![]() The states of and in our definition can be discriminated directly by checking the phase in spatial mode. Then the state is injected into the black box to carry out the permutation transformations. The positive cyclic permutations and the corresponding unitary transformations are:Įspecially, when φ = π/2, the initial state turns to be which is expressed in Eq (7) when φ = 3π/2, the initial state turns to be. These eight output states and the corresponding transformations are divided into two categories as mentioned above. ![]() For the input state (1, 2, 3, 4), there are eight different possible output states. For example, considering a black box to realize permutation operation f( x) on a input set x ∈ . There is a permutation problem which is to determine the parity of the permutation realized by a black box. Due to its good scalability, easy-handling and high stability, linear optical system is a good candidate for implementing quantum algorithms. Some quantum algorithms have been demonstrated in different physical systems, such as ion traps 8, 9, 10, 11, superconducting devices 12, 13, 14, optical lattices 15, 16, quantum dots 17, 18 and linear optics 19, 20, 21, 22, 23, 24, 25. came up with a quantum scheme to decrease the computational complexity of solving linear system of equations from O( n) to log( n) and this was the first quantum algorithm to work out the most fundamental problems in engineering science 7. Lately, an increasing number of practical programs were presented, such as factoring large integer 4, Grover's searching algorithm for database 5 and Simon's exponential acceleration algorithm for the black box problem 6. Since then, the first efficient quantum algorithm was proposed by Deutsch in 1985 2 and generalized by Deutsch and Jozsa in 1987 3. ![]() The concept of simulating physics progresses with quantum computers was originated in Richard Feynman's observation that computers built from quantum mechanical components would be ideally suited to simulating quantum mechanics 1. ![]() It attracts particular concern to develop new quantum algorithms in recent years. Quantum algorithm is the sole of quantum computation, which shows the amazing power of quantum parallelism and quantum interference. As quantum counterpart of classical computer, quantum computer reveals incredible efficiency to execute arithmetic tasks and threatens the security of classical communication. ![]()
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