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Teleportation-Based Realization of an Optical Quantum Two-Qubit Entangling Gate

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Teleportation-Based Realization of an Optical Quantum Two-Qubit Entangling Gate Teleportation-based realization of an optical quantum two-qubit entangling gate Wei-Bo Gaoa,1, Alexander M. Goebelb,1, Chao-Yang Lua,1, Han-Ning Daia, Claudia Wagenknechtb, Qiang Zhanga, Bo Zhaoa, Cheng-Zhi Penga, Zeng-Bing Chena, Yu-Ao Chena,2, and Jian-Wei Pana,b,2 aHefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China; and bPhysikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany Edited by Paul Kwiat, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, and accepted by the Editorial Board October 20, 2010 (received for review April 29, 2010) In recent years, there has been heightened interest in quantum measurements have been used to implement a teleportation- teleportation, which allows for the transfer of unknown quantum based model of quantum computation. It has also been shown states over arbitrary distances. Quantum teleportation not only that one-way quantum computation based on cluster states (20) serves as an essential ingredient in long-distance quantum commu- is equivalent with the teleportation-based approaches (21, 22). In nication, but also provides enabling technologies for practical addition, the GC scheme can be used to implement a nearly quantum computation. Of particular interest is the scheme pro- deterministic quantum gate. It teleports the qubits through a non- posed by D. Gottesman and I. L. Chuang [(1999) Nature 402:390– deterministic gate that has already been realized. Using more 393], showing that quantum gates can be implemented by tele- and more qubits, an entangling gate with a probability of success porting qubits with the help of some special entangled states. approaching one can be implemented (1). Therefore, the construction of a quantum computer can be simply To implement the fundamental building block of the GC based on some multiparticle entangled states, Bell-state measure- scheme, teleportation-based C-NOT gate or controlled-Phase ments, and single-qubit operations. The feasibility of this scheme (C-Phase) gate, one has to use at least six qubits. All logic opera- relaxes experimental constraints on realizing universal quantum tions needed for quantum computation can be performed using computation. Using two different methods, we demonstrate the single-qubit operations in combination with a C-NOT gate or SCIENCES smallest nontrivial module in such a scheme—a teleportation- C-Phase gate (23). In our experiment, we first realize a teleporta- APPLIED PHYSICAL based quantum entangling gate for two different photonic qubits. tion-based C-NOT gate with six photons. We measure the fide- One uses a high-fidelity six-photon interferometer to realize lities for the truth table of the gate and an entangled output state. controlled-NOT gates, and the other uses four-photon hyperentan- Next, we implement a C-Phase gate by using a four-photon glement to realize controlled-Phase gates. The results clearly de- hyperentangled state (24). The fidelity of the gate is estimated. monstrate the working principles and the entangling capability Moreover, we show that quantum parallelism is achieved in our of the gates. Our experiment represents an important step toward C-phase gate, thus proving that the gate cannot be reproduced the realization of practical quantum computers and could lead to by local operations and classical communications (25). Our ex- many further applications in linear optics quantum information periment represents a nontrivial proof-of-principle implementa- processing. tion of the teleportation protocol introduced by Gottesman and Chuang. n 2001, Knill, Laflamme, and Milburn (KLM) showed that Theoretical Schemes Iscalable and efficient quantum computation is possible by using A key element in the scheme of Gottesman and Chuang is to im- linear optical elements, ancilla photons, and postselection (1). plement the C-NOT gate, which acts on a control and a target The KLM scheme is based on three principles. First, nondeter- qubit. Here the logic table of the C-NOT operation (UC-NOT)is ministic quantum computation is possible with linear optics. Sec- given by jHi1jHi2 → jHi1jHi2, jHi1jVi2 → jVi1jVi2, jVi1jHi2 → ond, universal quantum gates with the probability approaching jVi1jHi2, and jVi1jVi2 → jHi1jVi2, where we have encoded one can be implemented based on teleportation (2), a process qubits on the polarization degree of freedom of photons. A in which a qubit in an unknown state can be transferred to another schematic diagram of the procedure is shown in Fig. 1A. First, we