In this paper, I propose new models of quantum information processing using the exchange interaction in physical systems. The partial SWAP operator that can be realized using the exchange interaction is used as the underlying resource for defining models of quantum computation, quantum communication, quantum memory and decoherence-free subspaces. Given the noncommutativity of these operators (for adjacent operators operating on a common qubit), a number of quantum states and entanglement patters can be obtained. This zoo of states can be classified, due to the parity constraints and permutation symmetry of the states, into invariant subspaces that are used for the definition of some of the applications in this paper.
We propose a protocol to transmit three quantum states crossly in a butterfly network with prior entanglement, in the form of GHZ states, between three senders. The proposed protocol requires only one qubit transmission or two classical bits transmission in each channel of the network. We generalise this protocol to higher number of qubits with multiqubit GHZ states towards quantum network operability using network coding with multiqubit GHZ states on higher-order butterfly networks.Quantum correlations, particularly prior entanglement across quantum states, can be harnessed for transmitting more classical information through quantum communication links through teleportation and superdense coding schemes [1][2][3][4][5]. The physical realisation of quantum networked systems at atomic scale distances using such entangled quantum states is key towards realising high-throughput quantum communications at such scales. The ideas from classical network coding, such as coding over butterfly networks, can be naturally extended to the quantum case, mindful of the quantum no-go theorems [6,7]. In the butterfly network, two units of information can be sent crossly and the channels can transmit only one bit, with the bottleneck being the central channel in the network. It was recently shown that perfect quantum state transmission is impossible in the butterfly network and the bottleneck, in the form of the central channel, cannot be resolved for a quantum network [6]. This was subsequently extended to different kinds of networks with quantum network coding [8]. Leung et al proposed network coding using shared entanglement between two parties [9] through quantum teleportation and superdense coding. Hayashi demonstrated the impossibility of transmitting quantum states over the butterfly network between two senders without prior entanglement [11]. In this letter, we have formulated a non-trivial extension of Hayashi's results to the B M. G. Majumdar
A B S T R A C TThis paper considers throughput and memory requirements in architectures which operate on two-dimensional (2D) digital signals. We present a novel technique for retiming a 2D data-flow graph to meet a given throughput constraint while keeping the memory required by the architecture low. This technique, which we call orthogonal two-dimensional retiming, is posed as two linear programming problems which can be solved in polynomial time. Our results show that, for a given throughput constraint, the orthogonal two-dimensional retiming formulation leads to architectures which require less memory than architectures designed using previously known techniques. I N T R O D U C T I O NTwo-dimensional digital signal processing (2D DSP) is driven by applications such as digital image processing and video processing. Registers typically dominate the area of 2D DSP architectures (see e.g., [l]), and high data rates require architectures which exploit concurrency to meet realtime processing requirements. A good VLSI architecture for, a 2D DSP algorithm must meet the real-time throughput constraints while maintaining low memory requirements.While techniques for designing concurrent architectures for 2D systems have been explored in the past [2], [3], [4], these techniques can result in architectures which require large amounts of memory. In this paper, we address the problem of retiming to simultaneously achieve a desired throughput while keeping the amount of memory used by the architecture small. We use a linear programming formulation of 2D retiming with the required memory as the cost function. Using this formulation, we simultaneously consider the issues of throughput and memory requirements. M U L T I D I M E N S I O N A L R E T I M I N GOne-dimensional retiming, as described in [ 5 ] , is a technique for transforming a synchronous circuit to meet various design criteria.Constraint 1 Each edge in the retimed circuit contains a nonnegative number of delays.Constraint 2 The critical path of the retimed circuit is not greater than a desired value. Two-dimensional retiming [3], [4]offers a great deal of flexibility because a single frame of data can be processed using several linear scanning orders such as line-by-line, column-by-column, or diagonal, where the scanning order is the order in which the output pixels are generated. The fundamentals of 2D retiming remain the same as those of one-dimensional retiming, i.e., Constraints 1 and 2 must be satisfied given the scanning order for the 2D data set.The scanning order is specified using a scanning vector s = [ s1 s2 1' and an access vector a = [ a1 a2 1' .Lines orthogonal to the scanning vector are called access lines, and pixel (n1,nz) on access line k satisfies n1s1 + 71282 = IC. The scanning order is such that, for kl < k2, all pixels on access line IC1 are processed before the pixels on access line IC2. The access vector, which satisfies s . a = 0, defines the order in which pixels are processed on the access lines, such that pixel n + a is processed immedi...
In this paper, I propose new models of quantum information processing using the exchange interaction in physical systems. The partial SWAP operator that can be realized using the exchange interaction is used as the underlying resource for defining models of quantum computation, quantum communication, quantum memory and decoherence-free subspaces. Given the non-commutativity of these operators (for adjacent operators operating on a common qubit), a number of quantum states and entanglement patters can be obtained. This zoo of states can be classified, due to the parity constraints and permutation symmetry of the states, into invariant subspaces that are used for the definition of some of the applications in this paper.
In this paper, a controlled-phase-flip (P-CPF) gate using the polarisation and orbital angular momentum degrees of freedom for single-photon two-qubit quantum logic is proposed. This is critical to the realisation of quantum cluster states and graph networks using transverse degrees of freedom. A generalisation of the proposed scheme to arbitrary number and kinds of degrees of freedom, for optical systems, as well as arbitrary operations to be conditionally performed is proposed.
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