Generating Pseudo-Random Quantum States with Cluster Computation

Michael A. Nielsen

Yu‐Guang Yang, Qianqian Zhao

In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.

Luis José Mantilla Santa Cruz, Luis Fernando Faina, João Henrique de Souza Pereira

Abstract Quantum realizations have opened a new ways for computer science. The new characteristics and phenomenons allow us to create new algorithms for general proposes. An interesting topic is random number generation. There are two perspectives for this proposes. True random numbers generator (TRN) and pseudo random numbers generator (PRNG). True Random Number Generators has four significant characteristics: randomness, long Period, insensitivity to seeds, repeatability. Additionally, Pseudo Random Number Generators is a fascinating topic that leverages the principles of computer science to craft deterministic algorithms, enabling the creation of a sequence of pseudo-random numbers. A crucial element in this process is the 'seed', which serves as the initial value to generate the entire sequence. This document proposes a algorithm based on a quantum system and the quasi-probability of its possible states to generate a long set of numbers which has pseudo random properties. The quantum system is compound by n qubits, its initial conditions and a small set of rotation gates with a fixed angle. The tests were realized using the battery test called NIST SP800-22, and alpha=0.01 as a threshold to ensures 99\% of precision. The results demonstrate that it is possible generate a long set of pseudo numbers with random characteristics using a quantum simple operation. However, the experiments reveal that a real world implementation require a quantum system with at least 10-9 precision order.

Ivan B. Djordjević

Jaewan Kim, Juhui Lee, Se-Wan Ji +3 more

Defining a computational basis of pseudo-number states, we interpret a coherent state of large amplitude, |α|⪢d/2π, as a qudit — a d-level quantum system — that is an even (meaning same size of amplitudes) superposition of d pseudo-number basis states. A pair of such coherent-state qudits can be maximally entangled by generalized Controlled-Z operation that is based on cross-Kerr nonlinearity, which can be weak for large d. Hence, a coherent-state optical qudit cluster state can be prepared by repetitive application of the generalized Controlled-Z operation to a set of coherent states. We thus propose an optical qudit teleportation as a simple demonstration of cluster state quantum computation.

Philip John Walther, Kevin J. Resch, Terry Rudolph +5 more