qubit (3, 4). Third, the demanding resources can be reduced by prepare beforehand an entangled four-qubit state jχi. Next, by quantum coding. The first principle has been demonstrated in using quantum teleportation, we transfer the data of the two in- many experiments. For example, various approaches for realizing put qubits jTi1 (target) and jCi2 (control) onto jχi. Specifically, photonic controlled-NOT (C-NOT) gates have been reported this is done by projecting the target (control) qubit and one of the – (5 11). Recently, a three-qubit Toffoli gate has also been carried outer qubits of jχi onto a joint two-particle “Bell state.” To finish out in a photonic architecture (12). Additionally, there have been the procedure, we apply single-qubit (Pauli) operations to the many efforts aimed at reducing the resource requirements of the output qubits depending on the outcomes of the BSMs. Now – KLM protocol (13 16). Nevertheless, the teleportation-based the output is in the desired state given by two-qubit entangling gate, which plays an important role in the second principle of the KLM scheme, still remains an experimen- tal challenge. Author contributions: W.-B.G., A.M.G., C.-Y.L., Q.Z., Y.-A.C., and J.-W.P. designed research; Quantum teleportation is useful for quantum communication W.-B.G., A.M.G., C.-Y.L., H.-N.D., C.W., C.-Z.P., Z.-B.C., Y.-A.C., and J.-W.P. performed research; W.-B.G., A.M.G., C.-Y.L., and Y.-A.C. contributed new reagents/analytic tools; (17, 18) because it allows us to use entangled states as perfect W.-B.G., A.M.G., C.-Y.L., B.Z., and Y.-A.C. analyzed data; and W.-B.G., A.M.G., C.-Y.L., quantum channels. The unique scheme proposed by Gottesman H.-N.D., Q.Z., B.Z., Y.-A.C., and J.-W.P. wrote the paper. and Chuang (GC) in 1999 (2) opens the way for promising The authors declare no conflict of interest. applications in realizing quantum computation (1, 2, 13, 14, 19). This article is a PNAS Direct Submission. P.K. is a guest editor invited by the Editorial Board. In the GC scheme, qubits are teleported through special gates by 1W.-B.G., A.M.G., and C.-Y.L. contributed equally to this work. simply using multiparticle off-line entangled states, Bell-state 2To whom correspondence may be addressed. E-mail: [email protected] or measurements (BSM), and single-qubit operations. It can be ex- [email protected]. tended to implement universal measurement-based quantum This article contains supporting information online at www.pnas.org/lookup/suppl/ computation. For example, in refs. 13 and 19, joint two-qubit doi:10.1073/pnas.1005720107/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1005720107 PNAS Early Edition ∣ 1of6 Downloaded by guest on September 28, 2021 A PA PPBS´ PA Prism PPBS HWP 2 Pol. 4 6 UV BBO 1 3 5 B BSM HWP BSM Fig. 1. Quantum circuit for teleporting two qubits through a C-NOT gate A jTi and a C-Phase gate. ( ) The input consisting of the target qubit 1 and BSM PA PBS Detector control qubit jCi2 can be arbitrarily chosen. BSMs are performed between the input states and the left qubits of the special entangled state jχi. Depend- PA Filter 0 ing on the outcome of the BSMs, local unitary operations ðU;U Þ are applied HWP/ on the remaining qubits of jχi, which then form the output jouti¼UC- QWP jTi jCi j i¼UC-PhasejTi jCi B jχi PA NOT 1 2 or out 1 2.( ) The special entangled state PBS can be constructed by performing a C-NOT gate on two Bell pairs, with jΦþi¼p1ffiffi ðjHijHiþjVijViÞ SI Text 2 .See for details. Fig. 2. A schematic diagram of the experimental setup. We frequency double a mode-locked Ti∶sapphire laser system to create a high-intensity C-NOT jouti¼U jTi1jCi2: [1] pulsed UV laser beam at a central wavelength of 390 nm, a pulse duration of 180 fs, and a repetition rate of 76 MHz. The UV beam successively passes β This can be better understood by a closer look at the special en- through three -barium borate (BBO) crystals to generate three polarization jχi entangled photon pairs via type-II spontaneous parametric down-conversion tangled state . It is a four-particle cluster state (26) of the form (27). At the first BBO the UV generates a photon pair in modes 1 and 2 1 (i.e., the input consisting of the target and control qubit). After the crystal, jχi¼ ½ðjHi jHi 0 þjVi jVi 0 ÞjHi jHi 0 þðjHi jVi 0 2 3 4 3 4 5 6 3 4 the UV is refocused onto the second BBO to produce another entangled photon pair in modes 3 and 4 and correspondingly for modes 5 and 6. þjVi3jHi40 ÞjVi5jVi60 ; [2] Photons 4 and 6 are then overlapped at a PPBS and together with photons 3 and 5 constitute the cluster state. Two PPBSs are used for state normaliza- which can be created simply by performing a C-NOToperation on tion.
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