Realization of a Photonic Controlled-NOT Gate Sufficient for Quantum Computation

Abstract

We report the first experimental demonstration of a quantum controlled-NOT gate for different photons, which is classically feed-forwardable. In the experiment, we achieved this goal with the use only of linear optics, an entangled ancillary pair of photons and post-selection. The techniques developed in our experiment will be of significant importance for quantum information processing with linear optics. PACS numbers:Polarization-encoded qubits are well suited for information transmission in Quantum Information Processing (QIP) [1]. In recent years, the polarization state of single photons has been used to experimentally demonstrate quantum dense coding [2], quantum teleportation [3] and quantum cryptography [4,5,6]. However, due to the difficulty of achieving quantum logic operations between independent photons, the application of photon states has been limited primarily to the field of quantum communication. More precisely, the two-qubit gates suitable for quantum computation generically require strong interactions between individual photons, implying the need for massive, reversible non-linearities well beyond those presently available for photons, as opposed to other physical systems [7].Remarkably, Knill, Laflamme and Milburn [8] found a way to circumvent this problem and implement efficient quantum computation using only linear optics, photo-detectors and single-photon sources. In effect they showed that measurement induced nonlinearity was sufficient to obtain efficient quantum computation.The logic schemes KLM proposed were not, however, economical in their use of optical components or ancillary photons. Various groups have been working on reducing the complexity of these gates while improving their theoretical efficiency (see e.g. Koashi et al. [9]). In an exciting recent development, Nielsen [10] has shown that efficient linear optical quantum computation is in fact possible without the elaborate teleportation and Z-measurement error correction steps in KLM. This is achieved by creation of linear optical versions of Raussendorf and Briegel's [11] cluster states. Nielsen's method works for any non-trivial linear optical gate which succeeds with finite probability, but which, when it fails, effects a measurement in the computational * Present address: Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany † Present address: Imperial College, Blackett Labs, Prince Consort Rd, London SW7 2AZ ‡ also at Institut für Quantenoptik und Quanteninformation, Osterreichische Akademie der Wissenschaften basis.A crucial requirement of both KLM's and Nielsen's constructions is classical feed-forwardability. Specifically, it must be in principle possible to detect when the gate has succeeded by measurement of ancilla photons in some appropriate state. This information can then be fedforward in such a way as to condition future operations on the photon modes.Recently [12,13,14] destructive linear optical gate operations have been realized. As they necessarily destroy the output state, such sche...

Nearly Deterministic Linear Optical Controlled-NOT Gate

“…With this architecture for the CNOT gate and trivial single qubit rotations a universal set of gates is hence possible and a route forward for creating large devices can be seen. Since this original work there has been significant progress both theoretically [2,3,4,5,6] and experimentally [7,8,9], with a number of CNOT gates actually demonstrated.Much of the theoretical effort has focused on determining more efficient ways to perform the controlled logic. The standard model for linear logic uses only[1]:…”

Experimental Teleportation of a Quantum Controlled-NOT Gate

“…Through this method, we demonstrate that the teleported quantum CNOT gate has a mean fidelity of 0.84, averaged over all the input states. With linear optical manipulations, quantum CNOT gates on different photons have also been directly demonstrated in the coincidence basis by several recent experiments [9,10]. The demonstration of teleportation of the quantum CNOT gate, apart from its fundamental interest, is a significant step towards realization of quantum networking [3,4] and teleportation-based models of quantum computation [12][13][14].…”

Limitations of two-level emitters as nonlinearities in two-photon controlled-phase gates

“…Experimentally, probabilistic photonic gates have been demonstrated by using off-line nonlinearities in both free space [7,21,22] and in integrated platforms [5,23]. Strong in-line nonlinearities and photon switching have been achieved by using Rubidium atoms strongly coupled to optical cavities [17,[24][25][26], quantum dots in photonic crystal cavities [27][28][29][30], and nitrogen vacancy centers in diamond [31].…”