An introduction to quantum computing for non-physicists

Abstract

Richard Feynman's observation that certain quantum mechanical effects cannot be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used these quantum effects. This speculation proved justified when Peter Shor described a polynomial time quantum algorithm for factoring integers.In quantum systems, the computational space increases exponentially with the size of the system which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new non-traditional programming techniques.The aim of this paper is to guide computer scientists through the barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to exploiting the power of quantum parallelism are explained. We conclude with a discussion of quantum error correction.

Asymmetric Quantum Information Splitting of an Arbitrary N-qubit State via GHZ-like State and Bell States

“…Then the GHZ-like can be generated successfully. In fact, C-NOT gate operation [20], the generations of single photon and Bell state [21] have already been well demonstrated experimentally. Thus, the preparation of GHZ-like state is also feasible and it can be well demonstrated experimentally within the present technology.…”

Quantum programming languages: survey and bibliography

“…More detailed presentations can be found in the books by Gruska (1999) and Nielsen & Chuang (2000). Rieffel and Polak (2000) give an account aimed at computer scientists, and Preskill's (1998) lecture notes are another valuable resource. Arrighi (2003) covers similar material to this section, with a more detailed discussion of the fundamentals of quantum theory.…”

Is Fault‐Tolerant Quantum Computation Really Possible?

“…Below is a simplified example [12,18] of the quantum error correction using encoding. The simplification results from the assumption that the only errors allowed are rotations around the x axis, described by the matrix E = cos(θ/2)I − i sin(θ/2)σ x , where I is the unit matrix and σ x is the Pauli matrix.…”