Quantum optimal control theory is applied to two and three coupled Josephson charge qubits. It is shown that by using shaped pulses a CNOT gate can be obtained with a trace fidelity > 0.99999 for the two qubits, and even when including higher charge states, the leakage is below 1%. Yet, the required time is only a fifth of the pioneering experiment [T. Yamamoto et al., Nature 425 (2003), 941] for otherwise identical parameters. The controls have palindromic smooth time courses representable by superpositions of a few harmonics. We outline schemes to generate these shaped pulses such as simple network synthesis. The approach is easy to generalise to larger systems as shown by a fast realisation of TOFFOLI's gate in three linearly coupled charge qubits. Thus it is to be anticipated that this method will find wide application in coherent quantum control of systems with finite degrees of freedom whose dynamics are Lie-algebraically closed.
We investigate the realization of a simple solid-state quantum computer by implementing the Deutsch-Jozsa algorithm in a system of Josephson charge qubits. Starting from a procedure to carry out the one-qubit Deutsch-Jozsa algorithm we show how the N-qubit version of the Bernstein-Vazirani algorithm can be realized. For the implementation of the three-qubit Deutsch-Jozsa algorithm we study in detail a setup which allows to produce entangled states.
We revisit the harmonic approximation (HA) for a large Josephson junction interacting with some charge qubits through the variational approach for the quantum dynamics of the junction-qubit coupling system. By making use of numerical calculation and analytical treatment, the conditions under which HA works well can be precisely presented to control the parameters implementing the two-qubit quantum logical gate through the couplings to the large junction with harmonic oscillator (HO) Hamiltonian.
We propose a threshold detector with an operation principle, based on a parametric period-doubling bifurcation in an externally pumped nonlinear resonance circuit. The ac-driven resonance circuit includes a dc-current-biased Josephson junction ensuring parametric frequency conversion (period-doubling bifurcation) due to its quadratic nonlinearity. A sharp onset of oscillations at the half-frequency of the drive allows for detection of small variations of an effective inductance and, therefore, the read-out of the quantum state of a coupled Josephson qubit. The bifurcation characteristics of th…
We study decoherence due to random telegraph and 1/f noise in Josephson qubits. We illustrate differences between gaussian and non gaussian effects at different working points and for different protocols. Features of the intrinsically non-gaussian and non-Markovian low-frequency noise may explain the rich physics observed in the spectroscopy and the dynamics of charge based devices.
We study the novel nonlinear phenomena that emerge in a charge qubit due to the interplay between a strong microwave flux drive and a periodic Josephson potential. We first analyze the system in terms of the linear Landau-Zener-Stückelberg model, and show its inadequacy in a periodic system with several Landau-Zener crossings within a drive period. Experimentally, we probe the quasienergy levels of the driven qubit with an LC-cavity, which requires the use of linear response theory. We also show that our numerical calculations are in good agreement with the experimental data.
We analyze possible implementations of quantum algorithms in a system of (macroscopic) Josephson charge qubits. System layout and parameters to realize the Deutsch algorithm with up to three qubits are provided. Special attention is paid to the necessity of entangled states in the various implementations. Further, we demonstrate explicitely that the gates to implement the Bernstein-Vazirani algorithm can be realized by using a system of uncoupled qubits.
A macroscopic spintronic qubit based on spin superfluidity and spin Hall phenomena is proposed. This magnetic quantum information processing device realizes the spin-supercurrent analog of the superconducting phase qubit and allows for full electrical control and readout. We also show that an array of interacting magnetic phase qubits can realize a quantum annealer. These devices can be built through standard solid-state fabrication technology, allowing for scalability. However, the upper bound for the operational temperature can, in principle, be higher than the superconducting counterpart, a…
We propose a scheme for generating SU(2) adiabatic geometric phases in a circuit consisting of three capacitively coupled flux-biased Josephson phase qubits.
