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arXiv:0906.3141 · Physical Review A

Demonstration of a universal one-way quantum quadratic phase gate

Yoshichika Miwa, Jun–ichi Yoshikawa, Peter van Loock, Akira Furusawa

Published Nov 30, 2009• 56 citations
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Abstract

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.

DOI
10.1103/physreva.80.050303

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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.
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.
One-way quantum computation is a very promising candidate to fulfill the capabilities of quantum information processing. Here we demonstrate an important set of unitary operations for continuous variables using a linear cluster state of four entangled optical modes. These operations are performed in a fully measurement-controlled and completely unconditional fashion. We implement three different levels of squeezing operations and a Fourier transformation, all of which are accessible by selecting the correct quadrature measurement angles of the homodyne detections. Though not sufficient, these linear transformations are necessary for universal quantum computation.
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.
The sum gate is the canonical two-mode gate for universal quantum computation based on continuous quantum variables. It represents the natural analogue to a qubit C-NOT gate. In addition, the continuous-variable gate describes a quantum nondemolition (QND) interaction between the quadrature components of two light modes. We experimentally demonstrate a QND sum gate, employing the scheme by R. Filip, P. Marek, and U. L. Andersen [Phys. Rev. A 71, 042308 (2005)10.1103/PhysRevA.71.042308], solely based on off-line squeezed states, homodyne measurements, and feedforward. The results are verified by simultaneously satisfying the criteria for QND measurements in both conjugate quadratures.
We propose an experimental design for universal continuous-variable quantum computation that incorporates recent innovations in linear-optics-based continuous-variable cluster state generation and cubic-phase gate teleportation. The first ingredient is a protocol for generating the bilayer-square-lattice cluster state (a universal resource state) with temporal modes of light. With this state, measurement-based implementation of Gaussian unitary gates requires only homodyne detection. Second, we describe a measurement device that implements an adaptive cubic-phase gate, up to a random phase-space displacement. It requires a two-step sequence of homodyne measurements and consumes a (non-Gaussian) cubic-phase state.
Continuous-variable cluster states offer a potentially promising method of implementing a quantum computer. This paper extends and further refines theoretical foundations and protocols for experimental implementation. We give a cluster-state implementation of the cubic phase gate through photon detection, which, together with homodyne detection, facilitates universal quantum computation. In addition, we characterize the offline squeezed resources required to generate an arbitrary graph state through passive linear optics. Most significantly, we prove that there are universal states for which the offline squeezing per mode does not increase with the size of the cluster. Simple representations of continuous-variable graph states are introduced to analyze graph state transformations under measurement and the existence of universal continuous-variable resource states.