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 propose a scheme for generating SU(2) adiabatic geometric phases in a circuit consisting of three capacitively coupled flux-biased Josephson phase qubits.
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 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.
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 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 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.
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.
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…
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.
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…
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.
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.
In this paper we investigate the short-time decoherence from Ohmic and 1/f noise of single Josephson charge qubit (JCQ). At first, we use the short-time approximation to obtain the dynamics of the open JCQ. Then we calculate the decoherence the measure of which is chosen as the maximum norm of the deviation density operator. It is shown that the decoherence from 1/f noise plays the central role. The total decoherence from Ohmic and 1/f noise is serious at present experiential conditions according to the DiVincenzo criterion.
We demonstrate new experimental procedures for measuring small errors in a superconducting quantum bit (qubit). By carefully separating out gate and measurement errors, we construct a complete error budget and demonstrate single qubit gate fidelities of 0.98, limited by energy relaxation. We also introduce a new metrology tool -- a Ramsey interference error filter -- that can measure the occupation probability of the state $\ket{2}$ down to $10^{-4}$, a magnitude near the fault tolerant threshold.
Tunneling defects in disordered materials form spurious two-level systems which are a major source of decoherence for micro-fabricated quantum devices. For superconducting qubits, defects in tunnel barriers of submicrometer-sized Josephson junctions couple strongest to the qubit, which necessitates optimization of the junction fabrication to mitigate defect formation. Here, we investigate whether defects appear predominantly at the edges or deep within the amorphous tunnel barrier of a junction. For this, we compare defect densities in differently shaped Al/AlO$_x$/Al Josephson junctions that …
The process of measurement of a phase qubit by a resonant microwave cavity is considered for various interactions between the qubit and the cavity. A novel quasiclassical approach is described based on adiabatic reversals of the qubit state by an effective field. A similar approach was implemented earlier for the detection of electron and nuclear spins using magnetic resonance force microscopy (MRFM), but this approach has not previously been used for the measurement of a quantum state. Quasiclassical and quantum regimes are described. We consider both linear and nonlinear resonators. The effe…
In this paper, the scheme of quantum computing based on Stark chirped rapid adiabatic passage (SCRAP) technique [L. F. Wei et al., Phys. Rev. Lett. 100, 113601 (2008)] is extensively applied to implement the quantum-state manipulations in the flux-biased Josephson phase qubits. The broken-parity symmetries of bound states in flux-biased Josephson junctions are utilized to conveniently generate the desirable Stark-shifts. Then, assisted by various transition pulses universal quantum logic gates as well as arbitrary quantum-state preparations could be implemented. Compared with the usual PI-puls…
We compare two physical systems: polarization degrees of freedom of a macroscopic light beam and the Josephson junction (JJ) in the "charge qubit regime". The first system obviously cannot carry genuine quantum information and we show that the maximal entanglement which could be encoded into polarization of two light beams scales like 1/(photon number). Two theories of JJ, one leading to the picture of "JJ-qubit" and the other based on the mean-field approach are discussed. The later, which seems to be more appropriate, implies that the JJ system is, essentially, mathematically equivalent to t…
Superconducting qubits with tunable coupling are ideally suited for fast and accurate implementation of quantum logic. Here we present a simple approach, based on Weyl chamber steering, to CNOT gate design for inductively coupled phase qubits with tunable coupling strength g. In the presence of simultaneous rf pulses on the individual qubits that appropriately track the coupling strength as it is varied, we show that an infinite family of switching sequences preserving the time integral or "area" of g can be used to generate CNOT logic. We demonstrate our approach by considering time-dependenc…
We present a quantum computing scheme with atomic Josephson junction arrays. The system consists of a small number of atoms with three internal states and trapped in a far-off resonant optical lattice. Raman lasers provide the "Josephson" tunneling, and the collision interaction between atoms represent the "capacitive" couplings between the modes. The qubit states are collective states of the atoms with opposite persistent currents. This system is closely analogous to the superconducting flux qubit. Single qubit quantum logic gates are performed by modulating the Raman couplings, while two-qub…
A Josephson quantum filter (JQF) protects a data qubit (DQ) from the radiative decay into transmission lines in superconducting quantum computing architectures. A transmon, which is a weakly nonlinear harmonic oscillator rather than a pure two-level system, can play a role of a JQF or a DQ. However, in the previous study, a JQF and a DQ were modeled as two-level systems neglecting the effects of higher levels. We theoretically examine the effects of the higher levels of the JQF and the DQ on the control of the DQ. It is shown that the higher levels of the DQ cause the shift of the resonance fr…
