can be suppressed coherently. (4) Decrease the coupling bandwidth of qubit to the environment. In a circuit-QED readout scheme, a high- Q readout resonator that dispersively coupled to the qubit protects the qubit from exposed to the electromagnetic environment of the readout circuit. A ″Purcell filter″ can also be added to suppress such decoherence further. In conclusion, we overviewed some qubit engineering techniques or ideas to improve the coherence time, which is a very important figure for building practical quantum computer/simulator. We hope that someone can combine and optimize these ideas, while interact with developments in materials and micro-fabrication technologies, to develop novel new generation superconducting qubit structures in the near future.

Non-stoquastic Hamiltonians in quantum annealing via geometric phases

We argue that a complete description of quantum annealing implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquasticity in the effective quantum Ising Hamiltonians that are typically used to describe quantum annealing with flux qubits. We explicitly demonstrate the effect of this geometric non-stoquasticity when quantum annealing is performed with a system of one and two coupled flux qubits. The realization of non-stoquastic Hamiltonians has important implications from a computational complexity perspective, since it is believed that in many cases quantum annealing with stoquastic Hamiltonians can be efficiently simulated via classical algorithms such as Quantum Monte Carlo. It is well known that the direct implementation of non-stoquastic Hamiltonians with flux qubits is particularly challenging. Our results suggest an alternative path for the implementation of non-stoquasticity via geometric phases that can be exploited for computational purposes.

Erratum to: “An optimization method for the calculation of Hamiltonian matrix elements for Josephson flux qubits”

Erratum to: “An optimization method for the calculation of Hamiltonian matrix elements for Josephson flux qubits”

Superconducting Qubits as Mechanical Quantum Engines.

We propose the equivalence of superconducting qubits with a pistonlike mechanical quantum engine. The work reports a study on the nature of the nonequilibrium work exchanged with the quantum-nonadiabatic working medium, which is modeled as a multilevel coupled quantum well system subject to an external control parameter. The quantum dynamics is solved for arbitrary control protocols. It is shown that the work output has two components: one that depends instantaneously on the level populations and another that is due to the quantum coherences built in the system. The nonadiabatic coherent dynamics of the quantum engine gives rise to a resistance (friction) force that decreases the work output. We consider the functional equivalence of such a device and a rf-SQUID flux qubit.

Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

We revisit the issue of thermally assisted quantum annealing by a detailed study of the dissipative Landau-Zener problem in presence of a Caldeira-Leggett bath of harmonic oscillators, using both a weak-coupling quantum master equation and a quasi-adiabatic path-integral approach. Building on the known zero-temperature exact results (Wubs et al., PRL 97, 200404 (2006)), we show that a finite temperature bath can have a beneficial effect on the ground-state probability only if it couples also to a spin-direction that is transverse with respect to the driving field, while no improvement is obtained for the more commonly studied purely longitudinal coupling. In particular, we also highlight that, for a transverse coupling, raising the bath temperature further improves the ground-state probability in the fast-driving regime. We discuss the relevance of these findings for the current quantum-annealing flux qubit chips.

A high-fidelity memory scheme for quantum data buses**Project supported by the National Natural Science Foundation of China (Grant Nos. 61673389, 61273202, 61134008, and 11404113).

A novel quantum memory scheme is proposed for quantum data buses in scalable quantum computers by using adjustable interaction. Our investigation focuses on a hybrid quantum system including coupled flux qubits and a nitrogen–vacancy center ensemble. In our scheme, the transmission and storage (retrieval) of quantum state are performed in two separated steps, which can be controlled by adjusting the coupling strength between the computing unit and the quantum memory. The scheme can be used not only to reduce the time of quantum state transmission, but also to increase the robustness of the system with respect to detuning caused by magnetic noises. In comparison with the previous memory scheme, about 80% of the transmission time is saved. Moreover, it is exemplified that in our scheme the fidelity could achieve 0.99 even when there exists detuning, while the one in the previous scheme is 0.75.

Superconducting qubit-resonator-atom hybrid system

We propose a hybrid quantum system where an LC resonator inductively interacts with a flux qubit and is capacitively coupled to a Rydberg atom. Varying the external magnetic flux bias controls the flux qubit flipping and the flux qubit-resonator interface. The atomic spectrum is tuned via an electrostatic field, manipulating the qubit-state transition of atom and the atom-resonator coupling. Different types of entanglement of superconducting, photonic and atomic qubits can be prepared via simply tuning the flux bias and electrostatic field, leading to the implementation of three-qubit Toffoli logic gate.

