ISSN 0030-400X, Optics and Spectroscopy, 2012, Vol. 112, No. 3, pp. 394–400. © Pleiades Publishing, Ltd., 2012. Original Russian Text © S.N. Andrianov, S.A. Moiseev, 2012, published in Optika i Spektroskopiya, 2012, Vol. 112, No. 2, pp. 436–443. 394 1 1. INTRODUCTION Creation of quantum computer is the important fundamental problem of quantum informatics. It can be used for the solution of problems not executing by classical computers. The first prototype of solid state quantum computer was created in 2009 on supercon- ducting qubits [1]. However, this approach suffers from decoherence connected with spontaneous radia- tion, and it is desirable to find some other quantum systems for realization of qubits with long decoher- ence time. Ions and neutral atoms in cold gases, impu- rity centers or vacancies in solids could be such sys- tems [2] but an interaction of single quantum systems with electromagnetic radiation is rather weak. There- fore, multiatomic systems with separated resonance transitions and dipole blockade mechanism for extrac- tion of two-level subspaces from the large number of possible quantum states in united ensemble of atoms were suggested for using as qubits [3]. But the dipole- dipole interaction used for blockade introduces deco- herence itself in the evolution of atomic system. Therefore, we propose in this paper the collective blockade of states not leading to the additional deco- herence of quantum states. It is possible to use such a collective blockade for spatially separated atomic ensembles interacting with each other via the field of virtual photons in the system of cavities that is described by transverse Heisenberg model [4, 5]. Heisenberg interaction yields the possibility for realization of fast two-qubit gates, but the realization of as fast single-qubit gates remains to be a problem since they are based on the weak local interactions. It 1 The article was translated by the authors. was shown [6–9] that it is possible to construct using only Heisenberg type interactions the set of gates uni- versal for some Heisenberg subspace with encoding of each logical qubit on three physical qubits. This approach was named as an approach of encoded uni- versality [9]. However, it is rather difficult to achieve an encoded controlled not operation since it is required to use 7 parallel exchange interactions or 19 subsequent gates. In papers [10, 11], various variants of Heisenberg model for interaction of qubits are con- sidered for realization of basic gates that are accompa- nied by significant complications because of large number of steps in the interaction of qubits. In this connection, we show in this paper that it is possible with encoding of one logical qubit on the pair of phys- ical qubits to realize controlled not operation in one step at using of multiatomic ensembles nonlinear fre- quency shift besides transverse Heisenberg interac- tion. We describe principal scheme of this protocol for realization of two-qubit gates where atomic nonlinear frequency shift emerges naturally in quantum electro- dynamic cavity. 2. SWAPPING GATES Let’s consider the set of atomic systems (nodes) containing in common electro-dynamic cavity together with quantum memory (QM) node (Fig. 1). Earlier, we have considered conditions for the realiza- tion of highly effective multi-qubit QM in the cavity [12]. For realization of two-qubit gates, we transfer sequentially in the beginning two qubits from QM into the first and then into the second processor nodes. Transfer process realizes when equalizing resonance Quantum Computers on Multiatomic Ensembles in Quantum Electrodynamic Cavity 1 S. N. Andrianov a and S. A. Moiseev a, b a Institute for Informatics of Tatarstan Republic Academy of Sciences, Kazan, 420012 Russia b Kazan Physical and Technical Institute of Russian Academy of Sciences, Kazan, 420029 Russia e-mail: samoi@yandex.ru Received July 22, 2011 Abstract—Schemes for the construction of quantum computers on multiatomic ensembles in quantum elec- trodynamic cavity are considered. With that, both encoding of physical qubits on each separate multiatomic ensemble and logical encoding of qubits on the pairs of ensembles are introduced. Possible constructions of swapping (SWAP, ) and controlled swapping gates (CSWAP) are analyzed. Mechanism of collective blockade and dynamical elimination procedure are proposed for realization of these gates. The comparison of the scheme solutions is carried out for the construction of quantum computer at using of physical and log- ical qubits. DOI: 10.1134/S0030400X12030034 SWAP SEVENTH DAVID KLYSHKO MEMORIAL SEMINAR