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A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior using specialized hardware. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer. In particular, a large-scale quantum computer could break widely used encryption schemes and aid physicists in performing physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications.
In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. A classical algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is generally reserved for algorithms that seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement.
A quantum sort is any sorting algorithm that runs on a quantum computer. Any comparison-based quantum sorting algorithm would take at least steps, which is already achievable by classical algorithms. Thus, for this task, quantum computers are no better than classical ones, and should be disregarded when it comes to time complexity. However, in space-bounded sorts, quantum algorithms outperform their classical counterparts.
Quantum neural networks are computational neural network models which are based on the principles of quantum mechanics. The first ideas on quantum neural computation were published independently in 1995 by Subhash Kak and Ron Chrisley, engaging with the theory of quantum mind, which posits that quantum effects play a role in cognitive function. However, typical research in quantum neural networks involves combining classical artificial neural network models with the advantages of quantum information in order to develop more efficient algorithms. One important motivation for these investigations is the difficulty to train classical neural networks, especially in big data applications. The hope is that features of quantum computing such as quantum parallelism or the effects of interference and entanglement can be used as resources. Since the technological implementation of a quantum computer is still in a premature stage, such quantum neural network models are mostly theoretical proposals that await their full implementation in physical experiments.
String diagrams are a formal graphical language for representing morphisms in monoidal categories, or more generally 2-cells in 2-categories. They are a prominent tool in applied category theory. When interpreted in the monoidal category of vector spaces and linear maps with the tensor product, string diagrams are called tensor networks or Penrose graphical notation. This has led to the development of categorical quantum mechanics where the axioms of quantum theory are expressed in the language of monoidal categories.
Reservoir computing is a framework for computation derived from recurrent neural network theory that maps input signals into higher dimensional computational spaces through the dynamics of a fixed, non-linear system called a reservoir. After the input signal is fed into the reservoir, which is treated as a "black box," a simple readout mechanism is trained to read the state of the reservoir and map it to the desired output. The first key benefit of this framework is that training is performed only at the readout stage, as the reservoir dynamics are fixed. The second is that the computational power of naturally available systems, both classical and quantum mechanical, can be used to reduce the effective computational cost.
Categorical quantum mechanics is the study of quantum foundations and quantum information using paradigms from mathematics and computer science, notably monoidal category theory. The primitive objects of study are physical processes, and the different ways that these can be composed. It was pioneered in 2004 by Samson Abramsky and Bob Coecke. Categorical quantum mechanics is entry 18M40 in MSC2020.
Bob Coecke is a Belgian theoretical physicist and logician who was professor of Quantum foundations, Logics and Structures at Oxford University until 2020, when he became Chief Scientist of Cambridge Quantum Computing, and after the merger with Honeywell Quantum Systems, Chief Scientist of Quantinuum. In January 2023 he also became Distinguished Visiting Research Chair at the Perimeter Institute for Theoretical Physics. He pioneered categorical quantum mechanics, Quantum Picturalism, ZX-calculus, DisCoCat model for natural language, and quantum natural language processing (QNLP). He is a founder of the Quantum Physics and Logic community and conference series, and of the applied category theory community, conference series, and diamond-open-access journal Compositionality.
Quantum machine learning is the integration of quantum algorithms within machine learning programs.
Edward Henry Farhi is a physicist working on quantum computation as a principal scientist at Google. In 2018 he retired from his position as the Cecil and Ida Green Professor of Physics at the Massachusetts Institute of Technology. He was the director of the Center for Theoretical Physics at MIT from 2004 until 2016. He made contributions to particle physics, general relativity and astroparticle physics before turning to his current interest, quantum computation.
Cloud-based quantum computing is the invocation of quantum emulators, simulators or processors through the cloud. Increasingly, cloud services are being looked on as the method for providing access to quantum processing. Quantum computers achieve their massive computing power by initiating quantum physics into processing power and when users are allowed access to these quantum-powered computers through the internet it is known as quantum computing within the cloud.
In quantum computing, quantum supremacy or quantum advantage is the goal of demonstrating that a programmable quantum computer can solve a problem that no classical computer can solve in any feasible amount of time, irrespective of the usefulness of the problem. The term was coined by John Preskill in 2012, but the concept dates to Yuri Manin's 1980 and Richard Feynman's 1981 proposals of quantum computing.
Continuous-variable (CV) quantum information is the area of quantum information science that makes use of physical observables, like the strength of an electromagnetic field, whose numerical values belong to continuous intervals. One primary application is quantum computing. In a sense, continuous-variable quantum computation is "analog", while quantum computation using qubits is "digital." In more technical terms, the former makes use of Hilbert spaces that are infinite-dimensional, while the Hilbert spaces for systems comprising collections of qubits are finite-dimensional. One motivation for studying continuous-variable quantum computation is to understand what resources are necessary to make quantum computers more powerful than classical ones.
