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**Paul A. Benioff**^{[1]} is an American physicist who helped pioneer the field of quantum computing. Benioff is best known for his research in quantum information theory that demonstrated the theoretical possibility of quantum computers.

## Contents

## Early life and education

Benioff was born on May 1, 1930, in Pasadena, California.^{[2]} His father was a professor of seismology at the California Institute of Technology, and his mother received a master’s degree in English from the University of California, Berkeley.

Benioff also attended Berkeley, where he earned an undergraduate degree in botany, in 1951. After a two-year stint working in nuclear chemistry for Tracerlab, he returned to Berkeley, in 1959, to obtain his Ph.D. in nuclear chemistry.

## Career and research

In 1960, Benioff spent a year at the Weizmann Institute of Science in Israel as a postdoctoral fellow. He then spent six months at the Niels Bohr Institute in Copenhagen, as a Ford Fellow. In 1961, he began a long career at Argonne National Laboratory, first with its Chemistry Division and later in 1978 in the lab’s Environmental Impact Division. Benioff remained at Argonne until he retired in 1995. He continues to conduct research at the laboratory as a post-retirement research participant for the Physics Division. In 1979, Benioff taught the foundations of quantum mechanics as a visiting professor at Tel Aviv University, and worked as a visiting scientist at CNRS Marseilles, in 1979 and 1982.

In the 1970s, Benioff began to research the theoretical feasibility of quantum computing. His early research culminated in a paper, published in 1980 that described a quantum mechanical model of Turing Machines.^{[3]} This work was based on a classical description in 1973 of reversible Turing machines by Bennett.^{[4]} Benioff’s model of a quantum computer was reversible, and did not dissipate energy.^{[5]} At the time, there were several papers arguing that the creation of a reversible model of quantum computing was impossible. Benioff’s paper was the first to show that reversible quantum computing was theoretically possible. This work and other later work by several authors initiated the field of quantum computing. After publishing several more papers on quantum computers, the idea began to gain traction with industry, banking, and government agencies. The field is now a fast-growing area of research.

Throughout his career at Argonne, Benioff conducted research in many fields, including mathematics, physics and chemistry. While in the Chemistry Division, he conducted research on nuclear reaction theory, as well as the relationship between the foundations of physics and mathematics.

After joining Argonne’s Environmental Impact Division in 1978, Benioff continued work on quantum computing and on foundational issues. This included descriptions of quantum robots, quantum mechanical models of different types of numbers, and other topics. More recently, his work has been on the effects of number scaling and local mathematics on physics and geometry. As an emeritus, he continues to work on these and other foundational topics.

## Awards and recognition

In 2000, Benioff received the Quantum Communication Award of the International Organization for Quantum Communication, Computing, and Measurement, as well as the Quantum Computing and Communication Prize from Tamagawa University in Japan. He became a fellow of the American Physical Society in 2001. The following year, he was awarded the Special University of Chicago Medal for Distinguished Performance at Argonne National Laboratory. In 2016, Argonne held a conference in honor of his quantum computing work.

