We investigate the performance of a three qubit error correcting code in the framework of superconducting qubit implementations. Such a code can recover a quantum state perfectly in the case of dephasing errors but only in situations where the dephasing rate is low. Numerical studies in previous work have however shown that the code does increase the fidelity of the encoded state even in the presence of high error probability, during both storage and processing. In this work we give analytical expressions for the fidelity of such a code. We consider two specific schemes for qubit-qubit interaction realizable in superconducting systems; one $σ_zσ_z$-coupling and one cavity mediated coupling. With these realizations in mind, and considering errors during storing as well as processing, we calculate the maximum operation time allowed in order to still benefit from the code. We show that this limit can be reached with current technology.
We investigate theoretically the magnetic spin-flip transitions of neutral atoms trapped near a superconducting slab. Our calculations are based on a quantum-theoretical treatment of electromagnetic radiation near dielectric and metallic bodies. Specific results are given for rubidium atoms near a niobium superconductor. At the low frequencies typical of the atomic transitions, we find that BCS theory greatly overestimates coherence effects, which are much less pronounced when quasiparticle lifetime effects are included through Eliashberg theory. At 4.2 K, the typical atomic spin lifetime is f…
2.4 GHz Flip-flop Device within Nonequilibrium Superconducting Diode
National Laboratory of Solid State Microstructures and Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固态微结构国家重点实验室与先进微结构协同创新中心）；College of Engineering and Applied Sciences, Nanjing University（南京大学工程与应用科学院）；School of Materials Science and Engineering, Zhangjiang Institute for Advanced Study, Shanghai Jiao Tong University（上海交通大学张江高等研究院材料科学与工程学院）；School of Physics, Nanjing University（南京大学物理学院）；State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Science（中国科学院上海硅酸盐研究所高性能陶瓷与超微结构国家重点实验室）
We study trapping of a cold atom by a single vortex line in an extreme type II superconducting chip, allowing for pinning and friction. We evaluate the atom's spin flip rate and its dephasing due to the vortex fluctuations in equilibrium and find that they decay rapidly when the distance to the vortex exceeds the magnetic penetration length. We find that there are special spin orientations, depending on the spin location relative to the vortex, at which spin dephasing is considerably reduced while perpendicular directions have a reduced spin flip rate. We also show that the vortex must be perp…
This paper gives an introduction to the physics and principles of operation of quantized superconducting electrical circuits for quantum information processing.
We propose a realization of flux qubit based on the hybrid ferromagnetic-superconducting device where the flux bias is induced purely by vector potential of the vanishing magnetic field. We support our conclusions with theoretical analysis and self-consistent three-dimensional simulations for material specific parameters.
We show that an LC parametric transducer can be effectively used to monitor an adiabatic evolution of the superconducting flux qubit. We propose a new scheme to measure the qubit's state, which is a quantum nondemolition measurement. The scheme can be easily extended to a three-qubit system, and allows the reading out of the qubits' states while the system remains in the ground state. An implementation of the adiabatic quantum algorithm MAXCUT for three superconducting flux qubits is discussed.
Single-shot readout experiments were performed on the two lowest-energy states of a superconducting qubit with three Josephson junctions embedded in a superconducting loop. We measured the qubit state via switching current Isw of a current-biased dc-SQUID, a quantum detector surrounding the qubit loop. The qubit signals were measured in a small Isw regime of the SQUID, typically less than 100 nA, where the Isw distribution is particularly narrow. The obtained single-shot data indicate that the qubit state is readout, through the flux generated by the qubit persistent-current, as energy eigenst…
We propose a method for switchable coupling between superconducting qubits using double resonance. The inter-qubit coupling is achieved by applying near-resonant oscillating fields to the two qubits. The deviation from resonance relaxes the criterion of strong driving fields while still allowing for a fully entangling two-qubit gate. This method avoids some of the shortcomings of previous proposals for switchable coupling. We discuss the possible application of our proposal to a pair of inductively coupled flux qubits, and we consider the extension to phase qubits.
