The Physics of Quantum Computation

Alice Flarend, Robert C. Hilborn

Abstract Quantum Computing: From Alice to Bob provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science (QIS) and quantum computing (QC). The book is designed for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics beyond secondary school algebra and trigonometry. While broadly accessible, the book provides a solid conceptual and formal understanding of quantum states and entanglement—the key ingredients in quantum computing. The authors give detailed treatments of many of the classic quantum algorithms that demonstrate how and when QC has an advantage over classical computers. The book provides a solid explanation of the physics of QC and QIS and then weds that knowledge to the mathematics of QC algorithms and how those algorithms deploy the principles of quantum physics to solve the problem. This book connects the physics concepts, the computer science vocabulary, and the mathematics, providing a complete picture of how QIS and QC work. The authors give multiple representations of the concept—textual, graphical, and symbolic (state vectors, matrices, and Dirac notation)—which are the lingua franca of QIS and QC. Those multiple representations allow the readers to develop a broader and deeper understanding of the fundamental concepts and their applications. In addition, the book provides examples of recent experimental demonstrations of quantum teleportation and the applications of quantum computational chemistry. The last chapter connects to the growing commercial world of QC and QIS and provides recommendations for further study.

Craig S. Lent

Stephen Fenner

P. Heszler, László B. Kish

A model of parallel optical computer for Fourier transform tasks is built. The computer operates in both quantum and classical modes. The quantum computer (QC) works with entangled photons and the input gates are n-qubit sensitive, while the classical computer (CC) operates without entanglement. The information capacity (I) for both CC and QC is given as a function of number of qubits and Np (number of photons per input pixel). It is shown that the information capacity significantly increases for the quantum computer compared to the classical one as the number of qubits is increased, assuming that Np is constant for both the QC and CC, i.e. same amount of energy input is assumed for the computers. However, it is also pointed out that the complexity of the QC significantly increases, too. To quantify this, we introduce a new physical quantity called physical complexity (noted as Q). We define the physical complexity (Q) of a computer as ∑i,klog2nkai where k runs over all the gates/elements in the computer; nai is the number of distinguishable states what a gate can set for ai. For QC ai is defined as the ith coefficient of the wave function. For CC it is the ith independent component of the Fourier transform of the energy flow what a particular gate is able to control. By using this definition we show that, for both the quantum and classical computers built in this work, I ≤ Q, in other words the information capacity is less or equal than the physical complexity. Intuitively we suggest that this is a general law that is valid for every computer irrespectively of type, quantum or classic, and architecture.

Paola Zizzi, Massimo Pregnolato

We discuss the modalities by which we humans should (and in fact, do) compute. That is, we investigate about the logical languages and the computational modes of human reasoning, and the corresponding physical interpretation. In this context, however, the classical world (physical, logical, and computational) does not seem sufficient to give a complete description of the Mind. In fact, the Mind accomplishes different tasks, where it exhibits, alternatively, both classical and quantum features. There are some novelties in two important issues: the long-standing debate on the mind-body relationship, and Turing’s question about a possible identification of the Mind with a computer. The introduction of a quantum metalanguage (QML) for the logic of reasoning is the most important feature to deal with both issues. As far as the first issue is considered, the QML is physically interpreted as a Dissipative Quantum Field Theory (DQFT) of the brain. The corresponding quantum object-language (QOL), which is the logic of reasoning, and is controlled by the QML, is physically interpreted as the Quantum Mechanics of qubits, that is, Quantum Computing (QC). Therefore, the Mind is both language and metalanguage, and the brain is its physical interpretation.

Giuseppe Castagnoli