REFERENCES

Citations

1. Dirac, P. A. M. (1930). The Principles of Quantum Mechanics. Oxford University Press, Oxford.

2. Von Neumann, J. (1955). Mathematical Foundations of Quantum Mechanics. Princeton University Press.

3. Heisenberg, W. (1927). "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik." Zeitschrift für Physik, 43(3-4), 172-198.

4. Schrödinger, E. (1926). "An Undulatory Theory of the Mechanics of Atoms and Molecules." Physical Review, 28(6), 1049.

5. Einstein, A., Podolsky, B., & Rosen, N. (1935). "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?" Physical Review, 47(10), 777.

6. Bell, J. S. (1964). "On the Einstein Podolsky Rosen Paradox." Physics Physique Физика, 1(3), 195-200.

7. Everett, H. (1957). "Relative State Formulation of Quantum Mechanics." Reviews of Modern Physics, 29(3), 454.

8. Deutsch, D. (1985). "Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer." Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 400(1818), 97-117.

9. Bennett, C. H., & Shor, P. W. (1998). "Quantum Information Theory." IEEE Transactions on Information Theory, 44(6), 2724-2742.

10. Nielsen, M. A., & Chuang, I. L. (2000). Quantum Computation and Quantum Information. Cambridge University Press.

11. Zurek, W. H. (2003). "Decoherence, einselection, and the quantum origins of the classical." Reviews of Modern Physics, 75(3), 715.

12. Aspect, A., Dalibard, J., & Roger, G. (1982). "Experimental Test of Bell's Inequalities Using Time‐Varying Analyzers." Physical Review Letters, 49(25), 1804.

13. Kitaev, A. Y. (2003). "Fault-tolerant quantum computation by anyons." Annals of Physics, 303(1), 2-30.

14. Raussendorf, R., & Briegel, H. J. (2001). "A One-Way Quantum Computer." Physical Review Letters, 86(22), 5188.

15. Shor, P. W. (1995). "Scheme for reducing decoherence in quantum computer memory." Physical Review A, 52(4), R2493.

16. Grover, L. K. (1996). "A fast quantum mechanical algorithm for database search." Proceedings, 28th Annual ACM Symposium on the Theory of Computing, p. 212.

17. Aharonov, Y., & Ben-Or, M. (1996). "Fault-Tolerant Quantum Computation with Constant Error." Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, p. 176.

18. Lloyd, S. (1996). "Universal Quantum Simulators." Science, 273(5278), 1073-1078.

19. Preskill, J. (1998). "Quantum Information and Computation." Physics Today, 52(10), 24-30.

20. Wootters, W. K., & Zurek, W. H. (1982). "A single quantum cannot be cloned." Nature, 299(5886), 802-803.

21. Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik, 43(3-4), 167-181.

22. Bell, J. S. (1964). On the Einstein-Podolsky-Rosen paradox. Physics, 1(3), 195-200.

23. Joos, E., & Zeh, H. D. (1985). The emergence of classical properties through decoherence. Zeitschrift für Physik B Condensed Matter, 59(2), 223-243.

24. Joos, E., & Zeh, H. D. (1985). The emergence of classical properties through decoherence. Zeitschrift für Physik B Condensed Matter, 59(2), 223-243.

25. Bell, J. S. (1964). On the Einstein-Podolsky-Rosen paradox. Physics, 1(3), 195-200.

26. von Neumann, J. (1955). Mathematical Foundations of Quantum Mechanics. Princeton University Press.

Citations/References:

1. Nielsen, M. A., & Chuang, I. L. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press.

• Citation: Nielsen and Chuang (2010) provide foundational concepts of quantum computation, including the principles of quantum mechanics that govern quantum computers.

1. Deutsch, D. (1997). The Fabric of Reality. Penguin Books.

• Citation: Deutsch (1997) explores the philosophical implications of quantum mechanics and its impact on the perceptions of reality and determinism.

1. Preskill, J. (2018). Quantum Computing in the NISQ era and beyond. Quantum, 2, 79.

• Citation: Preskill (2018) discusses the capabilities and limitations of current quantum technologies in the so-called "Noisy Intermediate-Scale Quantum" (NISQ) era.

1. Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik, 43(3-4), 172-198.

• Citation: Heisenberg (1927) introduces the uncertainty principle, a fundamental limit on the precision with which certain pairs of physical properties can be simultaneously known.

1. Lorenz, E. N. (1963). Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences, 20(2), 130-141.

• Citation: Lorenz (1963) provides an analysis of chaos theory, emphasizing the sensitivity of systems to initial conditions and its implications for predictability.

1. Zurek, W. H. (1991). Decoherence and the Transition from Quantum to Classical. Physics Today, 44(10), 36-44.

• Citation: Zurek (1991) discusses how quantum systems interact with their environments leading to decoherence, which is critical in understanding the collapse of the wave function and the transition from quantum to classical behavior.

1. Gleick, J. (1987). Chaos: Making a New Science. Viking Penguin.

• Citation: Gleick (1987) offers an accessible introduction to chaos theory and its profound impact across scientific disciplines, including its role in limiting the predictability of complex systems.

1. Penrose, R. (2004). The Road to Reality: A Complete Guide to the Laws of the Universe. Knopf.

• Citation: Penrose (2004) examines the laws of physics from the universe's smallest components to its grandest scales, including discussions on the limitations of current theories in physics and the potential roles of quantum mechanics in the universe.

1. Bekenstein, J. D. (1981). Universal upper bound on the entropy-to-energy ratio for bounded systems. Physical Review D, 23(2), 287.

• Citation: Bekenstein (1981) introduces the Bekenstein bound, which is crucial in discussions about the physical limits of information storage and processing capabilities.

1. Everett, H. (1957). "Relative State" Formulation of Quantum Mechanics. Reviews of Modern Physics, 29(3), 454.

• Citation: Everett (1957) explores the relative state formulation of quantum mechanics, which is foundational in understanding the probabilistic nature of quantum mechanics and challenges to determinism.

1. Schlosshauer, M. (2005). Decoherence and the Quantum-To-Classical Transition. Springer.

• Citation: Schlosshauer (2005) elaborates on the process of decoherence, which is crucial for understanding how quantum systems exhibit classical behavior post-measurement.

1. Kiefer, C. (2007). Quantum Gravity. Oxford University Press.

• Citation: Kiefer (2007) discusses the interface of quantum mechanics with gravitational theories, pertinent to discussions about simulating the universe.

1. Rovelli, C. (2004). Quantum Gravity. Cambridge University Press.

• Citation: Rovelli (2004) provides insights into quantum gravity, a theoretical framework essential for understanding quantum cosmology and its implications on time and predictability.

1. Bell, J. S. (1964). On the Einstein Podolsky Rosen Paradox. Physics, 1(3), 195-200.

• Citation: Bell (1964) introduces Bell's theorem, which challenges local realism and has profound implications for the entanglement and non-locality in quantum mechanics.

1. Aspect, A., Dalibard, J., & Roger, G. (1982). Experimental Test of Bell's Inequalities Using Time‐Varying Analyzers. Physical Review Letters, 49(25), 1804.

• Citation: Aspect et al. (1982) discuss the experimental validation of quantum entanglement, reinforcing the concepts of non-locality and the limitations of classical predictions in quantum systems.

1. Wheeler, J. A., & Zurek, W. H. (Eds.). (1983). Quantum Theory and Measurement. Princeton University Press.

• Citation: Wheeler and Zurek (1983) compile key papers that explore the measurement problem in quantum mechanics, pertinent to the discussion of wave function collapse and observer effects.

1. Greenstein, G., & Zajonc, A. (2006). The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics. Jones and Bartlett Publishers.

• Citation: Greenstein and Zajonc (2006) provide a comprehensive review of the experimental challenges and questions in the foundation of quantum mechanics, directly relevant to discussions about the limits of quantum computing.

1. Wootters, W. K., & Zurek, W. H. (1982). A single quantum cannot be cloned. Nature, 299(5886), 802-803.

• Citation: Wootters and Zurek (1982) introduce the no-cloning theorem, which is crucial for understanding the limitations in copying quantum information and its implications for quantum computing.

