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The transfer of quantum information between physical systems of a different nature is a central matter in quantum technologies. Particularly challenging is the transfer between discrete and continuous degrees of freedom of various harmonic oscillator systems. Here we implement a protocol for teleporting a continuous-variable optical qubit, encoded by means of low-amplitude coherent states, onto a discrete-variable, single-rail qubit-a superposition of the vacuum and single-photon optical states-via a hybrid entangled resource. We test our protocol on a one-dimensional manifold of the input qubit space and demonstrate the mapping onto the equator of the teleported qubit's Bloch sphere with an average fidelity of 0.83±0.04. Our work opens up the way to the wide application of quantum information processing techniques where discrete- and continuous-variable encodings are combined within the same optical circuit.

We propose a novel implementation of discrete time quantum walks for a neutral atom in an array of optical microtraps or an optical lattice. We analyze a one-dimensional walk in position space, with the coin, the additional qubit degree of freedom that controls the displacement of the quantum walker, implemented as a spatially delocalized qubit, i.e., the coin is also encoded in position space. We analyze the dependence of the quantum walk on temperature and experimental imperfections as shaking in the trap positions. Finally, combining a spatially delocalized qubit and a hyperfine qubit, we also give a scheme to realize a quantum walk on a two-dimensional square lattice with the possibility of implementing different coin operators., Comment: 10 pages, 8 figures; v2: some comments added and other minor changes

Entanglement can exist not only in the microscopic system (e.g., atom, photon, and ion trap) but also in macroscopic systems. According to recent research, entanglement can be achieved and controlled in superconducting devices. The quantum dynamics and entanglement mechanism of the coupled superconducting phase qubit and a two-level system (TLS) were demonstrated when the bipartite system was under microwave driving. Besides, the results reveal that when the system was experiencing decoherence, entanglement (concurrence) of the coupled superconducting phase qubit and TLS would oscillate damply with microwave driving time, even exhibiting concurrence sudden death and revival. The coupling effect of the superconducting qubit and TLS system and the resonant microwave together help to achieve entanglement, while concurrence death and concurrence revival are dependent on the decoherence source and mechanism, for example, the resonant microwave driving time acting on the bipartite coupling system. Furthermore, the simulation results show the entanglement of the coupled qubit and TLS system also depends on the purity of the initial states of the system. The article carried out a numerical simulation on the entanglement of different initial states, and the results showed that the entanglement of the coupled system changes with different initial states. For different initial states, entanglement, sudden death, and rejuvenation are still visible.

In this work, the variational method of the Pekar type is used to theoretically study the temperature effects on the bound polaron in the triangular quantum dot (QD) qubit subjected to an electromagnetic field. We analyze and discuss in detail the numerical results and show that the relationships of the ground and first excited state energies, the electron probability density and the electron oscillation period in the superposition state of the ground state and the first-excited state with the temperature, the cyclotron frequency, the electron-phonon coupling constant, the electric field strength, the confinement strength and the Coulomb impurity potential, respectively.

In this work, using the non-Hermitian Hamiltonian method, the transmission of a single photon in a one-dimensional waveguide interacting with the cavity containing an arbitrary number of photons and the two-level artificial atom is studied with allowance for the relaxation of the latter. For transport factors, analytical expressions which explicitly take into account the qubit relaxation parameter have been obtained. The form of the transmission (reflection) coefficient when there is more than one photon in the cavity qualitatively differs from the single-photon cavity and contains the manifestation of the photon blockade effect. The qubit lifetime depends on the number of photons in the cavity.

A quantum-memory unit scheme on the base of a semiconductor structure with quantum dots is proposed. The unit includes a microresonator with single and double quantum dots performing frequencyconverter and charge-qubit functions, respectively. The writing process is carried out in several stages and it is controlled by optical fields of the resonator and laser. It is shown that, to achieve high writing probability, it is necessary to use high-Q resonators and to be able to suppress relaxation processes in quantum dots.