We demonstrate theoretically the noise-stimulated enhancement of quantum coherence in a superconducting flux qubit. First, an external classical noise can increase the off-diagonal components of the qubit density matrix. Second, in the presence of noise, the Rabi oscillations survive for times significantly longer than the Rabi decay time in a noiseless system. These Rabi oscillations appear as a modulation of the forced response of the qubit to the ac driving field. These effects can be considered as a manifestation of quantum stochastic resonance and are relevant to experimental techniques, …
We propose and demonstrate a new read-out technique for a superconducting qubit by dispersively coupling it to a Josephson parametric oscillator. We employ a tunable quarter-wavelength superconducting resonator and modulate its resonant frequency at twice its value with an amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillation: one oscillating state, with $185\pm15$ photons in the resonator, and one with zero oscillation amplitude. This high contrast obviates a following quantum-limited amplifier. We d…
Conventional superconducting qubits have used Josephson junctions as an essential part to provide anharmonicity for well-separated energy-level spacings. However, because a superconducting ring without Josephson junctions has intrinsically well-separated energy-level spacings, Josephson junctions are not necessary as long as one can achieve single-qubit operations. We show that the orbital angular momentum of light can be adopted as a qubit-control means and can eliminate the need for Josephson junctions. The feasibility study reveals that the proposed qubit has many advantages over the previo…
We propose a protected qubit based on a modular array of superconducting islands connected by semiconductor Josephson interferometers. The individual interferometers realize effective $\cos2ϕ$ elements that exchange `pairs of Cooper pairs' between the superconducting islands when gate-tuned into balance and frustrated by a half flux quantum. If a large capacitor shunts the ends of the array, the circuit forms a protected qubit because its degenerate ground states are robust to offset charge and magnetic field fluctuations for a sizable window around zero offset charge and half flux quantum. Th…
There are two elementary superconducting qubit types that derive directly from the quantum harmonic oscillator. In one the inductor is replaced by a nonlinear Josephson junction to realize the widely used charge qubits with a compact phase variable and a discrete charge wavefunction. In the other the junction is added in parallel, which gives rise to an extended phase variable, continuous wavefunctions and a rich energy level structure due to the loop topology. While the corresponding rf-SQUID Hamiltonian was introduced as a quadratic, quasi-1D potential approximation to describe the fluxonium…
We demonstrate that two coupled Bose-Einstein condensates (BEC) at zero temperature can be used to realize a qubit which is the counterpart of Josephson charge qubits. The two BEC are weakly coupled and confined in an asymmetric double-well trap. When the "charging energy" of the system is much larger than the Josephson energy and the system is biased near a degeneracy point, the two BEC represent a qubit with two states differing only by one atom. The realization of the BEC qubits in realistic BEC experiments is briefly discussed.
We establish theoretical bounds on qubit detuning for high fidelity controlled-NOT logic gate implementations with weakly coupled Josephson phase qubits. It is found that the value of qubit detuning during the entangling pulses must not exceed 2g for two-step, and g for single-step control sequences, where g is the relevant coupling constant.
Low-capacitance Josephson junctions, where Cooper pairs tunnel coherently while Coulomb blockade effects allow the control of the total charge, provide physical realizations of quantum bits (qubits), with logical states differing by one Cooper-pair charge on an island. The single- and two-bit operations required for quantum computation can be performed by applying a sequence of gate voltages. A basic design, described earlier [cond-mat/9706016], is sufficient to demonstrate the principles, but requires a high precision time control, and residual two-bit interactions introduce errors. Here we s…
The two-level systems (TLSs) naturally occurring in Josephson junctions constitute a major obstacle for the operation of superconducting phase qubits. Since these TLSs can possess remarkably long decoherence times, we show that such TLSs can themselves be used as qubits, allowing for a well controlled initialization, universal sets of quantum gates, and readout. Thus, a single current-biased Josephson junction (CBJJ) can be considered as a multiqubit register. It can be coupled to other CBJJs to allow the application of quantum gates to an arbitrary pair of qubits in the system. Our results in…
The consistency test and error estimation for the data concerning recently reported violation of Bell inequality for Josephson phase qubits are presented in details. It is pointed out that the deviation of the Bell signal from the classical limit might still be challenged.