We theoretically investigate selective coupling of superconducting charge qubits mediated by a superconducting stripline cavity with a tunable resonance frequency. The frequency control is provided by a flux biased dc-SQUID attached to the cavity. Selective entanglement of the qubit states is achieved by sweeping the cavity frequency through the qubit-cavity resonances. The circuit is scalable, and allows to keep the qubits at their optimal points with respect to decoherence during the whole operation. We derive an effective quantum Hamiltonian for the basic, two-qubit-cavity system, and analy…
We use a scanning superconducting quantum interference device (SQUID) to image the magnetic flux produced by a superconducting device designed for quantum computing. The nanometer-scale SQUID-on-tip probe reveals the flow of superconducting current through the circuit as well as the locations of trapped magnetic flux. In particular, maps of current flowing out of a flux-control line in the vicinity of a qubit show how these elements are coupled, providing insight on how to optimize qubit control.
Dielectric measurements on insulating materials at cryogenic temperatures can be challenging, depending on the frequency and temperature ranges of interest. We present a technique to study the dielectric properties of bulk dielectrics at GHz frequencies. A superconducting coplanar Nb resonator is deposited directly on the material of interest, and this resonator is then probed in distant-flip-chip geometry with a microwave feedline on a separate chip. Evaluating several harmonics of the resonator gives access to various probing frequencies, in the present studies up to 20 GHz. We demonstrate t…
We revisit the problem of diffusive proximity systems involving superconductors and normal metals (or ferromagnets) with magnetic disorder. On the length scales much larger than its correlation length, the effect of sufficiently weak magnetic disorder may be incorporated as a local spin-flip term in the Usadel equations. We derive this spin-flip term in the general case of a three-dimensional disordered Zeeman-type field with an arbitrary correlation length. Three different regimes may be distinguished: pointlike impurities (the correlation length is shorter than the Fermi wavelength), medium-…
Superconducting flux qubits are considered to investigate macroscopic many-qubit interactions. Many-qubit states based on current states can be manipulated through the current-phase relation in each superconducting loop. For flux qubit systems comprised of $N$ qubit loops, a general expression of low energy Hamiltonian is presented in terms of low energy levels of qubits and macroscopic quantum tunnelings between the many-qubit states. Many-qubit interactions classified by {\em Ising type- or tunnel-}exchange interactions can be observable experimentally. Flux qubit systems can provide various…
Detailed schemes are investigated for experimental verification of Quantum Zeno effect with a superconducting qubit. A superconducting qubit is affected by a dephasing noise whose spectrum is 1/f, and so the decay process of a superconducting qubit shows a naturally non-exponential behavior due to an infinite correlation time of 1/f noise. Since projective measurements can easily influence the decay dynamics having such non-exponential feature, a superconducting qubit is a promising system to observe Quantum Zeno effect. We have studied how a sequence of projective measurements can change the …
We provide insight into the qubit measurement process involving a switching type of detector. We study the switching-induced decoherence during escape events. We present a simple method to obtain analytical results for the qubit dephasing and bit-flip errors, which can be easily adapted to various systems. Within this frame we investigate potential of switching detectors for a fast but only weakly invasive type of detection. We show that the mechanism that leads to strong dephasing, and thus fast measurement, inverts potential bit flip errors due to an intrinsic approximate time reversal symme…
We propose a superconducting qubit design, based on a tunable RF-SQUID and nanowire kinetic inductors, which has a dramatically reduced transverse electromagnetic coupling to its environment, so that its excited state should be metastable. If electromagnetic interactions are in fact responsible for the current excited-state decay rates of superconducting qubits, this design should result in a qubit lifetime orders of magnitude longer than currently possible. Furthermore, since accurate manipulation and readout of superconducting qubits is currently limited by spontaneous decay, much higher fid…
We present a way to realize a 3-qubit quantum controlled-phase gate with superconducting qubit systems coupled to a cavity. This proposal does not require adjustment of the qubit level spacings or identical qubit-cavity coupling constants. Moreover, since only a resonant interaction is applied, the gate can be performed fast, within $\sim $ 10 nanosecond. This proposal is quite general, which can be applied to various types of superconducting qubits, atoms trapped in a cavity, or quantum dots coupled to a resonator.
