Quantum information processing in a decoherence-free subspace for the $$\hat{\sigma }_{x}$$-type collective noise

Based on a cavity-assisted single-photon input–output process, we first construct the hybrid controlled-phase-flip gate between photon and the single-logic qubit in decoherence-free subspaces. And we also achieve the universal single-qubit logic operations. We realize the distributed quantum information processing with the hybrid controlled-phase-flip gate and single-qubit logic operations. Finally, we discuss the experimental feasibility of our scheme, which is satisfied with currently available technology.     

Quantum computation in the decoherence-free subspaces with cavity QED

We present a scheme to implement quantum computation in decoherence-free subspaces (DFSs) with four atoms in a single-mode cavity. A four-dimensional DFS is constituted to protect quantum information when the full symmetry of interaction between system and environment is broken in a specific way, and entangling two-qubit logic gates and noncommuting single-qubit gates are implemented in such DFS. The gate fidelity is numerically calculated, and the feasibility of the approximations taken in this work is verified based on the numerical calculations.     

An atom�Cmolecule platform for quantum computing

We propose a combined atom–molecule system for quantum information processing in individual traps, such as provided by optical lattices. In this platform, different species of atoms—one atom carrying a qubit and the other enabling the interaction—are used to store and process quantum information via intermediate molecular states. We show how gates, initialization, and readout operations could be implemented using this approach. In particular, we describe in some detail the implementation of a two-qubit phase gate in which a pair of atoms is transferred into the ground rovibrational state of a polar molecule with a large dipole moment, thus allowing atoms transferred into molecules to interact via their dipole-dipole interaction. We also discuss how the reverse process could be used as a non-destructive readout tool of molecular qubit states. Finally, we generalize these ideas to use a decoherence-free subspace for qubit encoding to minimize the decoherence due to magnetic field fluctuations. In this case, qubits will be encoded into field-insensitive states of two identical atoms, while a third atom of a different species will be used to realize a phase gate.     

Classical rules and quantum strategies in penny flip game

We study the quantum single penny flip game under various classical rules of the game. For every rule of the game, there exist unitary transformations which ensure the winning for quantum player. With the aim to understand the role of entangling gate for a sequential zero sum game, we extend the single penny problem to two penny problem. While entangling gates are found to be not useful, local gates are necessary and sufficient to win the game. Further, importance of one qubit operations is indicated. Various rules of two penny game is also indicated.     

A nearest neighbor architecture to overcome dephasing

We design a nearest-neighbor architectural layout that uses fixed positive and negative couplings between qubits, to overcome the effects of relative phases due to qubit precessions, both during idle times and gate operations. The scheme uses decoherence-free subspaces, and we show how to realize gate operations on these encoded qubits. The main advantage of our scheme is that most gate operations are realized by only varying a single control parameter, which greatly reduces the circuit complexity. Moreover, the scheme is robust against phase errors occurring as a result of finite rise and fall times due to non-ideal pulses.     

Construction of quantum gates for concatenated Greenberger–Horne–Zeilinger-type logic qubit

Concatenated Greenberger–Horne–Zeilinger (C-GHZ) state is a kind of logic qubit which is robust in noisy environment. In this paper, we encode the C-GHZ state as the logic qubit and design two kinds of quantum gates for such logic qubit. The first kind is the single logic-qubit gate which contains the logic-qubit bit-flip gate and phase-flip gate. The second kind is the logic-qubit controlled-not (CNOT) gate. We exploit the single quantum gate for physical qubit, such as bit-flip gate and phase-flip gate, and two-qubit CNOT gate to realize the logic-qubit gate. We also calculated the success probability of such logic-qubit gate based on the imperfect physical quantum gate. This protocol may be useful for future quantum computation.     

Compact quantum gates for hybrid photon–atom systems assisted by Faraday rotation

We present some compact circuits for a deterministic quantum computing on the hybrid photon–atom systems, including the Fredkin gate and SWAP gate. These gates are constructed by exploiting the optical Faraday rotation induced by an atom trapped in a single-sided optical microcavity. The control qubit of our gates is encoded on the polarization states of the single photon, and the target qubit is encoded on the ground states of an atom confined in an optical microcavity. Since the decoherence of the flying qubit with atmosphere for a long distance is negligible and the stationary qubits are trapped inside single-sided microcavities, our gates are robust. Moreover, ancillary single photon is not needed and only some linear-optical devices are adopted, which makes our protocols efficient and practical. Our schemes need not meet the condition that the transmission for the uncoupled cavity is balanceable with the reflectance for the coupled cavity, which is different from the quantum computation with a double-sided optical microcavity. Our calculations show that the fidelities of the two hybrid quantum gates are high with the available experimental technology.     

