Measurement-based one-way quantum computation using cluster states as resources provides an efficient model to perform computation and information processing of quantum codes. Arbitrary Gaussian quantum computation can be implemented sufficiently by long single-mode and two-mode gate sequences. However, continuous variable gate sequences have not been realized so far due to an absence of cluster states larger than four submodes. Here we present the first continuous variable gate sequence consisting of a single-mode squeezing gate and a two-mode controlled-phase gate based on a six-mode cluster state. The quantum property of this gate sequence is confirmed by the fidelities and the quantum entanglement of two output modes, which depend on both the squeezing and controlled-phase gates. The experiment demonstrates the feasibility of implementing Gaussian quantum computation by means of accessible gate sequences. Measurement-based one-way quantum computation with cluster states is an efficient route to processing quantum information, yet gate sequences for large states remain elusive. Su et al. present a continuous variable squeezed gate and controlled-phase gate sequence using a six-mode cluster state.
Measurement-based one-way quantum computation using cluster states as resources provides an efficient model to perform computation and information processing of quantum codes. Arbitrary Gaussian quantum computation can be implemented sufficiently by long single-mode and two-mode gate sequences. However, continuous variable gate sequences have not been realized so far due to an absence of cluster states larger than four submodes. Here we present the first continuous variable gate sequence consisting of a single-mode squeezing gate and a two-mode controlled-phase gate based on a six-mode cluster state. The quantum property of this gate sequence is confirmed by the fidelities and the quantum entanglement of two output modes, which depend on both the squeezing and controlled-phase gates. The experiment demonstrates the feasibility of implementing Gaussian quantum computation by means of accessible gate sequences. Measurement-based one-way quantum computation with cluster states is an efficient route to processing quantum information, yet gate sequences for large states remain elusive. Su et al. present a continuous variable squeezed gate and controlled-phase gate sequence using a six-mode cluster state.
We experimentally demonstrate a controlled-phase gate for continuous variables using a cluster-state resource of four optical modes. The two independent input states of the gate are coupled with the cluster in a teleportation-based fashion. As a result, one of the entanglement links present in the initial cluster state appears in the two unmeasured output modes as the corresponding entangling gate acting on the input states. The genuine quantum character of this gate becomes manifest and is verified through the presence of entanglement at the output for a product two-mode coherent input state. By combining our gate with the recently reported module for single-mode Gaussian operations [R. Ukai et al., Phys. Rev. Lett. 106, 240504 (2011)], it is possible to implement any multimode Gaussian operation as a fully measurement-based one-way quantum computation.
We demonstrate a quadratic phase gate for one-way quantum computation in the continuous-variable regime. This canonical gate, together with phase-space displacements and Fourier rotations, completes the set of universal gates for realizing any single-mode Gaussian transformation such as arbitrary squeezing. As opposed to previous implementations of measurement-based squeezers, the current gate is fully controlled by the local oscillator phase of the homodyne detector. Verifying this controllability, we give an experimental demonstration of the principles of one-way quantum computation over continuous variables. Moreover, we can observe sub-shot-noise quadrature variances in the output states, confirming that nonclassical states are created through cluster computation.
Single-mode squeezing and Fourier transformation operations are two essential logical gates in continuous-variable quantum computation, which have been experimentally implemented by means of an optical four-mode cluster state. In this paper, we present a simpler and more efficient protocol based on the use of Einstein-Podolsky-Rosen two-mode entangled states to realize the same operations. The theoretical calculations and the experimental results demonstrate that the presented scheme not only decreases the requirement to the resource quantum states at the largest extent but also enhances significantly the squeezing degree and the fidelity of the resultant modes under an identical resource condition. That is because in our system the influence of the excess noises deriving from the imperfect squeezing of the resource states is degraded. The gate operations applying two-mode entanglement can be utilized as a basic element in a future quantum computer involving a large-scale cluster state.
Quantum computers offer impressive computational speed-ups over their present-day (classical) counterparts. In the measurement-based model, quantum computation is driven by single-site measurements on a large entangled quantum state known as a cluster state. This thesis explores extensions of the measurement-based model for quantum computation in qubit and continuous-variable systems. Within the qubit setting, we consider the task of characterizing how well a small-scale measurement-based quantum device can perform logic gates. We adapt a pre-existing scheme known as randomized benchmarking into the setting of measurement-based quantum computation on a one-dimensional cluster state. A key feature of randomized benchmarking is that it uses random sequences of gates. We show how the intrinsic randomness of measurement-based quantum computation can be harnessed when implementing them. Within the continuous-variable setting, we consider optical cluster states that can be generated with current technology. We propose a compact method for generating universal cluster states based on optical-parametric-oscillator technology. We consider how finite squeezing effects manifest in computation and show that pre-existing measurement-based protocols are suboptimal. We propose new measurement-based protocols that have better noise properties, compactness, and circuit flexibility. As an application, we introduce a measurement-based method for implementing interferometry. In this model, the finite squeezing noise can be dealt with as a photon-loss process. Building further on this work, we investigate the resource requirements of a measurement-based boson-sampling device, proving simultaneous efficiency in time, space, and squeezing (energy) resources. These results offer new insights into how to build, use, and characterize a measurement-based quantum computer.