We propose a topological qubit in which braiding and readout are mediated by the $4π$ Majorana-Josephson effect. The braidonium device consists of three Majorana nanowires that come together to make a tri-junction; in order to control the superconducting phase differences at the tri-junction the nanowires are enclosed in a ring made of a conventional superconductor; and in order to perform initialization/readout one of the nanowires is coupled to a fluxonium qubit through a topological Josephson junction. We analyze how flux-based control and readout protocols can be used to demonstrate braidi…
We demonstrate Josephson junction based double-balanced mixer and phase shifter circuits operating at 6-10 GHz, and integrate these components to implement both a monolithic amplitude/phase vector modulator and a quadrature mixer. The devices are actuated by flux signals, dissipate no power on chip, exhibit input saturation powers in excess of 1 nW, and provide cryogenic microwave modulation solutions for integrated control of superconducting qubits.
We construct a semiclassical theory for the transport of topological junctions starting from a microscopic Hamiltonian that comprehensively includes the interplay among the Majorana qubit, the Josephson phase, and the dissipation process. With the path integral approach, we derive a set of semiclassical equations of motion that can be used to calculate the time evolution of the Josephson phase and the Majorana qubit. In the equations we reveal rich dynamical phenomena such as the qubit induced charge pumping, the effective spin-orbit torque, and the Gilbert damping. We demonstrate the influenc…
In superconducting circuits with interbit untunable (e.g., capacitive) couplings, ideal local quantum operations cannot be exactly performed on individual Josephson qubits. Here we propose an effective dynamical decoupling approach to overcome the "fixed-interaction" difficulty for effectively implementing elemental logical gates for quantum computation. The proposed single-qubit operations and local measurements should allow testing Bell's inequality with a pair of capacitively-coupled Josephson qubits. This provides a powerful approach, besides spectral-analysis [Nature \textbf{421}, 823 (20…
We have incorporated a single crystal silicon shunt capacitor into a Josephson phase qubit. The capacitor is derived from a commercial silicon-on-insulator wafer. Bosch reactive ion etching is used to create a suspended silicon membrane; subsequent metallization on both sides is used to form the capacitor. The superior dielectric loss of the crystalline silicon leads to a significant increase in qubit energy relaxation times. T1 times up to 1.6 micro-second were measured, more than a factor of two greater than those seen in amorphous phase qubits. The design is readily scalable to larger integ…
We report single-shot readout of a superconducting flux qubit by using a flux-driven Josephson parametric amplifier (JPA). After optimizing the readout power, gain of the JPA and timing of the data acquisition, we observe the Rabi oscillations with a contrast of 74% which is mainly limited by the bandwidth of the JPA and the energy relaxation of the qubit. The observation of quantum jumps between the qubit eigenstates under continuous monitoring indicates the nondestructiveness of the readout scheme.
We introduce a suit of simple entangling protocols for generating tripartite GHZ and W states in systems with anisotropic exchange interaction g(XX+YY)+g'ZZ. An interesting example is provided by macroscopic entanglement in Josephson phase qubits with capacitive (g'=0) and inductive (0<|g'/g|<0.1) couplings.