An interaction-free measurement protocol is described for a quantum circuit consisting of a superconducting qubit and a read-out Josephson junction. By measuring the state of the qubit one can ascertain the presence of a current pulse through the circuit at a previous time without any energy exchange between the qubit and the pulse.
We demonstrate coherent control and measurement of a superconducting qubit coupled to a superconducting coplanar waveguide resonator with a dynamically tunable qubit-cavity coupling strength. Rabi oscillations are measured for several coupling strengths showing that the qubit transition can be turned off by a factor of more than 1500. We show how the qubit can still be accessed in the off state via fast flux pulses. We perform pulse delay measurements with synchronized fast flux pulses on the device and observe $T_1$ and $T_2$ times of 1.6 and 1.9 $μ$s, respectively. This work demonstrates how…
We present a new experimental protocol for performing universal gates in a register of superconducting qubits coupled by fixed on-chip linear reactances. The qubits have fixed, detuned Larmor frequencies and can remain, during the entire gate operation, biased at their optimal working point where decoherence due to fluctuations in control parameters is suppressed to first order. Two-qubit gates are performed by simultaneously irradiating two qubits at their respective Larmor frequencies with appropriate amplitude and phase, while one-qubit gates are performed by the usual single-qubit irradiat…
Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at the left and right ends of the chain in the Majorana-fermion representation. We also show this Majorana qubit in the spin representation and its advantage, over a single superconducting qubit, regarding quantum coherence. Moreover, we propose to use four superconducting qubits as the smallest…
We have developed an adiabatic Abelian geometric quantum computation strategy based on the non-degenerate energy eigenstates in (but not limited to) superconducting phase-qubit systems. The fidelity of the designed quantum gate was evaluated in the presence of simulated thermal fluctuation in superconducting phase qubits circuit and was found to be rather robust against the random errors. In addition, it was elucidated that the Berry phase in the designed adiabatic evolution may be detected directly via the quantum state tomography developed for superconducting qubits.
A composite system of Majorana-hosted semiconductor nanowire and superconducting flux qubit is inves- tigated. It is found that the coupling between these two subsystems can be controlled electrically, supplying a convenient method to implement π/8 phase gate of a Majorana-based topological qubit. We also present a scheme to transfer information from the flux qubit to the topological qubit using Landau-Zener transition. In addition, a structure named top-flux-flux is proposed to retrieve the information stored in the topological qubit. With the demonstration of the entanglement of two topologi…
We study the quantum operation of coupled superconducting flux qubits under a microwave irradiation. The flux qubits can be described as magnetic dipole moments in the limit of weak microwave field amplitude consistent with usual experimental situations. With the Hamiltonian for coupled qubits under a microwave field, we show that a strong coupling enables to realize the high performance controlled-NOT gate operation. For practical quantum computing we analyze the effect of microwave on switching function of phase-coupled qubits.