Generation of an arbitrary four-photon polarization-entangled decoherence-free state with cross-Kerr nonlinearity

We present a new scheme to provide an arbitrary four-photon polarization-entangled state, which enables the encoding of single logical qubit information into a four-qubit decoherence-free subspace robustly against collective decoherence. With the assistance of the cross-Kerr nonlinearities, a spatial entanglement gate and a polarization entanglement gate are inserted into the circuit, where the X-quadrature homodyne measurement is properly performed. According to the outcomes of homodyne measurement in the spatial entanglement process, some swap gates are inserted into the corresponding paths of the photons to swap their spatial modes. Apart from Kerr media, some basic linear optical elements are necessary, which make it feasible with current experimental techniques.     

An efficient quantum circuit analyser on qubits and qudits

This paper presents a highly efficient decomposition scheme and its associated Mathematica notebook for the analysis of complicated quantum circuits comprised of single/multiple qubit and qudit quantum gates. In particular, this scheme reduces the evaluation of multiple unitary gate operations with many conditionals to just two matrix additions, regardless of the number of conditionals or gate dimensions. This improves significantly the capability of a quantum circuit analyser implemented in a classical computer. This is also the first efficient quantum circuit analyser to include qudit quantum logic gates.

Program summary

Program title:CUGates.mCatalogue identifier: AEJM_v1_0Program summary: URL: http://cpc.cs.qub.ac.uk/summaries/AEJM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 8168No. of bytes in distributed program, including test data, etc.: 173 899Distribution format: tar.gzProgramming language: MathematicaComputer: Any computer installed with Mathematica 6.0 or higher.Operating system: Any system with a copy of Mathematica 6.0 or higher installed.Classification: 4.15Nature of problem: The CUGates notebook simulates arbitrarily complex quantum circuits comprised of single/multiple qubit and qudit quantum gates.Solution method: It utilizes an irreducible form of matrix decomposition for a general controlled gate with multiple conditionals and is highly efficient in simulating complex quantum circuits.Running time: Details of CPU time usage for various example runs are given in Section 4.     

One-step implementation of a multi-target-qubit controlled phase gate in a multi-resonator circuit QED system

Circuit quantum electrodynamics system composed of many qubits and resonators may provide an excellent way to realize large-scale quantum information processing (QIP). Because of key role for large-scale QIP and quantum computation, multi-qubit gates have drawn intensive attention recently. Here, we present a one-step method to achieve a multi-target-qubit controlled phase gate in a multi-resonator system, which possesses a common control qubit and multiple different target qubits distributed in their respective resonators. Noteworthily, the implementation of this multi-qubit phase gate does not require classical pulses, and the gate operation time is independent of the number of qubits. Besides, the proposed scheme can in principle be adapted to a general type of qubits like natural atoms, quantum dots, and solid-state qubits (e.g., superconducting qubits and NV centers).     

Mapping from multiple-control Toffoli circuits to linear nearest neighbor quantum circuits

In recent years, quantum computing research has been attracting more and more attention, but few studies on the limited interaction distance between quantum bits (qubit) are deeply carried out. This paper presents a mapping method for transforming multiple-control Toffoli (MCT) circuits into linear nearest neighbor (LNN) quantum circuits instead of traditional decomposition-based methods. In order to reduce the number of inserted SWAP gates, a novel type of gate with the optimal LNN quantum realization was constructed, namely NNTS gate. The MCT gate with multiple control bits could be better cascaded by the NNTS gates, in which the arrangement of the input lines was LNN arrangement of the MCT gate. Then, the communication overhead measurement model on inserted SWAP gate count from the original arrangement to the new arrangement was put forward, and we selected one of the LNN arrangements with the minimum SWAP gate count. Moreover, the LNN arrangement-based mapping algorithm was given, and it dealt with the MCT gates in turn and mapped each MCT gate into its LNN form by inserting the minimum number of SWAP gates. Finally, some simplification rules were used, which can further reduce the final quantum cost of the LNN quantum circuit. Experiments on some benchmark MCT circuits indicate that the direct mapping algorithm results in fewer additional SWAP gates in about 50%, while the average improvement rate in quantum cost is 16.95% compared to the decomposition-based method. In addition, it has been verified that the proposed method has greater superiority for reversible circuits cascaded by MCT gates with more control bits.     

Using non-ideal gates to implement universal quantum computing between uncoupled qubits

In many physical systems, when implementing quantum gate operations unavoidable global and relative phases occur as by-products due to the internal structure of the governing Hamiltonian. To correct, additional phase rotation gates are used, which increases the computational overhead. Here, we show how these phase by-products can actually be used to our advantage by using them to implement universal quantum computing between qubits not directly coupled to each other. The gate operations, CNOT, Toffoli, and swap gates, require much less computational overhead than present schemes, and are achieved with fidelity greater than 99%. We then present a linear nearest-neighbor architecture that takes full advantage of the phase by-products, and we show how to implement gates from a universal set efficiently in this layout. In this scheme gate operations are realized by only varying a single control parameter per data qubit, and the ability to tune couplings is not required.     