Fast and high fidelity quantum control is the key technology of quantum computing. The hybrid system composed of the nitrogen-vacancy center and nearby Carbon-13 nuclear spin is expected to solve this problem. The nitrogen-vacancy center electron spin enables fast operations for its strong coupling to the control field, whereas the nuclear spins preserve the coherence for their weak coupling to the environment. In this paper, we describe a strategy to achieve time-optimal control of the Carbon-13 nuclear spin qubit by alternating controlling the nitrogen-vacancy center electron spin as an actuator. We transform the qubit gate operation into a switched system. By using the maximum principle, we study the minimum time control of the switched system and obtain the time-optimal control of the qubit gate operation. We show that the X gate and Y gate operations are within 10 μs while the fidelity reaches 0.995.

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...

We propose an efficient qubit initialization protocol based on a dissipative environment that can be dynamically adjusted. Here the qubit is coupled to a thermal bath through a tunable harmonic oscillator. On-demand initialization is achieved by sweeping the oscillator rapidly into resonance with the qubit. This resonant coupling with the engineered environment induces fast relaxation to the ground state of the system, and a consecutive rapid sweep back to off resonance guarantees weak excess dissipation during quantum computations. We solve the corresponding quantum dynamics using a Markovian master equation for the reduced density operator of the qubit-bath system. This allows us to optimize the parameters and the initialization protocol for the qubit. Our analytical calculations show that the ground-state occupation of our system is well protected during the fast sweeps of the environmental coupling and, consequently, we obtain an estimate for the duration of our protocol by solving the transition rates between the low-energy eigenstates with the Jacobian diagonalization method. Our results suggest that the current experimental state of the art for the initialization speed of superconducting qubits at a given fidelity can be considerably improved., 17 pages, 6 figures

We study the quantum tunneling of a two-level multi-crossing system in an accelerating one-dimensional optical parabolic potential manifested in a 3D heterostructure magnetic quantum wire. By direct integration using the Dynamic matrix approach (DMA), we establish the time and magnetic field dependencies of the generalized analytic expressions of the survival and transition probabilities, respectively in the presence and in the absence of a harmonic confinement potential. The system causes a modulation of the transition frequency which differs from the one observed in the Landau-Zener (LZ) theory that appear when such magnetic inhomogeneity occurs. It is shown that in the absence of a curved confinement and for exceedingly low and extremely high frequencies of the magnetic field, the phase difference of the two wave packets acquired between subsequent crossings allows us to probe Landau-Zener-Stuckelberg (LZS) interferometry effects. Otherwise, in the presence of a curved confinement and for low values of the LZ parameter, the system readily exhibits more multi-crossings in the tunneling probabilities. The probe qubit spectrum obtained from this approach can be used to characterize the qubit evolution in the sample while the DMA is used for the modeling of dynamic spins in order to satisfy an optimum control quality with high accuracy.

Summary Accessing multiple data through a common bus in quantum information processing is challenging. Experimental demonstration of quantum state transfer between a pair of superconducting phase qubit [M. A. Sillanpaa et al., Nature 449, 438 (2007)] motivates us to construct a scheme for accessing and transferring multi-qubit quantum information through a common cavity bus. Here, we have presented an efficient scheme to access multiple data through single channel using superconducting qubit and superconducting cavity resonator. The qubit–cavity photon coupling offers transfer of quantum data in different location of a quantum processing system from multiple users through a common superconducting cavity resonator. Instead of phase qubit, charge qubit is found to be more advantageous in qubit–cavity interaction for quantum data transformation, because charge qubit is immune to flux and external flux is used to select specific qubit from a set of qubits. The scheme is very generic and provides M-output from N-number of inputs via a common cavity in circuit quantum electrodynamics. The flexibility of the scheme allows us to implement multiplexer, demultiplexer, and so on for quantum data manipulation in a similar manner as in classical digital electronics. This scheme is useful to reduce the circuit complexity in quantum processor named as ‘quprocessor’. Copyright © 2017 John Wiley & Sons, Ltd.

In the present paper, an analytical description of a superconducting charge qubit, coupled to a dissipative on-chip cavity in thermal bath, is found. We investigate the entropy squeezing and variance squeezing of the charge qubit under the parameters of the damping rate, thermal photons, the intensity of coherent state and qubit distribution angle. It is interesting to note that: (i) The charge qubit squeezing can be protected for a long time when both the damping rate and thermal photons effects are simultaneously considered. (ii) The appearance and disappearance of the squeezing phenomena depend on the coherence intensity and the qubit distribution angle. (iii) Entropy squeezing is more precise than variance squeezing as a measure of the squeezing. The entanglement and the coherence loss, by using the Bloch vector, of a superconducting qubit are investigated. It was found that the coupling to the thermal reservoirs leads to persistent purity loss and entanglement death, they remain nearly invariant regardless of the increase of time.

Arrays of transmon qubits coupled to a λ/2 superconducting coplanar waveguide resonator have been studied by microwave spectroscopy. The emergence of a collective mode has been discovered for a cluster of N > 5 qubits, whose coupling constant to the electromagnetic field in the resonator is √N times greater compared to a single qubit. In addition, the emergence of collective multiphoton transitions exciting higher levels of a qubit cluster has been demonstrated and the interaction of an individual qubit with such a cluster has been investigated.

通过使用Lewis-Riesenfeld不变量理论，我们研究了大约瑟夫逊结量子比特中拉比振荡的几何相位。发现几何相位与偏置电流的直流和微波脉冲无关，也与微波的转换频率无关。 By using the Lewis–Riesenfeld invariant theory, we have studied the geometric phase of Rabi oscillations in a large Josephson-junction qubit. The geometric phase has nothing to do with the dc and microwave pulses of bias current, and is independent of the transitions frequencies of microwaves.

The non-dissipative non-linearity of a Josephson junction converts macroscopic superconducting circuits into artificial atoms, enabling some of the best controlled quantum bits (qubits) today. Three fundamental types of superconducting qubits are known, each reflecting a distinct behavior of quantum fluctuations in a Cooper pair condensate: single charge tunneling (charge qubit), single flux tunneling (flux qubit), and phase oscillations (phase qubit). Yet, the dual nature of charge and flux suggests that circuit atoms must come in pairs. Here we introduce the missing one, named "blochnium". It exploits a coherent insulating response of a single Josephson junction that emerges from the extension of phase fluctuations beyond the $2\pi$-interval. Evidence for such effect was found in an out-of-equilibrium dc-transport through junctions connected to high-impedance leads, although a full consensus is absent to date. We shunt a weak junction with an exceptionally high-value inductance -- the key technological innovation behind our experiment -- and measure the rf-excitation spectrum as a function of external magnetic flux through the resulting loop. The junction's insulating character manifests by the vanishing flux-sensitivity of the qubit transition between the ground and the first excited states, which nevertheless rapidly recovers for transitions to higher energy states. The spectrum agrees with a duality mapping of blochnium onto transmon, which replaces the external flux by the offset charge and introduces a new collective quasicharge variable in place of the superconducting phase. Our result unlocks the door to an unexplored regime of macroscopic quantum dynamics in ultrahigh-impedance circuits, which may have applications to quantum computing and quantum metrology of direct current., Comment: close to published version, supplementary information available at www.superconducting-circuits.com

In this chapter we will discuss the high frequency properties of Josephson junctions. In the first part we review the effect of a large ac perturbation on the current voltage characteristic (IVC) of a Josephson junction. Here we follow closely the original treatment by Barone and Paterno [1]. For large ac perturbations the externally applied microwave frequency (and integer multiples of it) lock to the Josephson oscillation causing distinct current steps at fixed voltage values in the IVC. In the second part we give a short overview on the response of an underdamped Josephson junction to small microwave perturbations. In this case, when the applied microwave frequency is in resonance with the electromagnetic plasma frequency higher levels of this plasma mode get excited. This mechanism, also called resonant activation, leads for instance to a premature switching from the zero voltage state to the finite voltage state of a current biased Josephson junction. This procedure can be exploited to detect the quantized nature, i.e. the quantized energy levels, of the plasma modes. In fact the lowest two quantized energy levels of the plasma resonance mode are the key ingredient of superconducting qubits, such as the phase qubit and the transmon qubit.

This paper reports on the results of the investigation of a superconducting flux quantum bit (qubit) in the quasi-dispersive regime, where the frequency of a probe signal even though is lower than, but, nevertheless, close to the excitation frequency of the qubit. In this regime, in contrast to the known experiments, the interaction of the qubit with a waveguide leads not only to a shift of the resonance frequency, which is characteristic of the dispersive regime, but also to a significant broadening of the resonance line due to the spontaneous emission of the qubit. On the basis of the analysis of the amplitude–frequency characteristic of the transmission signal, this makes it possible to determine, under single-frequency excitation, the characteristic parameters of the qubit inductively coupled to the coplanar resonator.

Selective measurements of the states are studied for a single quantum system, viz, a Josephson qubit, by a nonlinear oscillator operating in the mesoscopic regime in which the number of quanta during measurements is varied from a few dozen to several hundreds. The quantum Monte Carlo method is used to simulate the dissipative dynamics of the qubit–oscillator system and the process of measurements of the qubit states from the change in the number of oscillator quanta. It is shown that for π-pulses in the recording of qubit states, discrimination of states is possible in single realizations (measurements), while statistical projective measurements can be made for the prepared superposition state.

Using the variational method of the Pekar type, we study the influences of the temperature on the parabolic quantum dot qubit in the magnetic field under the condition of electric–LO-phonon strong coupling. Then we derive the numerical results and formulate the derivative relationships of the oscillation period of the electron in the superposition state of the ground state and the first-excited state with the magnetic field, the electron–LO-phonon coupling constant and the confinement length at different temperatures, respectively.

The transient scattered spectrum with Haar wavelet window function is calculated analytically for a resonant pulsed driven qubit (taken as spin-12 2-level atom). The pulse shape is taken as the sequential laser sin2-pulse. Effect of the window function dilation and shift parameters are associated with the pulse strength and the initial atomic state. In particular, for strong pulse strength and increasing shift parameter: (i) the 3-peak structure turns into a central broader peak with ‘hole burning’ at its centre, only, for the case of initial ground state, and not with the initial excited state, (ii) for the case of initial atomic coherent state, the 3-peak structure has an oscillatory envelope due to the non-zero initial coherent dipole field.

Employing the Pekar variational method, quantum statistics theory and the Fermi golden rule, the temperature and magnetic field effects on the qubit in rubidium chloride (RbCl) parabolic quantum dots (PQDs) are investigated. We then obtain the eigenenergies and corresponding eigenfunctions of ground and first-excited states coupled strongly to an electron to bulk longitudinal optical phonons in a RbCl PQD with applied magnetic field. A two-level system of PQDs may be regarded as a single qubit. The spontaneous emission of phonons causes the qubit decoherence. The numerical results indicate that the coherence time decreases with elevating temperature. The coherence increases the effective confinement length, whereas there is a decrease of the magnetic field’s cyclotron frequency.

We investigate entanglement and mixedness of a superconducting qubit coupled to the damped cavity field. We introduce a new measure for the mixedness and find that the phase damping of the cavity leads to simultaneous long-death of the entropy squeezing, the purity of the qubit states, and the entanglement of the field–qubit system.

Measurement device independent Quantum Key Distribution (MDI-QKD), is immune to all attacks on detection and achieve immense improvement with respect to quantum key distribution system security. However, Bell state measurement (BSM), the kernel processing in MDI-QKD, can only identify two of the four Bell states, which limits the efficiency of the protocol. In this paper, a modified MDI-QKD with hybrid qubit is proposed to provide a major step towards answering this question. The hybrid qubits, which are composed of single photon qubit qubits and coherent qubit, are sent to the quantum relay to perform parallel BSMs synchronously and bit flip can be easily operated to complete the whole key distribution process. The secure key rate can be improved with our modified protocol owing to the higher success probability of BSM, which is increased by adding the parity check of coherent qubit. Furthermore, though our protocol requires photon number resolving detectors, the BSM of coherent state could be in...

We propose an efficient scheme for generating entangled states between a single nitrogen-vacancy (NV) centre in diamond and a superconducting qubit in a hybrid set-up. In this device, the NV centre and the superconducting qubit couple to a nanomechanical resonator and a superconducting coplanar waveguide cavity, respectively, while the microwave cavity and the mechanical resonator are parametrically coupled with a tunable coupling strength. We show that, highly entangled states between the NV centre and the superconducting qubit can be achieved, by means of the Jaynes–Cummings interactions in the NV-resonator and qubit-cavity subsystems which transfer the entanglement between the vibration phonons and the cavity photons to the NV centre and the superconducting qubit. This work may provide interesting applications in quantum computation and communication with single NV spins and superconducting qubits.

Engineering desired operations on qubits subjected to the deleterious effects of their environment is a critical task in quantum information processing, quantum simulation and sensing. The most common approach relies on open-loop quantum control techniques, including optimal-control algorithms based on analytical or numerical solutions, Lyapunov design and Hamiltonian engineering. An alternative strategy, inspired by the success of classical control, is feedback control. Because of the complications introduced by quantum measurement, closed-loop control is less pervasive in the quantum setting and, with exceptions, its experimental implementations have been mainly limited to quantum optics experiments. Here we implement a feedback-control algorithm using a solid-state spin qubit system associated with the nitrogen vacancy centre in diamond, using coherent feedback to overcome the limitations of measurement-based feedback, and show that it can protect the qubit against intrinsic dephasing noise for milliseconds. In coherent feedback, the quantum system is connected to an auxiliary quantum controller (ancilla) that acquires information about the output state of the system (by an entangling operation) and performs an appropriate feedback action (by a conditional gate). In contrast to open-loop dynamical decoupling techniques, feedback control can protect the qubit even against Markovian noise and for an arbitrary period of time (limited only by the coherence time of the ancilla), while allowing gate operations. It is thus more closely related to quantum error-correction schemes, although these require larger and increasing qubit overheads. Increasing the number of fresh ancillas enables protection beyond their coherence time. We further evaluate the robustness of the feedback protocol, which could be applied to quantum computation and sensing, by exploring a trade-off between information gain and decoherence protection, as measurement of the ancilla-qubit correlation after the feedback algorithm voids the protection, even if the rest of the dynamics is unchanged.

In the following study, the time evolution of the quantum mechanical state of a magnetopolaron using the Pekar type variational method on the electric-LO-phonon was considered. A strong coupling of polaron in triangular RbCl quantum dot with Coulomb impurity was duly derived. The Eigen energies and the Eigen functions of the ground state and the first excited state were obtained respectively. The obtained system in a quantum dot was treated as a two-level quantum system qubit and the numerical calculations were performed. The relations of polaron life time, the probability density, the Coulomb binding parameter and the polar angle were derived.

We propose a scheme for perfect quantum teleportation of a special form of four-qubit state by using a six-qubit cluster state as quantum channel. In our scheme, the sender only needs six-qubit von-Neumann projective measurements, and the receiver can reconstruct the original four-qubit state by applying the appropriate unitary operation.

Phosphorus donor spins in silicon are promising quantum bit (qubit) candidates. They have a natural confinement potential, long spin lifetimes and decades of use in the semiconductor fabrication industry. Readout of a single qubit is a necessary step to build a quantum computer, which could potentially solve particular problems exponentially faster than conventional computers. Electrically detected magnetic resonance has previously been used to measure the spin state of an ensemble of spins. In this literature review, the concept of a quantum computer is introduced before the potential of using electrically detected magnetic resonance to measure the spin state of a single donor spin qubit in a silicon transistor is discussed.

The properties of a superconducting flux quantum bit (qubit) in the quasidispersive mode, where the frequency of a probe signal is lower than the qubit excitation frequency but is close to it, have been experimentally studied. It has been shown that all parameters of the qubit inductively coupled to a coplanar resonator can be determined at the single-frequency excitation from the analysis of the frequency responses of the transmission of the probe signal at the output of this resonator. Under the additional excitation of the qubit by the signal at the second harmonic of the cavity, resonance dips have been observed because of resonance between the probe signal and induced Rabi splitting. It has been shown that the positions of these dips are in good agreement with the parameters of the qubit that are obtained by analyzing the amplitude–frequency response within the width of the fundamental resonance frequency.

In this paper, we examine the time evolution of the quantum mechanical state of a magnetopolaron using the Pekar type variational method on the electric-LO-phonon strong coupling in a triangular quantum dot with Coulomb impurity. We obtain the Eigen energies and the Eigen functions of the ground state and the first excited state, respectively. This system in a quantum dot is treated as a two-level quantum system qubit and numerical calculations are done. The Shannon entropy and the expressions relating the period of oscillation and the electron-LO-phonon coupling strength, the Coulomb binding parameter and the polar angle are derived.

By using a variational method of Pekar type, the Fermi Golden Rule and the quantum statistics theory (VMPTFGRQST), we investigate the effects of the hydrogen-like impurity and temperature on the coherence time of a parabolic quantum dot (PQD) qubit with a hydrogen-like impurity at the center. We then derive the ground and the first excited states' (GFES) eigenenergies and the eigenfunctions in a PQD. A single qubit can be realized in this two-level quantum system. The phonon spontaneous emission causes the decoherence of the qubit. The numerical results show that the coherence time is a decreasing function of the temperature, the strength of the Coulombic impurity potential (CIP) and the polaron radius (PR).

We study the effects of the temperature and electric field on the coherence time of a RbCl parabolic quantum dot (PQD) qubit by using the variational method of Pekar type, the Fermi Golden Rule and the quantum statistics theory (VMPTFGRQST). The ground and the first excited states’ (GFES) eigenenergies and the eigenfunctions of an electron in the RbCl PQD with an applied electric field are derived. A single qubit can be realized in this two-level quantum system. It turns out that the coherence time is a decreasing function of the temperature and the electric field, whereas it is an increasing one of the effective confinement length (ECL). By changing the electric field, the temperature and the ECL one can adjust the coherence time. Our research results may be useful for the design and implementation of solid-state quantum computation.

We propose a deterministic scheme to implement the multiqubit controlled-NOT gate of photons and multiqubit controlled-phase gate of electron spins with one control qubit and multiple target qubits using quantum dots in double-sided optical cavities. The scheme is based on spin selective photon reflection from the cavity and can be achieved in a nondestructive way. We assess the feasibility of the scheme and show that the gates can be implemented with high average fidelities by choosing the realistic system parameters appropriately. The scheme is useful in quantum information processing such as entanglement preparation, quantum error correction, and quantum algorithms.

We present a protocol for perfectly teleporting a five-qubit state of specific type. We utilize a sixqubit entangled quantum channel for this purpose. In this protocol only four out of 26 possible measurement outcomes appear. This leads to a substantial convenience in the implementation of the protocol.

Quantum Information The parity of a quantum mechanical wave function simply tells you if there is an odd or even number of excitations in the system it describes. Without the need to know the exact number of excitations within a system, being able to measure changes in parity is important and can be exploited in operations such as quantum error correction and stabilizing quantum communication protocols. Besse et al . demonstrate a detector that can determine the parity of a propagating microwave field. Using a superconducting phase qubit embedded in a cavity, they show that they can engineer the system such that transmission of the microwaves is conditional on there being an odd or even number of microwave photons in the radiation field. The simplicity of the detector design should have applications across a broad range of setups for quantum information processing. Phys. Rev. X 10 , 011046 (2020).