From a physicist's standpoint, the most interesting part of quantum computing research may well be the possibility to probe the boundary between the quantum and the classical worlds. The more macroscopic are the structures involved, the better. So far, the most "macroscopic" qubit prototypes that have been studied in the laboratory are certain kinds of superconducting qubits. To get a feeling for how macroscopic these systems can be, the states of flux qubits which are brought in a quantum superposition corresponds to currents composed of as much as 10^5-10^6 electrons flowing in opposite dire…
A general method for directly measuring the low-frequency flux noise (below 10 Hz) in compound Josephson junction superconducting flux qubits has been used to study a series of 85 devices of varying design. The variation in flux noise across sets of qubits with identical designs was observed to be small. However, the levels of flux noise systematically varied between qubit designs with strong dependence upon qubit wiring length and wiring width. Furthermore, qubits fabricated above a superconducting ground plane yielded lower noise than qubits without such a layer. These results support the hy…
We propose an architecture based on superconducting qubits and resonators for the implementation of a variety of exotic lattice systems, such as spin and Hubbard models in higher or fractal dimensions and higher-genus topologies. Spin systems are realized naturally using qubits, while superconducting resonators can be used for the realization of Bose-Hubbard models. Fundamental requirements for these designs, such as controllable interactions between arbitrary qubit pairs, have recently been implemented in the laboratory, rendering our proposals feasible with current technology.
We investigate theoretically the implementation of two-qubit gates in a system of two coupled superconducting qubits. In particular, we analyze two-qubit gate operations under the condition that the coupling strength is comparable to or even larger than the anharmonicity of the qubits. By numerically solving the time-dependent Schrödinger equation, we obtain the dependence of the two-qubit gate fidelity on the system parameters in the case of direct and indirect qubit-qubit coupling. Our numerical results can be used to identify the "safe" parameter regime for experimentally implementing two-q…
We measure the coherence of a new superconducting qubit, the {\em low-impedance flux qubit}, finding $T_2^* \sim T_1 \sim 1.5μ$s. It is a three-junction flux qubit, but the ratio of junction critical currents is chosen to make the qubit's potential have a single well form. The low impedance of its large shunting capacitance protects it from decoherence. This qubit has a moderate anharmonicity, whose sign is reversed compared with all other popular qubit designs. The qubit is capacitively coupled to a high-Q resonator in a $λ/2$ configuration, which permits the qubit's state to be read out disp…
We present a way for fast implementation of a two-qubit controlled phase gate with superconducting flux qubits coupled to a cavity. A distinct feature of this proposal is that since only qubit-cavity resonant interaction and qubit-pulse resonant interaction are used, the gate can be performed much faster when compared with the previous proposals. This proposal does not require adjustment of the qubit level spacings during the gate operation. In addition, neither uniformity in the qubit parameters nor exact placement of qubits in the cavity is needed by this proposal.
Following the demonstration of semiconductor-based Josephson junctions which are fully tuneable by electrical means, new routes have been opened for the study of hybrid semiconductor-superconductor qubits. These include semiconductor-based transmon qubits, single-spin Andreev qubits, and fault-tolerant topological qubits based on Majorana zero modes. In this perspective, we review recent progress in the path towards such novel qubit designs. After a short introduction and a brief digression about the historical roadmap that has led to the experimental state-of-the art, the emphasis is placed o…
Recent progress in superconducting qubits has demonstrated the potential of these devices for the future of quantum information processing. One desirable feature for quantum computing is independent control of qubit interactions as well as qubit energies. We demonstrate a new type of superconducting charge qubit that has a V-shaped energy spectrum and uses quantum interference to provide independent control over the qubit energy and dipole coupling to a superconducting cavity. We demonstrate dynamic access to the strong coupling regime by tuning the coupling strength from less than 200 kHz to …
We theoretically study macroscopic quantum entanglement in two superconducting flux qubits. To manipulate the state of two flux qubits, a Josephson junction is introduced in the connecting loop coupling the qubits. Increasing the coupling energy of the Josephson junction makes it possible to achieve relatively strong coupling between the qubits, causing two-qubit tunneling processes even dominant over the single-qubit tunneling process in the states of two qubits. It is shown that due to the two-qubit tunneling processes both the ground state and excited state of the coupled flux qubits can be…
We analyze simple quantum error detection and quantum error correction protocols relevant to current experiments with superconducting qubits. We show that for qubits with energy relaxation the repetitive N-qubit codes cannot be used for quantum error correction, but can be used for quantum error detection. In the latter case it is sufficient to use only two qubits for the encoding. In the analysis we demonstrate a useful technique of unraveling the qubit energy relaxation into "relaxation" and "no relaxation" scenarios. Also, we propose and numerically analyze several two-qubit algorithms for …
We study analytically and numerically the problem of two qubits with fixed coupling irradiated with quantum or classical fields. In the classical case, we derive an effective Hamiltonian, and construct composite pulse sequences leading to a CNOT gate. In the quantum case, we show that qubit-qubit-photon multiparticle entanglement and maximally entangled two-qubit state can be obtained by driving the system at very low powers (one quanta of excitation). Our results can be applied to a variety of systems of two superconducting qubits coupled to resonators.
