Nikolai Kiesel, Christian Schmid, Ulrich Weber, Otfried Guehne, Geza Toth, Rupert Ursin, Harald Weinfurter
Linear optics quantum logic operations enabled the observation of a four-photon cluster state. We prove genuine four-partite entanglement and study its persistency, demonstrating remarkable differences to the usual GHZ state. Efficient analysis tools are introduced in the experiment, which will be of great importance in further studies on multi-particle entangled states.
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Recently Yu and Sun [Int. J. Theor. Phys. DOI 10.1007/s10773-014-2360-x] have presented probabilistic teleportation of 3-qubit cat state via 6-qubit cluster state. The success probability depends on absolute value of only two of the coefficients of cluster state i.e. |c|^2 + |d|^2. We have demonstrated the feasibility to teleport 3-qubit cat state via 2-qubit non maximally entangled Bell state instead of a complex state like 6-qubit non maximally entangled cluster state. In this comment we have prescribed an optimal protocol for teleportation of n-qubit state of the form (α|x> + β|\bar{x}>)_n …
Cluster states for measurement-based quantum computing can be created with entangling operations of arbitrary low success probability. This will place a lower bound on the minimum lifetime of the qubits used in the implementation. Here, we present a simple scaling argument for the T2 time of the qubits for various cluster state geometries, and we estimate the size of the qubit reservoir that is needed for the creation of mini-clusters.
Based on resonant sideband excitation, we present a scheme for the generation of six-qubit cluster state in ion-trap system. One can realize experimentally this scheme with presently available techniques.
We investigate cluster states of qubits with respect to their non-local properties. We demonstrate that a Greenberger-Horne-Zeilinger (GHZ) argument holds for any cluster state: more precisely, it holds for any partial, thence mixed, state of a small number of connected qubits (five, in the case of one-dimensional lattices). In addition, we derive a new Bell inequality that is maximally violated by the 4-qubit cluster state and is not violated by the 4-qubit GHZ state.
Four-qubit cluster states of two photons entangled in polarization and linear momentum have been used to realize a complete set of single qubit rotations and the C-NOT gate for equatorial qubits with high values of fidelity. By the computational equivalence of the two degrees of freedom our result demonstrate the suitability of two photon cluster states for rapid and efficient one-way quantum computing.
This paper has been withdrawn by the author because it was a speculative investigation.
By using 2-photon 4-qubit cluster states we demonstrate deterministic one-way quantum computation in single qubit rotation algorithm. In this operation feed-forward measurements are automatically implemented by properly choosing the measurement basis of the qubits, while Pauli error corrections are realized by using two fast driven Pockels cells. We realized also a C-NOT gate for equatorial qubits and a C-Phase gate for a generic target qubit. Our results demonstrate that 2-photon cluster states can be used for rapid and efficient deterministic one-way quantum computing.
In this paper we utilize superoperator formalism to explore the entanglement evolution of four-qubit cluster states in a number of decohering environments. A four-qubit cluster state is a resource for the performance of an arbitrary single logical qubit rotation via measurement based cluster state quantum computation. We are specifically interested in the relationship between entanglement evolution and the fidelity with which the arbitrary single logical qubit rotation can be implemented in the presence of decoherence as this will have important experimental ramifications. We also note the exh…
We create a six-qubit linear cluster state by transforming a two-photon hyperentangled state in which three qubits are encoded in each particle, one in the polarization and two in the linear momentum degrees of freedom. For this state, we demonstrate genuine six-qubit entanglement, persistency of entanglement against the loss of qubits, and higher violation than in previous experiments on Bell inequalities of the Mermin type.