参数化的广义量子通用相位门

主要研究参数化的广义量子通用相位门,给出了单比特量子门、双比特量子门以及三比特量子门的参数化构造。证明参数化的广义量子门和M.Nielsen给出的广义量子门是等价的。举例说明了参数化的广义量子通用门在量子计算中的作用。     

Topological quantum computation within the anyonic system the Kauffman–Jones version of <Emphasis Type="Italic">SU</Emphasis>(2) Chern–Simons theory at level 4

By braiding and measuring anyons, we realize irrational qubit and qutrit phase gates within the anyonic system the Kauffman-Jones version of SU(2) Chern-Simons theory at level 4. We obtain universality on 1-qubit and 1-qutrit gates. In the qubit case, we also provide a protocol for realizing the controlled NOT gate, thus leading to universality on n-qubit gates.     

Scheme for implementing multitarget qubit controlled-NOT gate of photons and controlled-phase gate of electron spins via quantum dot-microcavity coupled system

We propose a deterministic scheme to implement the multiqubit controlled-NOT gate of photons and multiqubit controlled-phase gate of electron spins with one control qubit and multiple target qubits using quantum dots in double-sided optical cavities. The scheme is based on spin selective photon reflection from the cavity and can be achieved in a nondestructive way. We assess the feasibility of the scheme and show that the gates can be implemented with high average fidelities by choosing the realistic system parameters appropriately. The scheme is useful in quantum information processing such as entanglement preparation, quantum error correction, and quantum algorithms.     

Model and algorithm of quantum-inspired neural network with sequence input based on controlled rotation gates

To enhance the approximation and generalization ability of classical artificial neural network (ANN) by employing the principles of quantum computation, a quantum-inspired neuron based on controlled-rotation gate is proposed. In the proposed model, the discrete sequence input is represented by the qubits, which, as the control qubits of the controlled-rotation gate after being rotated by the quantum rotation gates, control the target qubit for rotation. The model output is described by the probability amplitude of state |1〉 in the target qubit. Then a quantum-inspired neural network with sequence input (QNNSI) is designed by employing the quantum-inspired neurons to the hidden layer and the classical neurons to the output layer. An algorithm of QNNSI is derived by employing the Levenberg–Marquardt algorithm. Experimental results of some benchmark problems show that, under a certain condition, the QNNSI is obviously superior to the ANN.     

Natural Majorization of the Quantum Fourier Transformation in Phase-Estimation Algorithms

We prove that majorization relations hold step by step in the Quantum Fourier Transformation (QFT) for phase-estimation algorithms. Our result relies on the fact that states which are mixed by Hadamard operators at any stage of the computation only differ by a phase. This property is a consequence of the structure of the initial state and of the QFT, based on controlled-phase operators and a single action of a Hadamard gate per qubit. The detail of our proof shows that Hadamard gates sort the probability distribution associated to the quantum state, whereas controlled-phase operators carry all the entanglement but are immaterial to majorization. We also prove that majorization in phase-estimation algorithms follows in a most natural way from unitary evolution, unlike its counterpart in Grover's algorithm. PACS: 03.67.-a, 03.67.Lx     

Scalable quantum computing model in the circuit-QED lattice with circulator function

We propose a model for a scalable quantum computing in the circuit quantum electrodynamics architecture. In the Kagome lattice of qubits, three qubits are connected to each other through a superconducting three-junction flux qubit at the vertices of the lattice. By controlling one of the three-Josephson-junction energies of the intervening flux qubit, we can achieve the circulator function that couples arbitrary pair of two qubits among three. This selective coupling enables the interaction between two nearest neighbor qubits in the Kagome lattice, and further the two-qubit gate operation between any pair of qubits in the whole lattice by performing consecutive nearest neighbor two-qubit gates.     

Single-photon controlled multi-photon polarization unitary gate based on weak cross-Kerr nonlinearities

With the help of weak cross-Kerr nonlinearities, we propose a single-photon controlled multi-photon polarization unitary gate, which can fulfill the task of n single-photon controlled one-photon polarization unitary gates, but only by adopting a nondestructive measurement and an auxiliary coherent state. Moreover, simple linear optical elements and mature existing techniques containing Homodyne measurement and classical feed-forward are applied. So this scheme provides an efficient and feasible approach for optimally fulfilling single-photon controlled multi-photon unitary gate.     

Fault-tolerant asymmetric quantum dialogue protocols against collective noise

In this paper, we propose two kinds of fault-tolerant asymmetric quantum dialogue (AQD) protocols and investigate the effect of collective noise on the proposed AQD protocols. In our work, logical qubits have been selected to build traveling blocks for constructing a decoherence-free subspace. Both communicants can encode each bit of secret message in the logical qubit with unitary logical operator. Compared with the previous quantum dialogue protocols, the proposed AQD protocols not only enable two users to transmit different amount of classical information to each other, but also can provide higher communication fidelity under the interference of collective noise. Furthermore, we will demonstrate the security of the AQD protocols against information leakage problem and Eve’s active eavesdropping attack.