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 two oppositely directed states of circulating current, leading to a vanishing of the splitting between the two qubit states. The suppression arises for interference between tunneling along different paths, and is analogous to that predicted previously for magnetic particles with half-integer spin.
Solid-state qubits have the potential for the large-scale integration and for the flexibility of layout for quantum computing. However, their short decoherence time due to the coupling to the environment remains an important problem to be overcome. We propose a new superconducting qubit which incorporates a spin-electronic device: the qubit consists of a superconducting ring with a ferromagnetic pi junction which has a metallic contact and a normal Josephson junction with an insulating barrier. Thus, a quantum coherent two-level state is formed without an external magnetic field. This feature …
We introduce simple qubit-encodings and logic gates which eliminate the need for certain difficult single-qubit operations in superconducting phase-qubits, while preserving universality. The simplest encoding uses two physical qubits per logical qubit. Two architectures for its implementation are proposed: one employing N physical qubits out of which N/2 are ancillas fixed in the |1> state, the other employing N/2+1 physical qubits, one of which is a bus qubit connected to all others. Details of a minimal set of universal encoded logic operations are given, together with recoupling schemes, th…
High fidelity quantum information processing requires a combination of fast gates and long-lived quantum memories. In this work, we propose a hybrid architecture, where a parity-protected superconducting qubit is directly coupled to a Majorana qubit, which plays the role of a quantum memory. The superconducting qubit is based upon a $π$-periodic Josephson junction realized with gate-tunable semiconducting wires, where the tunneling of individual Cooper pairs is suppressed. One of the wires additionally contains four Majorana zero modes that define a qubit. We demonstrate that this enables the …
Quantum computers promise to solve certain problems exponentially faster than possible classically but are challenging to build because of their increased susceptibility to errors. Remarkably, however, it is possible to detect and correct errors without destroying coherence by using quantum error correcting codes [1]. The simplest of these are the three-qubit codes, which map a one-qubit state to an entangled three-qubit state and can correct any single phase-flip or bit-flip error of one of the three qubits, depending on the code used [2]. Here we demonstrate both codes in a superconducting c…
We study an LC-circuit implemented using a current-biased Josephson junction (CBJJ) as a tunable coupler for superconducting qubits. By modulating the bias current, the junction can be tuned in and out of resonance and entangled with the qubits coupled to it. One can thus implement two-qubit operations by mediating entanglement. We consider the examples of CBJJ and charge--phase qubits. A simple recoupling scheme leads to a generalization to arbitrary qubit designs.
We analyze the crosstalk error mechanism in measurement of two capacitively coupled superconducting flux-biased phase qubits. The damped oscillations of the superconducting phase after the measurement of the first qubit may significantly excite the second qubit, leading to its measurement error. The first qubit, which is highly excited after the measurement, is described classically. The second qubit is treated both classically and quantum-mechanically. The results of the analysis are used to find the upper limit for the coupling capacitance (thus limiting the frequency of two-qubit operations…
Solid state qubits realized in superconducting circuits are potentially extremely scalable. However, strong decoherence may be transferred to the qubits by various elements of the circuits that couple individual qubits, particularly when coupling is implemented over long distances. We propose here an encoding that provides full protection against errors originating from these coupling elements, for a chain of superconducting qubits with a nearest neighbor anisotropic XY-interaction. The encoding is also seen to provide partial protection against errors deriving from general electronic noise.