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 to eliminate the effect of non-nearest-neighbor qubits in preparing cluster state with double-dot molecules. As the interaction Hamiltonians between qubits are Ising-model and mutually commute, we can get positive and negative effective interactions between qubits to cancel the effect of non-nearest-neighbor qubits by properly changing the electron charge states of each quantum dot molecule. The total time for the present multi-step cluster state preparation scheme is only doubled for one-dimensional qubit chain and tripled for two-dimensional qubit array comparing with the…
Bidirectional quantum teleportation is a fundamental protocol for exchanging quantum information between two quantum nodes. All bidirectional quantum teleportation protocols till now have achieved a maximum efficiency of $40\%$. Here, we propose a new scheme for symmetric bidirectional quantum teleportation using a six-qubit cluster state as the quantum channel, for symmetric ($3\leftrightarrow3$) qubit bidirectional quantum teleportation of a special three-qubit entangled state. The novelty of our scheme lies in its generalization for ($N\leftrightarrow N$) qubit bidirectional quantum telepor…
Cluster states, a type of highly entangled state, are essential resources for quantum information processing. Here we demonstrated the generation of a time-domain linear cluster state (t-LCS) using a superconducting quantum circuit consisting of only two transmon qubits. By recycling the physical qubits, the t-LCS equivalent up to four physical qubits was validated by quantum state tomography with fidelity of 59%. We further confirmed the true generation of t-LCS by examining the expectation value of an entanglement witness. Our demonstrated protocol of t-LCS generation allows efficient use of…
A class of architectures is advanced for cluster state quantum computation using quantum dots. These architectures include using single and multiple dots as logical qubits. Special attention is given to the supercoherent qubits introduced by Bacon, Brown, and Whaley [Phys. Rev. Lett. {\bf 87}, 247902 (2001)] for which we discuss the effects of various errors, and present means of error protection.
We reduce the necessary and sufficient biseparable conditions of the four qubit cluster diagonal state to concise forms. Only 4 out of the 15 parameters are proved to be relevant in specifying the genuine entanglement of the state. Using the relative entropy of entanglement as the entanglement measure, we analytically find the genuine entanglement of all the four qubit cluster diagonal states. The formulas of the genuine entanglement are of five kinds, for seven different parameter regions of entanglement.
We report an experimental realization of one-way quantum computing on a two-photon four-qubit cluster state. This is accomplished by developing a two-photon cluster state source entangled both in polarization and spatial modes. With this special source, we implemented a highly efficient Grover's search algorithm and high-fidelity two qubits quantum gates. Our experiment demonstrates that such cluster states could serve as an ideal source and a building block for rapid and precise optical quantum computation.
One of the problems concerning entanglement witnesses (EWs) is the construction of them by a given set of operators. Here several multi-qubit EWs called stabilizer EWs are constructed by using the stabilizer operators of some given multi-qubit states such as GHZ, cluster and exceptional states. The general approach to manipulate the multi-qubit stabilizer EWs by exact(approximate) linear programming (LP) method is described and it is shown that the Clifford group play a crucial role in finding the hyper-planes encircling the feasible region. The optimality, decomposability and non-decomposabil…
We propose schemes to create cluster states and W states by many superconducting-quantum-interference-device (SQUID) qubits in cavities under the influence of the cavity decay. Our schemes do not require auxiliary qubits, and the excited levels are only virtually coupled throughout the scheme, which could much reduce the experimental challenge. We consider the cavity decay in our model and analytically demonstrate its detrimental influence on the prepared entangled states.
Recently, Zhao et al., (Int. J. Theor. Phys. 57, 516-522 (2018)) have proposed a scheme for quantum teleportation of an eight-qubit quantum state using a six qubit cluster state. In this comment, it's shown that the quantum resource (multi-partite entangled state used as the quantum channel) used by Zhao et al., is excessively high and the task can be performed using any two Bell states as the task can be reduced to the teleportation of an arbitrary two qubit state. Further, a trivial conceptual mistake made by Zhao et al., in the description of the quantum channel has been pointed out. It's a…
We report on the experimental realization of a 4-qubit linear cluster state via two photons entangled both in polarization and linear momentum. This state was investigated by performing tomographic measurements and by evaluating an entanglement witness. By use of this state we carried out a novel nonlocality proof, the so-called ``stronger two observer all versus nothing'' test of quantum nonlocality.