A goal of quantum information technology is to control the quantum state of a system, including its preparation, manipulation, and measurement. However, scalability to many qubits and controlled connectivity between any selected qubits are two of the major stumbling blocks to achieve quantum computing (QC). Here we propose an experimental method, using Josephson charge qubits, to efficiently solve these two central problems. The proposed QC architecture is scalable since any two charge qubits can be effectively coupled by an experimentally accessible inductance. More importantly, we formulate …
Superconducting quantum circuits based on Josephson junctions have made rapid progress in demonstrating quantum behavior and scalability. However, the future prospects ultimately depend upon the intrinsic coherence of Josephson junctions, and whether superconducting qubits can be adequately isolated from their environment. We introduce a new architecture for superconducting quantum circuits employing a three dimensional resonator that suppresses qubit decoherence while maintaining sufficient coupling to the control signal. With the new architecture, we demonstrate that Josephson junction qubit…
A type of two qubits Josephson charge system is constructed in this paper, and properties of the quantum discord (QD) as well as the differences between thermal QD and thermal entanglement were investigated. A detailed calculation shows that the magnetic flux $Φ_{Xk}$ is more efficient than the voltage $V_{Xi}$ in tuning QD. By choosing proper system parameters, one can realize the maximum QD in our two qubits Josephson charge system.
In this paper we investigate the short-time decoherence of single Josephson charge qubit (JCQ). The measure of decoherence is chosen as the maximum norm of the deviation density operator. It is shown that when the temperature low enough (for example T=30mK), within the elementary gate-operation time tau{g}~12.7ps, the decoherence is smaller than 0.0001 at present setup of JCQ. The Josephson charge qubit is suitable to take the blocks for quantum computations according to the DiVincenzo low decoherence criterion.
Proposals to measure non-Abelian anyons in a superconductor by quantum interference of vortices suffer from the predominantly classical dynamics of the normal core of an Abrikosov vortex. We show how to avoid this obstruction using coreless Josephson vortices, for which the quantum dynamics has been demonstrated experimentally. The interferometer is a flux qubit in a Josephson junction circuit, which can nondestructively read out a topological qubit stored in a pair of anyons --- even though the Josephson vortices themselves are not anyons. The flux qubit does not couple to intra-vortex excita…
A scheme for the generation of the cluster states based on the Josephson charge qubit is proposed. The two-qubit generating case is first introduced, and then generalized to multi-qubit case. The scheme is simple and easily manipulated, because any two charge qubits can be selectively and effectively coupled by a common inductance. More manipulations can be realized before decoherence sets in. All the devices in the scheme are well within the current technology.
We discuss quantum evolution of a decaying state in relation to a recent experiment of Katz et al. Based on exact analytical and numerical solutions of a simple model, we identify a regime where qubit retains coherence over a finite time interval independently of the rates of three competing decoherence processes. In this regime, the quantum decay process can be continuously monitored via a ``weak'' measurement without affecting the qubit coherence.
We introduce a method for finding the required control parameters for a quantum computer that yields the desired quantum algorithm without invoking elementary gates. We concentrate on the Josephson charge-qubit model, but the scenario is readily extended to other physical realizations. Our strategy is to numerically find any desired double- or triple-qubit gate. The motivation is the need to significantly accelerate quantum algorithms in order to fight decoherence.
The recent experimental evidence for entangled states of two Josephson junction qubits is briefly discussed. It is argued that the interpretation of the experimental data strongly depends on the assumed theoretical model. Namely, the qubit states are supposed to be the lowest lying eigenstates of a certain effective Hamiltonian and hence automatically orthogonal, while the simple analysis within a more fundamental many-particle model shows that those states should strongly overlap. This makes the standard interpretation of the measurement procedure questionable.
Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We report evidence for such oscillations in a _continuously_ observed three-Josephson-junction flux qubit, coupled to a high-quality tank circuit tuned to the Rabi frequency. In addition to simplicity, this method of_Rabi spectroscopy_ enabled a long coherence time of about 2.5 microseconds, corresponding to an effective qubit quality factor \~7000.
We analyze the coupling of two flux qubits with a general many-body projector into the low-energy subspace. Specifically, we extract the effective Hamiltonians that controls the dynamics of two qubits when they are coupled via a capacitor and/or via a Josephson junction. While the capacitor induces a static charge coupling tunable by design, the Josephson junction produces a magnetic-like interaction easily tunable by replacing the junction with a SQUID. Those two elements allow to engineer qubits Hamiltonians with $XX$, $YY$ and $ZZ$ interactions, including ultra-strongly coupled ones. We pre…
We discuss a protected quantum computation process based on a hexagon Josephson junction array. Qubits are encoded in the punctured array, which is topologically protected. The degeneracy is related to the number of holes. The topological degeneracy is lightly shifted by tuning the flux through specific hexagons. We also show how to perform single qubit operation and basic quantum gate operations in this system.