We investigate the quantum dynamics of a system of two coupled superconducting qubits under microwave irradiation. We find that, with the qubits operated at the charge co-degeneracy point, the quantum evolution of the system can be described by a new effective Hamiltonian which has the form of two coupled qubits with tunable coupling between them. This Hamiltonian can be used for experimental tests on macroscopic entanglement and for implementing quantum gates.
We present a new readout method for a superconducting flux qubit, based on the measurement of the Josephson inductance of a superconducting quantum interference device that is inductively coupled to the qubit. The intrinsic flux detection efficiency and back-action are suitable for a fast and nondestructive determination of the quantum state of the qubit, as needed for readout of multiple qubits in a quantum computer. We performed spectroscopy of a flux qubit and we measured relaxation times of the order of 80 $μs$.
We introduce a frequency-multiplexed readout scheme for superconducting phase qubits. Using a quantum circuit with four phase qubits, we couple each qubit to a separate lumped-element superconducting readout resonator, with the readout resonators connected in parallel to a single measurement line. The readout resonators and control electronics are designed so that all four qubits can be read out simultaneously using frequency multiplexing on the one measurement line. This technology provides a highly efficient and compact means for reading out multiple qubits, a significant advantage for scali…
We propose an experimental scheme to simulate the dynamical quantum Hall effect and the related interaction-induced topological transition with a superconducting-qubit array. We show that a one-dimensional Heisenberg model with tunable parameters can be realized in an array of superconducting qubits. The quantized plateaus, which is a feature of the dynamical quantum Hall effect, will emerge in the Berry curvature of the superconducting qubits as a function of the coupling strength between nearest neighbor qubits. We numerically calculate the Berry curvatures of two-, four- and six-qubit array…
We present a superconducting qubit for the circuit quantum electrodynamics architecture that has a tunable coupling strength g. We show that this coupling strength can be tuned from zero to values that are comparable with other superconducting qubits. At g = 0 the qubit is in a decoherence free subspace with respect to spontaneous emission induced by the Purcell effect. Furthermore we show that in the decoherence free subspace the state of the qubit can still be measured by either a dispersive shift on the resonance frequency of the resonator or by a cycling-type measurement.
We present a method for measuring the internal state of a superconducting qubit inside an on-chip microwave resonator. We show that one qubit state can be associated with the generation of an increasingly large cavity coherent field, while the other remains associated with the vacuum. By measuring the outgoing resonator field with conventional devices, an efficient single-shot QND-like qubit readout can be achieved, enabling a high-fidelity measurement in the spirit of the electron-shelving technique for trapped ions. We expect that the proposed ideas can be adapted to different superconductin…
Although two-qubit entangling gates are necessary for universal quantum computing, they are notoriously difficult to implement with high fidelity. Recently, tunable couplers have become a key component for realizing high-fidelity two-qubit gates in superconducting quantum computers. However, it is still difficult to achieve tunable coupling free of unwanted residual coupling for highly detuned qubits, which are desirable for mitigating qubit-frequency crowding or errors due to crosstalk between qubits. We thus propose a design for this kind of tunable coupler, which we call a double-transmon c…
Exploiting the intrinsic nonlinearity of superconducting Josephson junctions, we propose a scalable circuit with superconducting qubits (SCQs) which is very similar to the successful one now being used for trapped ions. The SCQs are coupled to the "vibrational" mode provided by a superconducting LC circuit or its equivalent (e.g., a SQUID). Both single-qubit rotations and qubit-LC-circuit couplings/decouplings can be controlled by the frequencies of the time-dependent magnetic fluxes. The circuit is scalable since the qubit-qubit interactions, mediated by the LC circuit, can be selectively per…