Quil is a quantum instruction set architecture that first introduced a shared quantum/classical memory model. It was introduced by Robert Smith, Michael Curtis, and William Zeng in A Practical Quantum Instruction Set Architecture. Many quantum algorithms require a shared memory architecture. Quil is being developed for the superconducting quantum processors developed by Rigetti Computing through the Forest quantum programming API. A Python library called pyQuil was introduced to develop Quil programs with higher level constructs. A Quil backend is also supported by other quantum programming environments.
The ZX-calculus is a rigorous graphical language for reasoning about linear maps between qubits, which are represented as string diagrams called ZX-diagrams. A ZX-diagram consists of a set of generators called spiders that represent specific tensors. These are connected together to form a tensor network similar to Penrose graphical notation. Due to the symmetries of the spiders and the properties of the underlying category, topologically deforming a ZX-diagram does not affect the linear map it represents. In addition to the equalities between ZX-diagrams that are generated by topological deformations, the calculus also has a set of graphical rewrite rules for transforming diagrams into one another. The ZX-calculus is universal in the sense that any linear map between qubits can be represented as a diagram, and different sets of graphical rewrite rules are complete for different families of linear maps. ZX-diagrams can be seen as a generalisation of quantum circuit notation.
Quantinuum is a quantum computing company formed by the merger of Cambridge Quantum and Honeywell Quantum Solutions. The company's H-Series trapped-ion quantum computers set the highest quantum volume to date of 1,048,576 in April 2024. This architecture supports all-to-all qubit connectivity, allowing entangled states to be created between all qubits, and enables a high fidelity of quantum states.
Applied category theory is an academic discipline in which methods from category theory are used to study other fields including but not limited to computer science, physics, natural language processing, control theory, probability theory and causality. The application of category theory in these domains can take different forms. In some cases the formalization of the domain into the language of category theory is the goal, the idea here being that this would elucidate the important structure and properties of the domain. In other cases the formalization is used to leverage the power of abstraction in order to prove new results about the field.
This glossary of quantum computing is a list of definitions of terms and concepts used in quantum computing, its sub-disciplines, and related fields.
DisCoCat is a mathematical framework for natural language processing which uses category theory to unify distributional semantics with the principle of compositionality. The grammatical derivations in a categorial grammar are interpreted as linear maps acting on the tensor product of word vectors to produce the meaning of a sentence or a piece of text. String diagrams are used to visualise information flow and reason about natural language semantics.
In the mathematical field of category theory, FinVect is the category whose objects are all finite-dimensional vector spaces and whose morphisms are all linear maps between them.
References
- 1 2 3 Zeng, William; Coecke, Bob (2016-08-02). "Quantum Algorithms for Compositional Natural Language Processing". Electronic Proceedings in Theoretical Computer Science. 221: 67–75. arXiv: 1608.01406 . doi:10.4204/EPTCS.221.8. ISSN 2075-2180. S2CID 14897915.
- 1 2 Wiebe, Nathan; Bocharov, Alex; Smolensky, Paul; Troyer, Matthias; Svore, Krysta M. (2019-02-13). "Quantum Language Processing". arXiv: 1902.05162 [quant-ph].
- ↑ Coecke, Bob; de Felice, Giovanni; Meichanetzidis, Konstantinos; Toumi, Alexis (2020-12-07). "Foundations for Near-Term Quantum Natural Language Processing". arXiv: 2012.03755 [quant-ph].
- ↑ Ganguly, Srinjoy; Morapakula, Sai Nandan; Bertel, Luis Gerardo Ayala, "An Introduction to Quantum Natural Language Processing (QNLP)", Coded Leadership, CRC Press, pp. 1–23, retrieved 2022-11-11
- 1 2 Meichanetzidis, Konstantinos; Toumi, Alexis; de Felice, Giovanni; Coecke, Bob (2023). "Grammar-aware sentence classification on quantum computers". Quantum Machine Intelligence. 5. arXiv: 2012.03756 . doi:10.1007/s42484-023-00097-1. S2CID 256832721.
- ↑ Lorenz, Robin; Pearson, Anna; Meichanetzidis, Konstantinos; Kartsaklis, Dimitri; Coecke, Bob (2023). "QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer". Journal of Artificial Intelligence Research. 76: 1305–1342. arXiv: 2102.12846 . doi:10.1613/jair.1.14329. S2CID 232046044.
- ↑ Vicente Nieto, Irene (2021). Towards Machine Translation with Quantum Computers (PDF). Master thesis, Stockholm University, Faculty of Science, Department of Physics.
- ↑ Miranda, Eduardo Reck; Yeung, Richie; Pearson, Anna; Meichanetzidis, Konstantinos; Coecke, Bob (2022), Miranda, Eduardo Reck (ed.), "A Quantum Natural Language Processing Approach to Musical Intelligence", Quantum Computer Music: Foundations, Methods and Advanced Concepts, Cham: Springer International Publishing, pp. 313–356, arXiv: 2111.06741 , doi:10.1007/978-3-031-13909-3_13, ISBN 978-3-031-13909-3 , retrieved 2022-11-07