Quantum key agreement requires all participants to recover the shared key together, so it is crucial to resist the participant attack. In this paper, we propose a verifiable multi-party quantum key agreement protocol based on the six-qubit cluster states. A verifiable distributor who preserves some subsequences of the six-qubit cluster states is introduced into this protocol, thus the participants can not obtain the shared key in advance. Besides, the correctness and simultaneity of the shared key are guaranteed by the trusted design combiner and homomorphic hash function. Furthermore, the sec…
We provide a number of schemes for the splitting up of quantum information among $k$ parties using a $N$-qubit linear cluster state as a quantum channel, such that the original information can be reconstructed only if all the parties cooperate. Explicit circuits are provided for these schemes, which are based on the concept of measurement based locking and unlocking of quantum information. These are experimentally feasible as they require measurements to be performed only on product basis.
I explore the entanglement evolution of a four qubit cluster state in a dephasing environment concentrating on the phenomenon of entanglement sudden death (ESD). Specifically, I ask whether the onset of ESD has an effect on the utilization of this cluster state as a means of implementing a single qubit rotation in the measurement based cluster state model of quantum computation. To do this I compare the evolution of the entanglement to the fidelity, a measure of how accurately the desired state (after the measurement based operations) is achieved. I find that ESD does not cause a change of beh…
Cluster states serve as the central physical resource for the measurement-based quantum computation. We here present a simple experimental demonstration of the scalable cluster-state-construction scheme proposed by Browne and Rudolph. In our experiment, three-photon cluster states are created from two Bell states using linear optical devices. By observing a violation of three-particle Mermin inequality of $|< \textit{A}>| = 3.10\pm0.03 $, we also for the first time report a genuine three-photon entanglement. In addition, the entanglement properties of the cluster states are examined under $σ_z…
The usefulness of the recent experimentally realized six photon cluster state by C. Y. Lu et al. (2007, Nature {3} {91}), is investigated for quantum communication protocols like teleportation, quantum information splitting (QIS), remote state preparation and dense coding. We show that the present state can be used for the teleportation of an arbitrary two qubit state deterministically. Later we devise two distinct protocols for the QIS of an arbitrary two qubit state among two parties and systematically compare their relative merits in terms of classical communication and security. Sixteen or…
Cyclic Quantum Teleportation of Two-Qubit Entangled States by using Six-Qubit Cluster State and Six-Qubit Entangled State
提出一种利用十二量子比特态（六量子比特簇态与纠缠态）作为信道，通过贝尔测量和酉泡利算子，在三个合作者间循环完美传输三个任意未知两量子比特态的新方案。
We propose two experimental schemes to implement arbitrary unitary single qubit operations on single photons encoded in time-bin qubits. Both schemes require fiber optics components that are available with current technology.
A conditional scheme to prepare optical superposition of the vacuum and one-photon states using linear elements (beam splitters and phase-shifters) and avalanche photodetectors is suggested.
Continuous-variable (CV) qubits can be created on an optical longitudinal mode in which quantum information is encoded by the superposition of even and odd Schroedinger's cat states with quadrature amplitude. Based on the analogous features of paraxial optics and quantum mechanics, we propose a system to generate and detect CV qubits on an optical transverse mode. As a proof-of-principle experiment, we generate six CV qubit states and observe their probability distributions in position and momentum space. This enabled us to prepare a non-Gaussian initial state for CV quantum computing. Other p…
We propose a linear-optical setup for heralded qubit amplification with tunable output qubit fidelity. We study its success probability as a function of output qubit fidelity showing that at the expense of lower fidelity, the setup can considerably increase probability of successful operation. These results are subsequently applied in a proposal for state dependent qubit amplification. Similarly to state-dependent quantum cloning, the a priori information about the input state allows to optimize the qubit amplification procedure to obtain better fidelity versus success probability trade-off.