The zero-voltage state of a Josephson junction biased with constant current consists of a set of metastable quantum energy levels. We probe the spacings of these levels by using microwave spectroscopy to enhance the escape rate to the voltage state. The widths of the resonances give a measurement of the coherence time of the two states involved in the transitions. We observe a decoherence time shorter than that expected from dissipation alone in resonantly isolated 20 um x 5 um Al/AlOx/Al junctions at 60 mK. The data is well fit by a model including dephasing effects of both low-frequency curr…
Two-level system fluctuators (TLS's) in the tunnel barrier of a Josephson junction have recently been demonstrated to cause novel energy splittings in spectroscopic measurements of superconducting phase qubits. With their strong coupling to the Josephson junction and relatively long decoherence times, TLS's can be considered as potential qubits and demonstrate coherent quantum effects. Here, we study the effective interaction between the TLS qubits that is mediated by a Josephson junction resonator driven by an external microwave source. This effective interaction can enable controlled quantum…
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.
We propose a scheme for simulating 3+1, 2+1, 1+1 Dirac equation for a free spin-1/2 particle with superconducting josephson circuits consisting of five qubits, four qubits, two qubits respectively. In 3+1D and 2+1D, the flux qubit1 driven by a resonant pulse is in the superposition state of its own two eigenstatesis, and it is used as a bus to induce the (blue)red-sideband excitation consisting of a magnetic pulse acting resonantly on two levels of the flux qubit2 and the energy levels of one phase qubit, which yields two (Anti)Jaynes-Cummings interactions with one driving pulse and reduces th…
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 calculate the out-of-time-ordered correlation function (OTOC) of a single impurity qubit coupled to fully a connected many-particle system such as a bosonic Josephson junction or spins with long-range interactions. In these systems the qubit OTOC can be used to detect both ground state and excited state quantum phase transitions (QPTs), making it a robust order parameter that is considerably more sensitive than the standard one-body correlation function. Finite size scaling exponents for an $N$ body system can also be accurately extracted from the long-time OTOC dynamics, however, for short…
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.
Any quantum computational network can be constructed with a sequence of the two-qubit diagonal quantum gates and one-qubit gates in two-state quantum systems. The universal construction of these quantum gates in the quantum systems and of the quantum computational networks with these gates may be achieved with the help of the operator algebra structure of Hamiltonians of the systems and the properties of the multiple-quantum operator algebra subspaces of the Liouville operator space and the specific properties of the quantum algorithm corresponding to the quantum network. As an example, the tw…
Josephson-junction based parametric amplifiers have become a ubiquitous component in superconducting quantum machines. Although parametric amplifiers regularly achieve near-quantum limited performance, they have many limitations, including low saturation powers, lack of directionality, and narrow bandwidth. The first is believed to stem from the higher order Hamiltonian terms endemic to Josephson junction circuits, and the latter two are direct consequences of the nature of the parametric interactions which power them. In this work, we attack both of these issues. First, we have designed a new…
Scaling of quantum computers to fault-tolerant levels relies critically on the integration of energy-efficient, stable, and reproducible qubit control and readout electronics. In comparison to traditional semiconductor control electronics (TSCE) located at room temperature, the signals generated by Josephson junction (JJ) based rf sources benefit from small device sizes, low power dissipation, intrinsic calibration, superior reproducibility, and insensitivity to ambient fluctuations. Previous experiments to co-locate qubits and JJ-based control electronics resulted in quasiparticle poisoning o…
Multi-qubit quantum processors coupled to networking provides the state-of-the-art quantum computing platform. However, each qubit has unique eigenfrequency even though fabricated in the same process. To continue quantum gate operations besides the detection and correction of errors it is required that the qubits must be synchronized in the same frequency. This study uses Kuramoto model which is a link between statistical mean-field technique and non-linear dynamics to synchronize the qubits applying small noise in the system. This noise could be any externally applied noise function or just n…
Josephson junctions form the essential non-linearity for almost all superconducting qubits. The junction is formed when two superconducting electrodes come within $\sim$1 nm of each other. Although the capacitance of these electrodes is a small fraction of the total qubit capacitance, the nearby electric fields are more concentrated in dielectric surfaces and can contribute substantially to the total dissipation. We have developed a technique to experimentally investigate the effect of these electrodes on the quality of superconducting devices. We use $λ$/4 coplanar waveguide resonators to emu…
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.