The coupling between a superconducting qubit and a control line inevitably results in radiative decay of the qubit into the line. We propose a Josephson quantum filter (JQF), which protects the data qubit (DQ) from radiative decay through the control line without reducing the gate speed on DQ. JQF consists of a qubit strongly coupled to the control line to DQ, and its working principle is a subradiance effect characteristic to waveguide quantum electrodynamics setups. JQF is a passive circuit element and is therefore suitable for integration in a scalable superconducting qubit system.
We analyze a controllable generation of maximally entangled mixed states of a circuit containing two-coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Illustrative variational calculations were performed to demonstrate the effect on the two-qubits entanglement. At sufficiently deviation between the Josephson energies of the qubits and/or strong coupling regime, maximally entangled mixed states at certain instances of time is synthesized. We show that entanglement has an interesting subsequent time ev…
Josephson qubits without direct interaction can be effectively coupled by sequentially connecting them to an information bus: a current-biased large Josephson junction treated as an oscillator with adjustable frequency. The coupling between any qubit and the bus can be controlled by modulating the magnetic flux applied to that qubit. This tunable and selective coupling provides two-qubit entangled states for implementing elementary quantum logic operations, and for experimentally testing Bell's inequality.
In this paper we propose a control strategy based on a classical guidance law and consider its use for an example system: a Josephson charge qubit. We demonstrate how the guidance law can be used to attain a desired qubit state using the standard qubit control fields.
We show that a complete set of one-bit gates can be realized by coupling the two logical states of a phase qubit to a third level (at higher energy) using microwave pulses. Thus, one can achieve coherent control without invoking any tunneling between the qubit levels. We propose two implementations, using rf-SQUIDs and d-wave Josephson junctions.
We introduce a new Josephson junction circuit for which quantum operations are realized by low-bandwidth, nearly adiabatic magnetic-flux pulses. Coupling to the fundamental mode of a superconducting transmission line permits a stabilization of the rotation angle of the quantum operation against flux noise. A complete scheme for one-qubit rotations, and high-visibility Ramsey-fringe oscillations, is given. We show that high visibility depends on passing through a portal in the space of applied fluxes, where the width of the portal is proportional to the ramp-up rate of the flux pulse.
We show that the three-junction SQUID device designed for the Josephson flux qubit can be used to study the dynamics of quantum chaos when operated at high energies. We determine the parameter region where the system is classically chaotic. We calculate numerically the fidelity or Loschmidt echo (LE) in the quantum dynamics under perturbations in the magnetic field and in the critical currents, and study different regimes of the LE. We discuss how the LE could be observed experimentally considering both the preparation of the initial state and the measurement procedure.
In this paper we investigate decoherence time of superconducting Josephson charge qubit (JCQ). Two kinds of methods, iterative tensor multiplication (ITM) method derived from the qusiadiabatic propagator path integral (QUAPI) and Bloch equations method are used. Using the non-Markovian ITM method we correct the decoherence time predicted by Bloch equations method. By comparing the exact theoretical result with the experimental data we suggest that the Ohmic noise plays the central role to the decoherence of the JCQ.
