We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large capacity quantum computer. In this paper, entanglement is used as a resource for implementing non-local operations between two or more quantum computers. These non-local operations are used to implement a distributed factoring circuit with polynomially many gates. This distributed version of Shor's algorithm requires an additional overhead of O((log N )2 ) communication complexity, where N denotes the integer to be factored.Keywords: Shor's algorithm, factoring algorithm, distributed quantum algorithms, quantum circuit. INTRODUCTIONTo utilize the full power of quantum computation, one needs a scalable quantum computer with a sufficient number of qubits. Unfortunately, the first practical quantum computers are likely to have only small qubit capacity. One way to overcome this difficulty is by using the distributed computing paradigm. By a distributed quantum computer, we mean a network of limited capacity quantum computers connected via classical and quantum channels. Quantum entangled states, in particular generalized GHZ states, provide an effective way of implementing non-local operations, such as, non-local CNOTs and teleportation. 1, 2We use distributed quantum computing techniques to construct a distributed quantum circuit for the Shor factoring algorithm. Let n = log N , where N is the number to be factored. The gate complexity of this particular distributed implementation of Shor's algorithm is O(n 3 ) with O(n 2 ) communication overhead. *In section 2, the general principles of distributed quantum computing are outlined, and two primitive distributed computing operators, cat-entangler and cat-disentangler, are introduced. We use these two primitive operators to implement non-local operations, such as non-local CNOTs and teleportation. Then we discuss how to share the cost of implementing a non-local controlled U , where U can be decomposed into a number of gates. The section ends with an distributed implementation of the Fourier transform.In section 3, we give a detailed description of an implementation of Shor's non-distributed factoring algorithm. This implementation is based on the phase estimation and order finding algorithms. We discuss in detail how to implement "modular exponentiation," which implementation will be used later in this paper as a blueprint for creating a distributed quantum algorithm.In section 4, we implement a distributed factoring algorithm by partitioning the qubits into groups in such a way that each group fits on one of the computers making up the network. We then proceed to replace controlled gates with non-local controlled gates whenever necessary.Further author information: (Send correspondence to Anocha Yimsiriwattana) Anocha Yimsiriwattana: E-mail: ayimsi1@umbc.edu, URL: http:/userpages.umbc.edu/~ayimsi1 Samuel J. Lomonaco Jr.: E-m...

A key problem in quantum computing is finding a viable technological path toward the creation of a scalable quantum computer. One possible approach toward solving part of this problem is distributed computing, which provides an effective way of utilizing a network of limited capacity quantum computers.In this paper, we present two primitive operations, cat-entangler and catdisentangler, which in turn can be used to implement non-local operations, e.g. non-local CNOT and quantum teleportation. We also show how to establish an entangled pair, and use entangled pairs to efficiently create a generalized GHZ state. Furthermore, we present procedures which allow us to reuse channel qubits in a sequence of non-local operations.These non-local operations work on the principle that a cat-like state, created by cat-entangler, can be used to distribute a control qubit among multiple computers. Using this principle, we show how to efficiently implement non-local control operations in many situation, including a parallel implementation of a certain kind of unitary transformation. Finally, as an example, we present a distributed version of the quantum Fourier transform.1991 Mathematics Subject Classification. Primary 68Q85, 68Q05, 47N50, 47N70.