1. Hossenfelder, S. (2018). Lost in Math: How Beauty Leads Physics Astray. Basic Books.

• Citation: Hossenfelder (2018) critiques the current foundations of physics, including quantum mechanics, for relying heavily on aesthetic and philosophical assumptions, which is relevant for discussions about the theoretical limits in predicting quantum system behaviors.

1. Aaronson, S. (2013). Quantum Computing Since Democritus. Cambridge University Press.

• Citation: Aaronson (2013) provides a unique perspective on the computational aspects of quantum mechanics and the inherent philosophical and practical challenges.

1. Tegmark, M. (2014). Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. Knopf.

• Citation: Tegmark (2014) explores the deep relationships between physical reality and the mathematical structures underlying the universe, including implications for quantum computing and the nature of information.

1. Feynman, R. P. (1982). Simulating Physics with Computers. International Journal of Theoretical Physics, 21(6/7), 467-488.

• Citation: Feynman (1982) is foundational in establishing the field of quantum computing, discussing the simulation of physical systems with quantum computers, directly pertinent to discussions about their capabilities and limitations in simulating complex systems.

1. Nielsen, M. A., & Chuang, I. L. (2010). Quantum Computation and Quantum Information. Cambridge University Press.

• Citation: This book is a comprehensive resource on quantum computation and quantum information, providing detailed discussions on entanglement, quantum algorithms, and quantum error correction.

1. Bennett, C. H., & Brassard, G. (1984). Quantum cryptography: Public key distribution and coin tossing. Proceedings of IEEE International Conference on Computers, Systems, and Signal Processing.

• Citation: Bennett and Brassard (1984) introduce quantum key distribution, laying the groundwork for understanding quantum cryptographic protocols.

1. Eisert, J., & Plenio, M. B. (1999). A comparison of entanglement measures. Journal of Modern Optics, 46(1), 145-154.

• Citation: This paper discusses various measures of entanglement, crucial for understanding the different ways quantum information can be quantified and utilized.

1. Aspect, A., Grangier, P., & Roger, G. (1981). Experimental Tests of Realistic Local Theories via Bell's Theorem. Physical Review Letters, 47(7), 460.

• Citation: Aspect et al. (1981) provide experimental validation of quantum entanglement, challenging local hidden variable theories and supporting the non-locality of quantum mechanics.

1. Wootters, W. K., & Zurek, W. H. (1982). A single quantum cannot be cloned. Nature, 299(5886), 802-803.

• Citation: Introduces the no-cloning theorem, fundamental in the field of quantum information for its implications on the security and transmission of quantum information.

1. Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009). Quantum entanglement. Reviews of Modern Physics, 81(2), 865.

• Citation: Horodecki et al. (2009) offer a thorough review of the properties, applications, and measures of quantum entanglement.

1. Bouwmeester, D., Pan, J. W., Mattle, K., Eibl, M., Weinfurter, H., & Zeilinger, A. (1997). Experimental quantum teleportation. Nature, 390(6660), 575-579.

• Citation: This experimental study demonstrates quantum teleportation, highlighting the transfer of quantum information through entangled states.

1. Shor, P. W. (1995). Scheme for reducing decoherence in quantum computer memory. Physical Review A, 52(4), R2493.

• Citation: Shor (1995) discusses methods for combating decoherence, a major challenge in preserving quantum information in quantum computing.

1. Deutsch, D. (1985). Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. Series A, 400(1818), 97-117.

• Citation: Deutsch (1985) introduces the concept of a universal quantum computer, expanding on the computational possibilities of quantum systems.

1. Ekert, A. K. (1991). Quantum cryptography based on Bell's theorem. Physical Review Letters, 67(6), 661.

• Citation: Ekert (1991) proposes a protocol for quantum cryptography based on the principles of quantum entanglement and Bell's inequality.

1. Briegel, H. J., Dür, W., Cirac, J. I., & Zoller, P. (1998). Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication. Physical Review Letters, 81(26), 5932-5935.

• Citation: Discusses the concept of quantum repeaters, which enable long-distance quantum communication by overcoming decoherence and operational imperfections.