Quantum sensing

"Quantum sensing" describes the use of a quantum system, quantum properties or quantum phenomena to perform a measurement of a physical quantity. Historical examples of quantum sensors include magnetometers based on superconducting quantum interference devices and atomic vapors, or atomic clocks. More recently, quantum sensing has become a distinct and rapidly growing branch of research within the area of quantum science and technology, with the most common platforms being spin qubits, trapped ions and flux qubits. The field is expected to provide new opportunities - especially with regard to high sensitivity and precision - in applied physics and other areas of science. In this review, we provide an introduction to the basic principles, methods and concepts of quantum sensing from the viewpoint of the interested experimentalist.

One-step generation of continuous-variable quadripartite cluster states in a circuit QED system

We propose a dissipative scheme for one-step generation of continuous-variable quadripartite cluster states in a circuit QED setup consisting of four superconducting coplanar waveguide resonators and a gap-tunable superconducting flux qubit. With external driving fields to adjust the desired qubit-resonator and resonator-resonator interactions, we show that continuous-variable quadripartite cluster states of the four resonators can be generated with the assistance of energy relaxation of the qubit. By comparison with the previous proposals, the distinct advantage of our scheme is that only one step of quantum operation is needed to realize the quantum state engineering. This makes our scheme simpler and more feasible in experiment. Our result may have useful application for implementing quantum computation in solid-state circuit QED systems.

Single-photon-driven high-order sideband transitions in an ultrastrongly coupled circuit-quantum-electrodynamics system

We report the experimental observation of high-order sideband transitions at the single-photon level in a quantum circuit system of a flux qubit ultrastrongly coupled to a coplanar waveguide resonator. With the coupling strength reaching 10% of the resonator's fundamental frequency, we obtain clear signatures of higher-order red and first-order blue-sideband transitions, which are mainly due to the ultrastrong Rabi coupling. Our observation advances the understanding of ultrastrongly-coupled systems and paves the way to study high-order processes in the quantum Rabi model at the single-photon level.

Coherent Coupled Qubits for Quantum Annealing

Quantum annealing is an optimization technique which potentially leverages quantum tunneling to enhance computational performance. Existing quantum annealers use superconducting flux qubits with short coherence times, limited primarily by the use of large persistent currents $I_\mathrm{p}$. Here, we examine an alternative approach, using qubits with smaller $I_\mathrm{p}$ and longer coherence times. We demonstrate tunable coupling, a basic building block for quantum annealing, between two flux qubits with small ($\sim 50~\mathrm{nA}$) persistent currents. Furthermore, we characterize qubit coherence as a function of coupler setting and investigate the effect of flux noise in the coupler loop on qubit coherence. Our results provide insight into the available design space for next-generation quantum annealers with improved coherence.

23pPSB-8 超伝導磁束量子ビットとDC-SQUIDの結合によるサイドバンド遷移の理論解析

23pPSB-8 超伝導磁束量子ビットとDC-SQUIDの結合によるサイドバンド遷移の理論解析

Flux qubit interaction with rapid single-flux quantum logic circuits: Control and readout

We present the results of an analytical study and numerical simulation of the dynamics of a superconducting three-Josephson-junction (3JJ) flux qubit magnetically coupled with rapid single-flux quantum (RSFQ) logic circuit, which demonstrate the fundamental possibility of implementing the simplest logic operations at picosecond times, as well as rapid non-destructive readout. It is shown that when solving optimization problems, the qubit dynamics can be conveniently interpreted as a precession of the magnetic moment vector around the direction of the magnetic field. In this case, the role of magnetic field components is played by combinations of the Hamiltonian matrix elements, and the role of the magnetic moment is played by the Bloch vector. Features of the 3JJ qubit model are discussed during the analysis of how the qubit is affected by exposure to a short control pulse, as are the similarities between the Bloch and Landau-Lifshitz-Gilbert equations. An analysis of solutions to the Bloch equations made it possible to develop recommendations for the use of readout RSFQ circuits in implementing an optimal interface between the classical and quantum parts of the computer system, as well as to justify the use of single-quantum logic in order to control superconducting quantum circuits on a chip.

Coherent Coupling between 4300 Superconducting Flux Qubits and a Microwave Resonator

Coherent Coupling between 4300 Superconducting Flux Qubits and a Microwave Resonator

Scalable quantum computing model in the circuit-QED lattice with circulator function

We propose a model for a scalable quantum computing in the circuit-quantum electrodynamics(QED) architecture. In the Kagome lattice of qubits three qubits are connected to each other through a superconducting three-junction flux qubit at the vertices of the lattice. By controlling one of the three Josephson junction energies of the intervening flux qubit we can achieve the circulator function that couples arbitrary pair of two qubits among three. This selective coupling enables the interaction between two nearest neighbor qubits in the Kagome lattice, and further the two-qubit gate operation between any pair of qubits in the whole lattice by performing consecutive nearest neighbor two-qubit gates.