The one-way model of measurement-based quantum computation [1] is a fascinating alternative to the standard unitary-gate-based circuit model, for qubits as well as for continuous-variable (CV) encodings. Such one-way schemes are realized through single-qubit or single-mode measurements together with outcome-dependent feedforward operations on a preprepared multi-partite entangled state, the so-called "cluster state". By choosing an appropriate set of measurement bases on a sufficiently large cluster state, an arbitrary unitary operation can be implemented for the corresponding encoding.To date, various cluster states have been experimentally generated. Further, a fixed-strength entangling gate has been demonstrated by using an optical CV cluster state as a resource [2]. In the case of a fixed-strength entangling gate, unwanted noise might propagate along it during computations. Therefore, it is necessary for more efficient computation to have full tuneability of the entanglement strength. We demonstrate a fully tuneable entangling gate (TZ) by propagating two arbitrary, independent inputs through an optical graph state comprised of three quantum modes in a cluster state configuration. Its entangling strength is perfectly controlled by the selection of measurement on the cluster state. The schematic of our experiment is shown in Fig. 1(a). The three mode linear cluster state is represented, in the ideal case, as the zero eigenstate δ3 = p3 - x2. Here, x of linear combinations of the canonical operators: δ1 = p1 - x2, δ2 = p2 - x1 - x3, and andp are canonical position and momentum operators, respectively, satisfying the commutation relation [x, p] = i/2 (h = 1/2). Two input states (labeled by α and β) enter the cluster state via half beam splitters (HBSs). By measuring half of their outputs and mode 2, and then implementing appropriate corrections, we can teleport entanglement onto modes α and β, which are relabeled as μ and ν in the output of Fig. 1(a). The input-output relation is written as ξμν = S+K K ξ αβ + δ, where ξjk = (xj, pj, xk, pk)T , S = V 0 0 2 0 V , and K = V . K S+K 0 1/ 2 g/ 2 0 Here, the matrix S+K K corresponds to the TZ gate, whose gain g describes the entanglement strength. In K S+K our experiment, this entangling gain g = tanθ is perfectly controlled by the homodyne measurement angle θ for V mode 2. δ= 0,( δ1 + g δ2)/ V 2,0,( δ3 + g δ2)/ 2T represents the excess noises of our TZ gate, which vanishes in the limit of infinite squeezing. In order to verify the entangling ability of our TZ gate, we investigate the Partial Transposition(PT)-symplectic eigenvalues of the output states. They are identical to the logarithmic negativities in the case of Gaussian states [3]. A state is entangled if its PT-symplectic eigenvalue is below 0.25, and the smaller PT-symplectic eigenvalue shows stronger entanglement. The dependence of the PT-symplectic eigenvalues of the output states on the TZ gain g is shown in Fig. 1(b). When the entangling gain increases, our measurement results of them monotonically decrease and cross from separable region to inseparable region, which corresponds to monotonic increasing of entanglement strength. Furthermore, they agree with theoretical predictions, showing the successful implementation of the fully tuneable entangling gate.
We investigate experiments of continuous-variable quantum information processing based on the teleportation scheme. Quantum teleportation, which is realized by a two-mode squeezed vacuum state and measurement-and-feedforward, is considered as an elementary quantum circuit as well as quantum communication. By modifying ancilla states or measurement-and-feedforwards, we can realize various quantum circuits which suffice for universal quantum computation. In order to realize the teleportation-based computation we improve the level of squeezing, and fidelity of teleportation. With a high-fidelity teleporter we demonstrate some advanced teleportation experiments, i.e., teleportation of a squeezed state and sequential teleportation of a coherent state. Moreover, as an example of the teleportation-based computation, we build a QND interaction gate which is a continuous-variable analog of a CNOT gate. A QND interaction gate is constructed only with ancillary squeezed vacuum states and measurement-and-feedforwards. We also create continuous-variable four mode cluster type entanglement for further application, namely, one-way quantum computation.