1. Raussendorf, R., & Briegel, H. J. (2001). A One-Way Quantum Computer. Physical Review Letters, 86(22), 5188.

• Citation: Introduces the model of one-way quantum computing, which uses a highly entangled state as a resource for performing quantum gates.

1. Kimble, H. J. (2008). The quantum internet. Nature, 453(7198), 1023-1030.

• Citation: Kimble (2008) discusses the potential development and implications of a quantum internet based on quantum information technologies.

1. Monroe, C., Meekhof, D. M., King, B. E., & Wineland, D. J. (1996). A "Schrödinger Cat" Superposition State of an Atom. Science, 272(5265), 1131-1136.

• Citation: Experimental demonstration of a Schrödinger cat state, important for understanding quantum superposition and decoherence.

1. Preskill, J. (1998). Quantum Information and Computation. Lecture Notes for Physics, Caltech.

• Citation: Preskill’s lecture notes are a valuable resource for students and researchers, covering topics from basic quantum mechanics to quantum information theory.

1. Gisin, N., Ribordy, G., Tittel, W., & Zbinden, H. (2002). Quantum cryptography. Reviews of Modern Physics, 74(1), 145.

• Citation: Reviews the developments in quantum cryptography, particularly focusing on practical implementations of quantum key distribution.

1. Pan, J. W., Bouwmeester, D., Weinfurter, H., & Zeilinger, A. (1998). Experimental entanglement swapping: entangling photons that never interacted. Physical Review Letters, 80(18), 3891-3894.

Citation: Demonstrates entanglement swapping, a phenomenon where entanglement is transferred between particles that do not directly interact, essential for quantum networking and communication protocols. | Citation | Reference | URL | | :-- | :-- | :-- | | Nielsen and Chuang

Relative Areas of Research

1. Quantum State Space:

• Refers to the complete set of all possible states of a quantum system, represented within a Hilbert space.

1. Quantum Geometry:

• A field studying the geometric aspects of quantum states, focusing on how quantum properties such as entanglement and superposition can be described using geometric concepts.

1. Quantum Topology:

• Involves the study of continuous, and often non-intuitive, properties of quantum systems that are preserved under deformations, twistings, and stretchings, playing a crucial role in topological quantum computing.

1. Quantum Lattice:

• A framework for modeling quantum systems in discretized space, often used in lattice gauge theory and quantum field theory to simplify complex quantum systems into manageable computational models.

1. Quantum Fibre Bundle:

• Extends the idea of manifolds by including extra-dimensional structures; in quantum physics, it can represent how quantum states or fields vary over different points in space-time.

1. Complex Projective Space:

• Utilized in quantum mechanics to describe pure states of a quantum system as rays in a Hilbert space, emphasizing the projective nature of quantum measurements.

1. Bloch Sphere:

• Represents the state space of a two-level quantum system (qubit), providing a powerful geometric visualization of quantum state evolution and superposition.

1. Density Functional Space:

• Explores the distribution of probabilities or densities over a quantum system, crucial for understanding mixed states through density matrices.

1. Quantum Entanglement Graph:

• A graphical representation that describes the entanglement relationships between various parts of a quantum system, highlighting non-local interactions.

1. Quantum Phase Space:

• Combines classical phase space concepts with quantum mechanics to offer a quasi-probabilistic computation of states using techniques like Wigner quasi-probability distributions.

1. Fock Space:

• A more comprehensive framework used in quantum mechanics to describe quantum states in systems with varying particle numbers, such as in quantum field theory.

1. Symplectic Manifold:

• Often used in the mathematical formulation of quantum mechanics to describe the phase space of quantum systems, emphasizing conservation and transformation properties.

1. Spin Network:

• Used in quantum gravity to describe the quantum state of the gravitational field, representing a quantum manifold in terms of geometry and topology.

1. Hilbert Bundle:

• A concept extending Hilbert spaces into bundle structures to examine how quantum states might vary over another mathematical space, useful in fields like quantum field theory.

1. Quantum Foam:

• A conceptual model in quantum gravity representing the fluctuating, chaotic quantum state of space-time at the Planck scale, visualizing the fundamental granularity of space itself.

References: