This work describes how to implement a non-local xor function for coherent-state qubit using only linear optics. The setup proposed does not use gates based on teleportation and it has probability of success equal to 0.5, in the lossless case, when the necessary entangled state is available. The key element that makes possible the realization of the non-local xor function is a tripartite GHZ-type entangled coherent state. Its generation is proposed firstly using an ideal lossless setup and secondly considering the decoherence caused by losses in the optical devices.
We consider the CNOT quantum gate as a physical action, i.e. as unitary in time evolution of the two-qubit system. This points to the modeling of the interaction Hamiltonian of the two-qubit system which would correspond to the CNOT transformation; the analysis naturally generalizes to the Toffoli gate. Despite nonuniqueness of the model of the interaction Hamiltonian, the analysis distinguishes that the interaction Hamiltonian does not posses any global (rotational) symmetry. This forces us to conclude that the direct (non-mediated) interaction in the two-qubit system does not suffice for imp…
The dynamics of a quantum XOR gate operation in a two-qubit system being coupled to a bath of quantum harmonic oscillators is investigated. Upon applying the numerical quasiadiabatic propagator path integral method, we obtain the numerically precise time-resolved evolution of this interacting two-qubit system in presence of time-dependent external fields without further approximations. We simulate the dissipative gate operation for characteristic experimental realizations of condensed matter qubits; namely, the flux and charge qubits realized in superconducting Josephson systems and qubits for…
A Sharp Local-Question Threshold for GHZ-Equatorial Completeness in Four-Player XOR Games
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；QudeLeap Research；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
We propose a method to implement a kind of non-local operations between spatially separated two systems with arbitrary high-dimensions by using only low-dimensional qubit quantum channels and classical bit communications. The result may be generalized straightforwardly to apply for multiple systems, each of them with arbitrary dimensions. Compared with existed approaches, our method can economize classical resources and the needed low-dimensional quantum channels may be more easily established in practice. We also show the construction of the non-local quantum XOR gate for qutrit systems in te…
We study quantum teleportation between two different types of optical qubits using hybrid entanglement as a quantum channel under decoherence effects. One type of qubit employs the vacuum and single photon states for the basis, called a single-rail single-photon qubit, and the other utilizes coherent states of opposite phases. We find that teleportation from a single-rail single-photon qubit to a coherent state qubit is better than the opposite direction in terms of fidelity and success probability. We compare our results with those using a different type of hybrid entanglement between a polar…
Based on a pure solid-state device consisting of two superconducting LC circuits coupled to a superconducting flux qubit, we propose in this paper that the maximally entangled coherent states of the two LC modes can be generated for arbitrary coherent states through flux qubit controls.
Introducing classical fields, we can transfer entanglement completely from discrete qubits into entangled coherent state. The entanglement also can be retrieved from the continuous-variable state of the cavities to the atomic qubits. Via postselection measure, atomic entangled state and entangled coherent state can be mutual transformed fully.
We consider an $N$ qubit system and show that in the symmetric subspace, $\mathbb{S}$ a state is not globally entangled, iff it is a coherent state. It is also proven that in the orthogonal complement $\mathbb{S}_{\bot}$ all states are globally entangled.
We investigate the non-Markovian dynamics of a qubit-oscillator system embedded in a noisy environment by employing the hierarchical equations of motion approach. It is found that the decoherence rate of the whole qubit-oscillator-bath system can be significantly suppressed by enhancing the coupling strength between the qubit and the harmonic oscillator. Moreover, we find that the non-Markovian memory character of the bath is able to facilitate a robust quantum coherent dynamics in this qubit-oscillator-bath system. Our findings may be used to engineer some tunable coherent manipulations in me…
We introduce a new gate that transfers an arbitrary state of a qubit into a superposition of two quasi-orthogonal coherent states of a cavity mode, with opposite phases. This qcMAP gate is based on conditional qubit and cavity operations exploiting the energy level dispersive shifts, in the regime where they are much stronger than the cavity and qubit linewidths. The generation of multi-component superpositions of quasi-orthogonal coherent states, non-local entangled states of two resonators and multi-qubit GHZ states can be efficiently achieved by this gate.
We discuss and experimentally demonstrate a probabilistic Hadamard gate for coherent state qubits. The scheme is based on linear optical components, non-classical resources and the joint projective action of a photon counter and a homodyne detector. We experimentally characterize the gate for the coherent states of the computational basis by full tomographic reconstruction of the transformed output states. Based on the parameters of the experiment we simulate the fidelity for all coherent state qubits on the Bloch sphere.
We discuss the long distance transmission of qubits encoded in optical coherent states. Through absorption these qubits suffer from two main types of errors, the reduction of the amplitude of the coherent states and accidental application of the Pauli Z operator. We show how these errors can be fixed using techniques of teleportation and error correcting codes.
In this letter we propose a scheme to build up high coherent solid-state quantum bit (qubit) from two coupled quantum dots. Quantum information is stored in electron-hole pair state with the electron and hole locating in different dots, and universal quantum gates involving any pair of qubits are realized by effective coupling interaction via virtually exchanging cavity photons.
We propose a quantum state transfer from an atomic qubit to a cat-like qubit by means of one degenerate Raman interaction and one Hadamard gate operation for coherent states. We show that the coefficients of the atomic qubit can be mapped onto coherent state qubit, with an effective qubit state transfer.
Discrete coherent states for a system of $n$ qubits are introduced in terms of eigenstates of the finite Fourier transform. The properties of these states are pictured in phase space by resorting to the discrete Wigner function
We put forward a method of constructing discrete coherent states for n qubits. After establishing appropriate displacement operators, the coherent states appear as displaced versions of a fiducial vector that is fixed by imposing a number of natural symmetry requirements on its Q-function. Using these coherent states we establish a partial order in the discrete phase space, which allows us to picture some n-qubit states as apparent distributions. We also analyze correlations in terms of sums of squared Q-functions.
Readout of the state of a superconducting qubit by homodyne detection of the output signal from a dispersively coupled microwave resonator is a common technique in circuit quantum electrodynamics, and is often claimed to be quantum non-demolition (QND) up to the same order of approximation as in the dispersive approximation. However, in this work we show that only in the limit of infinite measurement time is this protocol QND, as the formation of a dressed coherent state in the qubit-cavity system applies an effective rotation to the qubit state. We show how this rotation can be corrected by a…
We demonstrate ultrafast coherent coupling between an atomic qubit stored in a single trapped cadmium ion and a photonic qubit represented by two resolved frequencies of a photon. Such ultrafast coupling is crucial for entangling networks of remotely-located trapped ions through photon interference, and is also a key component for realizing ultrafast quantum gates between Coulomb-coupled ions.
In this paper we investigate the entanglement of multi-qubit fermionic coherent states described by anticommutative Grassmann numbers. Choosing an appropriate weight function, we show that it is possible to construct some entangled pure states, consisting of {\bf{GHZ}}, {\bf{W}}, Bell and biseparable states, by tensor product of fermion coherent states. Moreover a comparison with maximal entangled bosonic coherent states is presented and it is shown that in some cases they have fermionic counterpart which are maximal entangled after integration with suitable weight functions.
The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit functions using pure coherent superpositions of Li$_{2}$ rovibrational eigenstates. The function's character, either constant or balanced, is evaluated by first imprinting the function, using a phase-shaped femtosecond pulse, on a coherent superposition of the molecular states, and then projecting the superposition onto an ionic final state, using a second femtosecond pulse at a specific time delay.
We study the exact dynamics of optical qubits encoded via coherent states with opposite phases which are interacting with an environment modeled as a collection of simple harmonic oscillators. Making use of a coherent-state path integral formulation, we are able to study memory effects on the dynamics of the coherent-state qubits due to strong environment coupling. We apply this formulation to examine the time evolution of a noisy quantum channel formed by two coherent-state qubits that are subject to uncorrelated local environment noises. In particular, we examine the time evolution of entang…
We use a single squeezed state to represent a qubit, which can be coherently processed in a deconvolution picture (DP) in the presence of noise. We avail ourselves of the fact that when evolution is governed by a quadratic dissipative equation, there exists a basis of squeezed states that evolves to another basis of such states in the DP. An operator acts as an impurity filter, restoring the coherence lost from the inexorable interactions of the qubit with its surroundings.
We show how entangled qubits can be encoded as entangled coherent states of two-dimensional centre-of-mass vibrational motion for two ions in an ion trap. The entangled qubit state is equivalent to the canonical Bell state, and we introduce a proposal for entanglement transfer from the two vibrational modes to the electronic states of the two ions in order for the Bell state to be detected by resonance fluorescence shelving methods.
We show that the coherent coupling of atomic qubits at distant nodes of a quantum network, composed of several cavities linked by optical fibers, can be arbitrarily controlled via the selective pairing of Raman transitions. The adiabatic elimination of the atomic excited states and photonic states leads to selective qubit-qubit interactions, which would have important applications in quantum information processing. Quantum gates between any pair of distant qubits and parallel two-qubit operations on selected qubit pairs can be implemented through suitable choices of the parameters of the exter…
Squeezed state of light is one of the important subjects in quantum optics which is generated by optical nonlinear interactions. In this paper, we especially focus on qubit like entangled squeezed states (ESS's) generated by beam splitters, phase-shifter and cross Kerr nonlinearity. Moreover the Wigner function of two-mode qubit and qutrit like ESS are investigated. We will show that the distances of peaks of Wigner functions for two-mode ESS are entanglement sensitive and can be a witness for entanglement. Like the qubit cases, monogamy inequality is fulfilled for qutrit like ESS. These trend…
We consider the problem of bi-directional controlled quantum teleportation of information encoded in phase opposite coherent state among two distant partners Alice and Bob, with the consent of controller, Charlie. We use five-mode cluster-type entangled coherent state as the quantum resource to achieve this task. The scheme uses linear optical devices such as beam splitter, phase shifters, and photon counters. We have shown that for moderately large coherent amplitude, near-perfect bi-directional controlled teleportation can be obtained in terms of the average fidelity of teleportation.
We propose a class of preparation schemes for orbital angular momentum and polarisation qubits carried by single photons or classical states of light based on coherent feedback control by an ancillary degree of freedom of light. The preparation methods use linear optics and include the transcription of an arbitrary polarisation state onto a two-level OAM system (swap) for arbitrary OAM values plus/minus "l" within a light beam, i.e. without spatial interferometer. The preparations can be carried out with unit efficiency independent from the potentially unknown initial state of the system. More…
We consider a unitary transfer of an arbitrary state of a two-level atomic qubit in a cavity to the finite amplitude coherent state cavity field. Such transfer can be used to either provide an effective readout measurement on the atom by a subsequent measurement on the light field or as a method for initializing a fixed atomic state - a so-called "attractor state", studied previously for the case of an infinitely strong cavity field. We show that with a suitable adjustment of the coherent amplitude and evolution time the qubit transfers all its information to the field, attaining a selected st…
To generate arbitrary one- and two-qubit gates, the universal decompositions are usually used in quantum computing, and the universality of these decompositions has been demonstrated. However, in realistic experiments, gate errors may affect the universality of the universal decompositions. Here, we focus on the single-qubit-gate decomposition scheme and study the coherent-error effects on universality. We prove that, in the parameter space which we studied, some kinds of coherent errors will not affect the original universality, but some others will destroy it. We provide the definition and a…
We consider multiple-period states in systems of periodically modulated qubits. In such states the discrete time-translation symmetry imposed by the modulation is broken. We explicitly show how multiple-period states emerge in the simplest quantum system, a single qubit subjected to a pulsed resonant modulation and/or a pulsed modulation of the transition frequency. We also show that a qubit chain with the qubit coupling modulated at twice the qubit frequency has symmetry that allows mapping it on the Kitaev chain and thus provides an example of a topologically nontrivial Floquet system. An ex…
Graph states are a central resource in measurement-based quantum information processing. In the photonic qubit architecture based on Gottesman-Kitaev-Preskill (GKP) encoding, the generation of high-fidelity graph states composed of realistic, finite-energy approximate GKP-encoded qubits thus constitutes a key task. We consider the finite-energy approximation of GKP qubit states given by a coherent superposition of shifted finite-squeezed vacuum states, where the displacements are Gaussian distributed. We present an exact description of graph states composed of such approximate GKP qubits as a …
In this work we extend a multi-qubit benchmarking technique known as the Binned Output Generation (BOG) in order to discriminate between coherent and incoherent noise sources in the multi-qubit regime. While methods exist to discriminate coherent from incoherent noise at the single and few-qubit level, these methods scale poorly beyond a few qubits or must make assumptions about the form of the noise. On the other end of the spectrum, system-level benchmarking techniques exist, but fail to discriminate between coherent and incoherent noise sources. We experimentally verify the BOG against Rand…
Motivated by the need for communication of coherent state-based qubits in quantum computers, we introduce a method for perfect transferring of an arbitrary superposition of coherent states between two distant nodes of a linear array of three semiconductor QDs. The QDs trapped in a system of coupled cavities. In this method, the field mode of the cavities, as the resource of transferring of quantum states, are only virtually excited which minimizes the effect of decoherence due to photon loss.
We demonstrate a simple pulse shaping technique designed to improve the fidelity of spin-dependent force operations commonly used to implement entangling gates in trapped-ion systems. This extension of the Mølmer-Sørensen gate can theoretically suppress the effects of certain frequency and timing errors to any desired order and is demonstrated through Walsh modulation of a two-qubit entangling gate on trapped atomic ions. The technique is applicable to any system of qubits coupled through collective harmonic oscillator modes.
We study the use of squeezed light for qubit coherent control and compare it with the coherent state control field case. We calculate the entanglement between a short pulse of resonant squeezed light and a two-level atom in free space and the resulting operation error. We find that the squeezing phase, the phase of the light field and the atomic superposition phase, all determine whether atom-pulse mode entanglement and the gate error are enhanced or suppressed. However, when averaged over all possible qubit initial states, the gate error would not decrease by a practicably useful amount and w…
We demonstrate the implementation of a spin qubit with a single Ca ion in a micro ion trap. The qubit is encoded in the Zeeman ground state levels mJ=+1/2 and mJ=-1/2 of the S1/2 state of the ion. We show sideband cooling close to the vibrational ground state and demonstrate the initialization and readout of the qubit levels with 99.5% efficiency. We employ a Raman transition close to the S1/2 - P1/2 resonance for coherent manipulation of the qubit. We observe single qubit rotations with 96% fidelity and gate times below 5mus. Rabi oscillations on the blue motional sideband are used to extract…
We propose a scheme to generate entanglement between a single-photon qubit in the polarization basis and a coherent state of light. The required resources are a superposition of coherent states, a polarization entangled photon pair, beam splitters, the displacement operation, and four photodetectors. Even when realistic detectors with a limited efficiency are used, an arbitrarily high fidelity can be obtained by adjusting a beam-splitter ratio and the displacement amplitude at the price of reducing the success probability. Our analysis shows that high fidelities may be obtained using on-off de…
The purpose of this paper is to study the dynamics of a quantum coherent feedback network composed of two two-level systems (qubits) driven by two counter-propagating photons, one in each input channel. The coherent feedback network enhances the nonlinear photon-photon interaction inside the feedback loop. By means of quantum stochastic calculus and the input-output framework, the analytic form of the steady-state output two-photon state is derived. Based on the analytic form, the applications on the Hong-Ou-Mandel (HOM) interferometer and marginally stable single-photon devices using this coh…
A recent work [1] proposed a type of cluster entangled coherent states and its generation. Here we present an alternative experimental arrangement for its generation in bimodal QED cavities. The scheme employs a single two-level atom that interacts dispersively with cavity modes initially prepared in coherent states. The fidelity and success probability of the state preparation are obtained considering the influence of atomic velocity spread and atomic efficiency detection.
We present a way to transfer maximally- or partially-entangled states of n single-photon-state (SPS) qubits onto n coherent-state (CS) qubits, by employing 2n microwave cavities coupled to a superconducting flux qutrit. The two logic states of a SPS qubit here are represented by the vacuum state and the single-photon state of a cavity, while the two logic states of a CS qubit are encoded with two coherent states of a cavity. Because of using only one superconducting qutrit as the coupler, the circuit architecture is significantly simplified. The operation time for the state transfer does not i…
We analyze the nonlinear optical response of a six-level atomic system under a configuration of electromagnetically induced transparency. The giant fifth-order nonlinearity generated in such a system with a relatively large cross-phase modulation effect can produce efficient three-way entanglement and may be used for realizing a three-qubit quantum phase gate. We demonstrate that such phase gate can be transferred to a Toffoli gate, facilitating practical applications in quantum information and computation.