Superconducting materials with non-centrosymmetric lattices lacking the space inversion symmetry are known to exhibit a variety of interesting parity-breaking phenomena, including the anomalous Josephson effect. Here we consider a Josephson junction consisting of two non-centrosymmetric superconductors (NCSs) connected by a uniaxial ferromagnet, and demonstrate that it exhibits a direct analog of the Chiral Magnetic Effect observed in Dirac and Weyl semimetals. We propose to use this "Chiral Magnetic Josephson junction" (CMJ junction) as an element of a qubit with a Hamiltonian tunable by the …
We investigate the physical implementation of Shor's factorization algorithm on a Josephson charge qubit register. While we pursue a universal method to factor a composite integer of any size, the scheme is demonstrated for the number 21. We consider both the physical and algorithmic requirements for an optimal implementation when only a small number of qubits is available. These aspects of quantum computation are usually the topics of separate research communities; we present a unifying discussion of both of these fundamental features bridging Shor's algorithm to its physical realization usin…
We show that the three-junction SQUID device designed for the Josephson flux qubit can be used to study quantum chaos when operated at high energies. In the parameter region where the system is classically chaotic we analyze the spectral statistics. The nearest neighbor distributions $P(s)$ are well fitted by the Berry Robnik theory employing as free parameters the pure classical measures of the chaotic and regular regions of phase space in the different energy regions. The phase space representation of the wave functions is obtained via the Husimi distributions and the localization of the sta…
In this paper we calculate the loss of fidelity due to quantum leakage for the Josephson charge qubit (JCQ) in virtue of the Mathieu functions. It is shown that for an present typical parameters of JCQ E_{J}/E_{ch}~0.02, the loss of the fidelity per elementary operation is about 10^(-4) which satisfy the DiVincenzo's low decoherence criterion. By appropriately improving the design of the Josephson junction, namely, decreasing E_{J}/E_{ch} to 0.01, the loss of fidelity per elementary operation can decrease to 10^(-6) even smaller.
We discuss the relaxation and dephasing rates that result from the control and the measurement setup itself in experiments on Josephson persistent-current qubits. For control and measurement of the qubit state, the qubit is inductively coupled to electromagnetic circuitry. We show how this system can be mapped on the spin-boson model, and how the spectral density of the bosonic bath can be derived from the electromagnetic impedance that is coupled to the qubit. Part of the electromagnetic environment is a measurement apparatus (DC-SQUID), that is permanently coupled to the single quantum syste…
A Josephson qubit is designed via the application of a tensile strain to a topological insulator surface sandwiched between two s-wave superconductors. The strain applied leads to a shift in the Dirac point without changing the pre-existing conducting states, on the surface of a topological insulator. Strain applied can be tuned to form a $π$ junction in such a structure. Combining two such junctions in a ring architecture leads to the ground state of the ring being in doubly degenerate state- the "0" and "1" states of a qubit. A qubit designed this way is quite easily controlled via the tunab…
At first, we generally investigate the short-time decoherence of a qubit nonlinearly coupling with a bath. The measure of the decoherence is chosen as the maximum norm of the deviation density operator. Then we concretely investigate the Josephson charge qubit (JCQ) model. It is shown that at the temperature T=30mK, the loss of fidelity (due to decoherence) of the JCQ is bigger than the DiVincenzo low decoherence criterion. The decoherence will decrease with the decrease of the experimental temperature. When the temperature decreases to T=0.3mK the DiVincenzo low decoherence criterion can be s…
Josephson junctions have been shown to be a promising solid-state system for implementation of quantum computation. The significant two-qubit gates are generally realized by the capacitive coupling between the nearest neighbour qubits. We propose an effective Hamiltonian to describe charge qubits coupled through the cavity. We find that nontrivial two-qubit gates may be achieved by this coupling. The ability to interconvert localized charge qubits and flying qubits in the proposed scheme implies that quantum network can be constructed using this large scalable solid-state system.
We propose an experimental approach to {\it macro}scopically test the Kochen-Specker theorem (KST) with superconducting qubits. This theorem, which has been experimentally tested with single photons or neutrons, concerns the conflict between the contextuality of quantum mechnaics (QM) and the noncontextuality of hidden-variable theories (HVTs). We first show that two Josephson charge qubits can be controllably coupled by using a two-level data bus produced by a Josephson phase qubit. Next, by introducing an approach to perform the expected joint quantum measurements of two separated Josephson …