Based on quantitative complementarity relations (QCRs), we analyze the multipartite correlations in four-qubit cluster-class states. It is proven analytically that the average multipartite correlation $E_{ms}$ is entanglement monotone. Moreover, it is also shown that the mixed three-tangle is a correlation measure compatible with the QCRs in this kind of quantum states. More arrestingly, with the aid of the QCRs, a set of hierarchy entanglement measures is obtained rigorously in the present system.
We develop a scheme for generating a universal qubit cluster state using probabilistic Bell measurements without the need for feed-forward or long-time quantum memories. Borrowing ideas from percolation theory we numerically show that using unambiguous Bell measurements that succeed with 75% success probability, one could build a cluster state with an underlying pyrochlore geometry such that the probability of having a spanning cluster in a chosen direction approaches unity in the limit of an infinite lattice size. The initial resources required for the generation of a universal state in our p…
We propose a scheme to perform probabilistic quantum gates on remote trapped atom qubits through interference of optical frequency qubits. The method does not require localization of the atoms to the Lamb-Dicke limit, and is not sensitive to interferometer phase instabilities. Such probabilistic gates can be used for scalable quantum computation.
Entangling superconducting quantum processors via light would enable new means of secure communication and distributed quantum computing. However, transducing quantum signals between these disparate regimes of the electromagnetic spectrum remains an outstanding goal, and interfacing superconducting qubits with electro-optic transducers presents significant challenges due to the deleterious effects of optical photons on superconductors. Moreover, many remote entanglement protocols require multiple qubit gates both preceding and following the upconversion of the quantum state, and thus an ideal …
We propose a complete, quantitative quantum computing system which satisfies the five DiVincenzo criteria. The model is based on magnetic clusters with uniaxial anisotropy, where standard, two-state qubits are formed utilizing the two lowest-lying states of an anisotropic potential energy. We outline the quantum dynamics required by quantum computing for single qubit structures, and then define a novel measurement scheme in which qubit sates can be measured by sharp changes in current as voltage across the cluster is varied. We then extend the single qubit description to multiple qubit interac…
We introduce a design of a superconducting flux qubit capable of holding a full magnetic flux quantum $ϕ_{0}$, which arguably is an essential property for applications in charged particle optics. The qubit comprises a row of $N$ constituent qubits, which hold a fractional magnetic flux quantum $ϕ_{0}/N$. Insights from physics of the transverse-field Ising chain reveal that properly designed interaction between these constituent qubits enables their collective behavior while also maintaining the overall quantumness.
We study the class of two qubit gates which can be achieved using only linear optical elements (beam splitters and phase shifters) and post-selection. We are able to exactly characterize this set, and find that it is impossible to implement most two qubit gates in this way. The proof also gives rise to an algorithm for calculating the optimal success probability of those gates which are achievable.
We report on the implementation of quantum state tomography for an ensemble of Eu$^{3+}$ dopant ions in a \YSO crystal. The tomography was applied to a qubit based on one of the ion's optical transitions. The qubit was manipulated using optical pulses and measurements were made by observing the optical free induction in a phase sensitive manner. Fidelities of $>90$% for the combined preparation and measurement process were achieved. Interactions between the ions due to the change in the ions' permanent electric dipole moment when excited optically were also measured. In light of these results,…
Experimental detection of entanglement in superconducting qubits has been mostly limited, for more than two qubits, to witness-based and related approaches that can certify the presence of some entanglement, but not rigorously quantify how much. Here we measure the entanglement of three- and four-qubit GHZ and linear cluster states prepared on the 16-qubit IBM Rueschlikon (ibmqx5) chip, by estimating their entanglement monotones. GHZ and cluster states not only have wide application in quantum computing, but also have the convenient property of having similar state preparation circuits and fid…
We analyze and demonstrate the feasibility and superiority of linear optical single-qubit fingerprinting over its classical counterpart. For one-qubit fingerprinting of two-bit messages, we prepare `tetrahedral' qubit states experimentally and show that they meet the requirements for quantum fingerprinting to exceed the classical capability. We prove that shared entanglement permits 100% reliable quantum fingerprinting, which will outperform classical fingerprinting even with arbitrary amounts of shared randomness.