Achieving individual qubit readout is a major challenge in the development of scalable superconducting quantum processors. We have implemented the multiplexed readout of a four transmon qubit circuit using non-linear resonators operated as Josephson bifurcation amplifiers. We demonstrate the simultaneous measurement of Rabi oscillations of the four transmons. We find that multiplexed Josephson bifurcation is a high-fidelity readout method, the scalability of which is not limited by the need of a large bandwidth nearly quantum-limited amplifier as is the case with linear readout resonators.
We show that two capacitively-coupled Josephson junctions, in the quantum limit, form a simple coupled qubit system with effective coupling controlled by the junction bias currents. We compute numerically the energy levels and wave functions for the system, and show how these may be tuned to make optimal qubits. The dependence of the energy levels on the parameters can be measured spectroscopically, providing an important experimental test for the presence of entangled multiqubit states in Josephson-junction based circuits.
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…
There exists a large number of experimental and theoretical results supporting the picture of macroscopic qubits implemented by nanoscopic Josephson junctions of three different types -- charge qubit, flux qubit and phase qubit. The standard unified description of such systems is based on the formal quantization of the phenomenological Kirchhoff equations for the corresponding circuits. In this paper a simplified version of the BCS theory for superconductors is used to derive microscopic models for all types of small Josephson junctions. For these models the state-dependent individual tunnelin…
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 …
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.
A process tomography based optimization scheme for open quantum systems is used to determine the performance limits of Josephson charge qubits within current experimental means. The qubit is modeled microscopically as an open quantum system taking into account state leakage, as well as environment-induced dephasing based on experimental noise spectra. Within time-optimal control theory, we show that the competing requirements for suppression of state leakage and dephasing can be met by an external control of the effective qubit-environment interaction, yielding minimal gate fidelity losses of …
We propose an effective scheme for manipulating quantum information stored in a superconducting nanocircuit. The Josephson qubits are coupled via their separate interactions with an information bus, a large current-biased Josephson junction treated as an oscillator with adjustable frequency. The bus is sequentially coupled to only one qubit at a time. Distant Josephson qubits without any direct interaction can be indirectly coupled with each other by independently interacting with the bus sequentially, via exciting/de-exciting vibrational quanta in the bus. This is a superconducting analog of …
We propose a generalisation of dispersive qubit readout which provides the time evolution of a flux qubit observable. Our proposal relies on the non-linear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc-SQUID. Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection. The measurement process is simulated for the example of coherent qubit oscillations. This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction an…
Quantum optimal control theory allows to design accurate quantum gates. We employ it to design high-fidelity two-bit gates for Josephson charge qubits in the presence of both leakage and noise. Our protocol considerably increases the fidelity of the gate and, more important, it is quite robust in the disruptive presence of 1/f noise. The improvement in the gate performances discussed in this work (errors of the order of 10^{-3}-10^{-4} in realistic cases) allows to cross the fault tolerance threshold.
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 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.
A quantum-mechanical model for the interaction of Josephson vortices (fluxons) embedded in superconducting transmission line is presented. The vortices interact through emission and absorption of linear waves (electromagnetic cavity modes). We show that in a classical regime this peculiar type of interaction is determined by the product of instantaneous velocities of fluxons. In a quantum regime, this property provides tunable coupling between vortices which can be used for entanglement of vortex qubits. The physical mechanism of the vortex interaction is similar to that proposed for qubits ba…
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…