We investigate the entanglement dynamics of two two-level emitters (qubits) mediated by a semiinfinite, one-dimensional (1D) photonic waveguide. The coupling of each qubit to the waveguide is chiral, which depends on the propagation direction of light. The finite end of the waveguide is terminated by a perfect mirror, such that coherent quantum feedback is introduced to the system. We show that the chirally generated entanglement between the qubits can be preserved by controlling the time delay of the feedback. Moreover, when the time delay is negligible, the qubit-qubit reduced system evolves…
Protocols for probabilistic entanglement-assisted quantum teleportation and for entanglement swapping of material qubits are presented. They are based on a protocol for postselective Bell-state projection which is capable of projecting two material qubits onto a Bell state with the help of ancillary coherent multiphoton states and postselection by balanced homodyne photodetection. Provided this photonic postselection is successful we explore the theoretical possibilities of realizing unit fidelity quantum teleportation and entanglement swapping with $25\%$ success probability. This photon-assi…
We explore reachable sets of open $n$-qubit quantum systems, the coherent parts of which are under full unitary control and that have just one qubit whose Markovian noise amplitude can be modulated in time such as to provide an additional degree of incoherent control. In particular, adding bang-bang control of amplitude damping noise (non-unital) allows the dynamic system to act transitively on the entire set of density operators. This means one can transform any initial quantum state into any desired target state. Adding switchable bit-flip noise (unital), on the other hand, suffices to explo…
Scalable quantum information processing requires the ability to tune multi-qubit interactions. This makes the precise manipulation of quantum states particularly difficult for multi-qubit interactions because tunability unavoidably introduces sensitivity to fluctuations in the tuned parameters, leading to erroneous multi-qubit gate operations. The performance of quantum algorithms may be severely compromised by coherent multi-qubit errors. It is therefore imperative to understand how these fluctuations affect multi-qubit interactions and, more importantly, to mitigate their influence. In this …
Execution of quantum algorithms requires a quantum computer architecture with a dedicated quantum instruction set that is capable of supporting translation of workloads into actual quantum operations acting on the qubits. State-of-the-art qubit control setups typically utilize general purpose test instruments such as arbitrary waveform generators (AWGs) to generate a limited set of waveforms or pulses. These waveforms are precomputed and stored prior to execution, and then used to produce control pulses during execution. Besides their prohibitive cost and limited scalability, such instruments …
The coherent-state qubit is a promising candidate for optical quantum information processing due to its nearly-deterministic nature of the Bell-state measurement (BSM). However, its non-orthogonality incurs difficulties such as failure of the BSM. One may use a large amplitude ($α$) for the coherent state to minimize the failure probability, but the qubit then becomes more vulnerable to dephasing by photon loss. We propose a hardware-efficient concatenated BSM (CBSM) scheme with modified parity encoding using coherent states with reasonably small amplitudes ($|α| \lessapprox 2$), which simulta…
We propose a new way of implementing several elementary quantum gates for qubits in the coherent state basis. The operations are probabilistic and employ single photon subtractions as the driving force. Our schemes for single-qubit phase gate and two-qubit controlled phase gate are capable of achieving arbitrarily large phase shifts with currently available resources, which makes them suitable for the near-future tests of quantum information processing with superposed coherent states.
In this work, we consider a model of two qubits driven by coherent and incoherent time-dependent controls. The dynamics of the system is governed by a Gorini-Kossakowski-Sudarshan-Lindblad master equation, where coherent control enters into the Hamiltonian and incoherent control enters into both the Hamiltonian (via Lamb shift) and the dissipative superoperator. We consider two physically different classes of interaction with coherent control and study the optimal control problem of state preparation formulated as minimization of the Hilbert-Schmidt distance's square between the final density …
We experimentally demonstrate the coherent manipulation of atomic states in far-detuned dipole traps and registers of dipole traps based on two-dimensional arrays of microlenses. By applying Rabi, Ramsey, and spin-echo techniques, we systematically investigate the dephasing mechanisms and determine the coherence time. Simultaneous Ramsey measurements in up to 16 dipole traps are performed and proves the scalability of our approach. This represents an important step in the application of scalable registers of atomic qubits for quantum information processing. In addition, this system can serve a…
We compare the performance of continuous coherent feedback, implemented using an ideal single-qubit controller, to that of continuous measurement-based feedback for the task of controlling the state of a single qubit. Here the basic dynamical resource is the ability to couple the system to a traveling-wave field (for example, a transmission line) via a system observable, and the fundamental limitation is the maximum rate that is available for this coupling. We focus on the question of the best achievable control given ideal controllers. To obtain a fair comparison we acknowledge that the ampli…
A quantum computing system is typically represented by a set of non-interacting (local) two-state systems - qubits. Many physical systems can naturally have more accessible states, both local and non-local. We show that the resulting non-local network of states connecting qubits can be efficiently addressed via continuous time quantum random walks, leading to substantial speed-up of multiqubit entanglement manipulations. We discuss a three-qubit Toffoli gate and a system of superconducting qubits as an illustration.