## Selected scientific works

- ”Cosmic-ray production rate and mean removal time of beryllium-7 from the atmosphere,"
*Physical Review*, Vol. 104, 1956, pp. 1122–1130. - ”Information theory in quantum statistical mechanics,"
*Physical Letters*, Vol. 14, 1965, pp. 196–197. - ”Some aspects of the relationship between mathematical logic and physics. I,"
*Journal of Mathematical Physics*, Vol. 11, 1970, pp. 2553–2569. - ”Some aspects of the relationship between mathematical logic and physics. II,"
*Journal of Mathematical Physics*, Vol. 12, 1971, pp. 360–376. - ”Operator valued measures in quantum mechanics: finite and infinite processes,"
*Journal of Mathematical Physics*, Vol. 13, 1972, pp. 231–242. - ”Decision procedures in quantum mechanics,"
*Journal of Mathematical Physics*, Vol. 13, 1972, pp. 908–915. - ”Procedures in quantum mechanics without Von Neumann's projection axiom,"
*Journal of Mathematical Physics*, Vol. 13, 1972, pp. 1347–1355. - ”Some consequences of the strengthened interpretative rules of quantum mechanics,"
*Journal of Mathematical Physics*, Vol. 15, 1974, pp. 552–559. - ”Models of Zermelo Frankel set theory as carriers for the mathematics of physics. I",
*Journal of Mathematical Physics*, Vol. 17, 1976, pp. 618–628. - ”Models of Zermelo Frankel set theory as carriers for the mathematics of physics. II,"
*Journal of Mathematical Physics*, Vol. 17, 1976, pp. 629–640. - ”Finite and infinite measurement sequences in quantum mechanics and randomness: The Everett interpretation,"
*Journal of Mathematical Physics*, Vol. 18, 1977, pp. 2289–2295. - "The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines",
*Journal of Statistical Physics*, Vol. 22, 1980, pp. 563–591. - "Quantum mechanical hamiltonian models of turing machines",
*Journal of Statistical Physics*, Vol. 29, 1982, pp. 515–546. - "Quantum Mechanical Models of Turing Machines That Dissipate No Energy",
*Phys. Rev. Lett.*, Vol. 48, 1982, pp. 1581–1585. - "Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: Application to Turing machines, Int. J".
*Theor. Phys.*, Vol. 21, 1982, pp. 177–201.^{[6]} - "Comment on 'Dissipation in Computation',"
*Physical Review Letters*, Vol. 53, 1984, pp. 1203. - "Quantum Mechanical Hamiltonian Models of Computers",
*Annals New York Academy of Sciences*, Vol. 480, 1986, pp. 475–486. - "Quantum ballistic evolution in quantum mechanics: Application to quantum computers",
*Phys. Rev. A*, Vol. 54, 1996, pp. 1106–1123, Arxiv. - "Tight binding Hamiltonians and Quantum Turing Machines",
*Phys. Rev. Lett.*, Vol. 78, 1997, pp. 590–593. - "Transmission and spectral aspects of tight binding hamiltonians for the counting quantum turing machine,"
*Physical Review B*, Vol. 55, 1997, pp. 9482–9493. - "Models of Quantum Turing Machines",
*Fortschritte der Physik*, Vol. 46, 1998, pp. 423–441, Arxiv. - "Quantum robots and environments",
*Phys. Rev. A*, Vol. 58, 1998, pp. 893–904, Arxiv. - "Quantum Robots and Quantum Computers", in: A. J. G. Hey (Hrsg.),
*Feynman and Computation*, Perseus Books 1999, pp. 155–176, Arxiv. - "A simple example of definitions of truth, validity, consistency, and completeness in quantum mechanics,"
*Physical Review A*, Vol. 59, 1999, pp. 4223–4252. - "The Representation of Natural Numbers in Quantum Mechanics",
*Phys. Rev. A*, Vol. 63, 2001, 032305, Arxiv. - "Efficient Implementation and the Product State Representation of Numbers",
*Phys. Rev. A*, Vol. 64, 2001, pp. 052310, Arxiv. - "Language is physical,"
*Quantum Information Proceedings*, Vol. 1, 2002, pp. 495–509. - "Use of mathematical logical concepts in quantum mechanics: an example,"
*Journal of Physics A: Mathematical and General*, Vol. 35, 2002, pp. 5843–5857. - "Towards a Coherent Theory of Physics and Mathematics",
*Found. Phys.*, Vol. 32, 2002, pp. 989–1029, Arxiv. - "The Representation of Numbers in Quantum Mechanics",
*Algorithmica*, Vol. 34, 2002, pp. 529–559, Arxiv. - "Towards a Coherent Theory of Physics and Mathematics: The Theory-Experiment Connection",
*Foundations of Physics*, Vol. 35, 2005, pp. 1825–1856, Arxiv. - "Representation of complex rational numbers in quantum mechanics",
*Phys. Rev. A*, Vol. 72, 2005, pp. 032314, Arxiv. - “Fields of quantum reference frames based on different representations of rational numbers as states of qubit strings.” Submitted to proceedings, 3rd Feynman Festival, University of Maryland, 2006,
*Journal of Physics*: Conference Series 70 (2007) 012003. - "A representation of real and complex numbers in quantum theory,"
*International Journal of Pure and Applied Mathematics*, Vol. 39, 2007, pp. 297–339. - "Reference frame fields based on quantum theory representations of real and complex numbers,"
*Advances in Quantum Computation*, Vol. 482, 2009, pp. 125–163. - “Effects on quantum physics of the local availability of mathematics and space time dependent scaling factors for number systems.” Chapter 2, in
*Advances in Quantum Theory*, I. I. Cotaescu (Ed.), Intech open access publisher, 2012. - “Gauge theory extension to include number scaling by boson field: Effects on some aspects of physics and geometry.” Chapter in
*Recent Developments in Bosons Research*, Ignace Tremblay (Ed.), Nova Press, 2013. - "Fiber bundle description of number scaling in gauge theory and geometry,"
*Quantum Studies: Mathematics and Foundations*, Vol. 2, 2015, pp. 289–313. - "Effects of a scalar scaling field on quantum mechanics,"
*Quantum Information Processing*, Vol. 15(7), 2016, pp. 3005–3034. - "The no information at a distance principle and local mathematics: some effects on physics and geometry,"
*Theoretical Information Studies*, submitted.

## References

**^**Date of birth and career information from*American Men and Women of Science*, Thomson Gale 2004**^**Date of birth and career information from*American Men and Women of Science*, Thomson Gale 2004**^**"The Computer as a Physical System: A Microscopic Quantum Mechanical Hamiltonian Model of Computers as Represented by Turing Machines", Paul Benioff,*Journal of Statistical Physics*, 22, 563, 1980.**^**"Logical reversibility of computation", C. H. Bennett,*IBM Journal of Research and Development*, Vol. 17, 525, (1973).**^**"Quantum Mechanical Models of Turing Machines That Dissipate No Energy", Paul Benioff,*Physical Review Letters*, 48, 1581 (1982).**^**Contribution to a 1981 MIT conference concerning quantum computing