A scheme for the deterministic joint remote preparation of a four- qubit cluster-type state using only two Greenberger-Horne-Zeilinger (GHZ) states as quantum channels is presented. In this scheme, the first sender per- forms a two-qubit projective measurement according to the real coefficient of the desired state. Then, the other sender utilizes the measurement result and the complex coefficient to perform another projective measurement. To obtain the desired state, the receiver applies appropriate unitary operations to his/her own two qubits and two CNOT operations to the two ancillary ones.…
We present a linear optics quantum computation scheme that employs a new encoding approach that incrementally adds qubits and is tolerant to photon loss errors. The scheme employs a circuit model but uses techniques from cluster state computation and achieves comparable resource usage. To illustrate our techniques we describe a quantum memory which is fault tolerant to photon loss.
We propose an efficient scheme for transferring quantum states and generating entangled states between two qubits of different nature. The hybrid system consists a single nitrogen vacancy (NV) center and a superconducting (SC) qubit, which couple to an optical cavity and a microwave resonator, respectively. Meanwhile, the optical cavity and the microwave resonator are coupled via the electro-optic effect. By adjusting the relative parameters, we can achieve high fidelity quantum state transfer as well as highly entangled states between the NV center and the SC qubit. This protocol is within th…
Six-qubit cluster states built on the simultaneous entanglement of two photons in three independent degrees of freedom, i.e. polarization and a double longitudinal momentum, have been recently demonstrated. We present here the peculiar entanglement properties of the linear cluster state $\LCtilde$ related to the three degrees of freedom. This state has been adopted to realize various kinds of Controlled NOT (CNOT) gates, obtaining in all the cases high values of the gate fidelity. Our results demonstrate that a number of qubits $\leq$10 in cluster states of two photons entangled in multiple de…
We describe the first experimental realization of the Deutsch-Jozsa quantum algorithm to evaluate the properties of a 2-bit boolean function in the framework of one-way quantum computation. For this purpose a novel two-photon six-qubit cluster state was engineered. Its peculiar topological structure is the basis of the original measurement pattern allowing the algorithm realization. The good agreement of the experimental results with the theoretical predictions, obtained at $\sim$1kHz success rate, demonstrate the correct implementation of the algorithm.
A quantum eigensolver is designed under a multi-layer cluster mean-field (CMF) algorithm by partitioning a quantum system into spatially-separated clusters. For each cluster, a reduced Hamiltonian is obtained after a partial average over its environment cluster. The products of eigenstates from different clusters construct a compressed Hilbert space, in which an effective Hamiltonian is diagonalized to determine certain eigenstates of the whole Hamiltonian. The CMF method is numerically verified in multi-spin chains and experimentally studied in a fully-connected three-spin network, both yield…
We report new techniques for driving high-fidelity stimulated Raman transitions in trapped ion qubits. An electro-optic modulator induces sidebands on an optical source, and interference between the sidebands allows coherent Rabi transitions to be efficiently driven between hyperfine ground states separated by 14.53 GHz in a single trapped 111Cd+ ion.
A protocol of quantum communication is proposed in terms of the multi-qubit quantum teleportation through cluster states (Phys. Rev. Lett. \textbf{86}, 910 (2001)). Extending the cluster state based quantum teleportation on the basic unit of three qubits (or qudits), the corresponding multi-qubit network is constructed for both the qubits and qudits (multi-level) cases. The classical information costs to complete this communication task is also analyzed. It is also shown that this quantum communication protocol can be implemented in the spin-spin system on lattices.
