Results 1 
3 of
3
Quantum Circuit Complexity
, 1993
"... We study a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomialsize quantum circuit. This result also enables us to construct a universal quantum compu ..."
Abstract

Cited by 278 (1 self)
 Add to MetaCart
We study a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomialsize quantum circuit. This result also enables us to construct a universal quantum computer which can simulate, with a polynomial factor slowdown, a broader class of quantum machines than that considered by Bernstein and Vazirani [BV93], thus answering an open question raised in [BV93]. We also develop a theory of quantum communication complexity, and use it as a tool to prove that the majority function does not have a linearsize quantum formula. Keywords. Boolean circuit complexity, communication complexity, quantum communication complexity, quantum computation AMS subject classifications. 68Q05, 68Q15 1 This research was supported in part by the National Science Foundation under grant CCR9301430. 1 Introduction One of the most intriguing questions in computation theroy ...
On Energy Expenditure per Unit of the Amount of Information
, 2008
"... It is shown that for an equilibrium state of timesymmetric system of nonrelativistic strings the energy per unit of information transfer (storage, processing) obeys the Bekenstein conjecture. The result is based on a theorem due to A.Kholevo relating the physical entropy and the amount of informat ..."
Abstract
 Add to MetaCart
It is shown that for an equilibrium state of timesymmetric system of nonrelativistic strings the energy per unit of information transfer (storage, processing) obeys the Bekenstein conjecture. The result is based on a theorem due to A.Kholevo relating the physical entropy and the amount of information. Interestingly, the energy in question is the difference between the ensemble averaged energy and the Helmholtz free energy. The problem about the energy requirements for the storage, transfer, and processing of information is one of the most important problems in the physics of information. In view of the recent keen interest ( and the attendant very large body of research work) in possible realizations of quantum computers, the above problem has direct relevance to quantum systems. Therefore it seems appropriate to revisit this problem. At the beginning of 1990’s B.Schumacher proposed (and later elaborated) [1] a conjecture (a generalization of earlier proposals by Bekenstein [2] and Pendry [3]) about an existence of a quantum limit for the power requirements of a communication channel. The conjecture relates an amount of information H conveyed by a quantum channel in a time interval δt and the energy E required for the physical representation of the information in the quantum
QUANTUM INFORMATION THEORY By
"... What are the information processing capabilities of physical systems? As recently as the first half of the 20 th century this question did not even have a definite meaning. What is information, and how would one process it? It took the development of theories of computing (in the 1930s) and informat ..."
Abstract
 Add to MetaCart
What are the information processing capabilities of physical systems? As recently as the first half of the 20 th century this question did not even have a definite meaning. What is information, and how would one process it? It took the development of theories of computing (in the 1930s) and information (late in the 1940s) for us to formulate mathematically what it means to compute or communicate. Yet these theories were abstract, based on axiomatic mathematics: what did physical systems have to do with these axioms? Rolf Landauer had the essential insight — “Information is physical ” — that information is always encoded in the state of a physical system, whose dynamics on a microscopic level are welldescribed by quantum physics. This means that we cannot discuss information without discussing how it is represented, and how nature dictates it should behave. Wigner considered the situation from another perspective when he wrote about “the unreasonable effectiveness of mathematics in the natural sciences”. Why are the computational techniques of mathematics so astonishingly useful in describing the physical world [1]? One might begin to suspect foul play in the universe’s operating principles.