© 2014, IJARCSMS All Rights Reserved 30 | P a g e ISSN: 232 7782 (Online) 1 Computer Science and Management Studies  International Journal of Advance Research in Volume 2, Issue 9, September 2014 Research Article / Survey Paper / Case Study Available online at: www.ijarcsms.com Quantum Simulation of Dijkstra's Algorithm Paramita Ray A.K.C School of Information Technology Calcutta University Calcutta – India Abstract: Quantum computers use quantum mechanical properties of matter to provide an exponential speed up in computation time and query processing capabilities compared to classical computing. There has been an increasing trend in finding efficient quantum algorithms for solving graph problems. Though there exist quite a good number of research works related to quantum algorithms for graph problems, but a limited amount of research exists in designing physically realizable quantum circuits for these algorithms. In this paper, we formulate the quantum algorithm for the Dijkastra’s shortest path algorithm named as Quantum Dijkastra algorithm (QDA) and propose its quantum circuit design, which is first of its kind. We further mapped our designed quantum circuit to quantum primitive operations for the various physical machine descriptions (PMDs) so that it can be implemented in real quantum devices. We have used Quantum computing language (QCL) for verifying our proposed algorithm. I. INTRODUCTION The idea of a quantum computer was first proposed by Richard Feynman in 1981 [10], which can accurately simulate quantum mechanical systems that can’t be possible on a classical computer. Quantum computers, exploit the unique, non- classical properties of the quantum systems like superposition, interference and entanglement thus allowing to process exponentially large quantities of information in polynomial time [11]. A. Qubits and Quantum state Qubits are represented in a similar way like classical bits using base-2 numbers, and they take on the value 1 or 0 when measured. To distinguish qubits from “classical” bits, it is common to use the Bra-ket or Dirac notation, (|>) of quantum mechanics. So the expression |0> represents quantum zero, and |1> represents quantum one. We can mathematically represent the state of a qubit at any given time is as a two-dimensional state space in C 2 with orthonormal basis vectors |1> and |0>. The superposition of a qubit is represented as a linear combination of those basis vectors: . Where a0 is the complex scalar amplitude of measuring |0>, and a1 the amplitude of measuring the value |1>. Amplitudes may be thought of as “quantum probabilities" in that they represent the chance that a given quantum state will be observed when the superposition is collapsed. B. Quantum Logic Gates A Quantum Gate (or Quantum logic gate) is a basic quantum circuit operating on a small number of qubits. Quantum logic tes are reversible and are represented by unitary matrices. Quantum gates operate on one, two or multiple qubits. Here we use Hadamard ,CNot, Taffoli, and Phase shift gate, CPhase gate.