In distributed quantum computation, small devices composed of a single or a few qubits are networker together to achieve a scalable machine. Typically there is an optically active matter qubit at each node, so that photons are exploited to achieve remote entanglement. However, in many systems the optically active states are unstable or poorly defined. We report a scheme to perform a high-fidelity entanglement operation even given severe instability. The protocol exploits the existence of optically excited states for phase acquisition without actually exciting those states; it functions with or…
The surface code cannot be used when qubits vanish during computation; instead, a variant known as the topological cluster state is necessary. It has a gate error threshold of $0.75% and only requires nearest-neighbor interactions on a 2D array of qubits. Previous work on loss tolerance using this code only considered qubits vanishing during measurement. We begin by also including qubit loss during two-qubit gates and initialization, and then additionally consider interaction errors that occur when neighbors attempt to entangle with a qubit that isn't there. In doing so, we show that even our …
We perform randomized benchmarking on neutral atomic quantum bits (qubits) confined in an optical lattice. Single qubit gates are implemented using microwaves, resulting in a measured error per randomized computational gate of 1.4(1) x 10^-4 that is dominated by the system T2 relaxation time. The results demonstrate the robustness of the system, and its viability for more advanced quantum information protocols.
Downloading many-qubit entanglement from continuous-variable cluster states
本文提出了一种结合量子比特和连续变量方法的方案，通过单比特传送从高效生成的连续变量簇态中下载多粒子纠缠，展示了在量子计算中的应用潜力。
We show that a cavity optomechanical system formed by a mechanical resonator simultaneously coupled to two modes of an optical cavity can be used for the implementation of a deterministic quantum phase gate between optical qubits associated with the two intracavity modes. The scheme is realizable for sufficiently strong single-photon optomechanical coupling in the resolved sideband regime, and is robust against cavity losses.
We propose an alternative scheme to generate W state via optical state truncation using quantum scissors. In particular, these states may be generated through three-mode optical state truncation in a Kerr nonlinear coupler. The more general three-qubit state may be also produced if the system is driven by external classical fields.
Generation of frequency-bin-encoded dual-rail cluster states via time-frequency multiplexing of microwave photonic qubits
本文提出通过微波光子量子比特的时间-频率复用生成频率桶编码的双轨簇状态，实现了高保真度的多量子比特纠缠态生成。
In this work, we present active and passive linear optical setups for error correction in quantum communication systems that employ polarization of single-photon and mesoscopic coherent states. Applications in quantum communication systems are described.
We show how an entangled cluster state encoded in the polarization of single photons can be straightforwardly expanded by deterministically entangling additional qubits encoded in the path degree of freedom of the constituent photons. This can be achieved using a polarization--path controlled-phase gate. We experimentally demonstrate a practical and stable realization of this approach by using a Sagnac interferometer to entangle a path qubit and polarization qubit on a single photon. We demonstrate precise control over phase of the path qubit to change the measurement basis and experimentally …
Quantum computers have the capability of out-performing their classical counterparts for certain computational problems. Several scalable quantum computing architectures have been proposed. An attractive architecture is a large set of physically independant qubits, arranged in three spatial regions where (i) the initialized qubits are stored in a register, (ii) two qubits are brought together to realize a gate, and (iii) the readout of the qubits is performed. For a neutral atom-based architecture, a natural way to connect these regions is to use optical tweezers to move qubits within the syst…
Qubit Health Analytics and Clustering for HPC-Integrated Quantum Processors
本文基于自研20量子比特NISQ设备超过250天的校准数据，提出数据驱动框架，通过时间模式分析、相关性分析和无监督聚类识别稳定与噪声量子比特，并用GHZ态实验验证，最终为HPCQC工作流提供健康指标及维护调度建议。
Aiming the construction of quantum computers and quantum communication systems based on optical devices, in this work we present possible implementations of quantum and classical CNOTs gates, as well an optical setup for generation and distribution of bipartite entangled states, using linear optical devices and photon number quantum non-demolition measurement.
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