B. FILTERING MODELS
B
231
Filtering models
1. Filtering models: Operate by ltering out of the solution molecules
that are not part of the solution.
2. A solution can be treated mathematically as a nite bag or multiset of
molecules,
and ltering operations
6
E. Rieffel and W. Polak
A
86
C
CHAPTER III. QUANTUM COMPUTATION
Finally, after filter B is inserted between A and C, a small amount of light will be visible
on the screen, exactly one eighth of the original amount of light.
A
B
C
Here we have a nonintui
B. BASIC CONCEPTS FROM QUANTUM THEORY
B.7
93
Uncertainty principle (supplementary)
You might be surprised that the famous Heisenberg uncertainty principle
is not among the postulates of quantum mechanics. That is because it is
not a postulate, but a theor
Chapter II
Physics of Computation
These lecture notes are exclusively for the use of students in Prof. MacLennans Unconventional Computation course. c 2016, B. J. MacLennan, EECS,
University of Tennessee, Knoxville. Version of August 21, 2016.
A
Energy di
sequence of gates has the following sequence of effects on a computational basis state
a, bi,
a, bi ! a, a
! a
! b, (a
bi
(a
b), a
b)
bi = b, a
bi
bi = b, ai ,
(1.20)
where all additions are done modulo 2. The effect of the circuit, therefore, is t
B. BASIC CONCEPTS FROM QUANTUM THEORY
B
77
Basic concepts from quantum theory
B.1
Introduction
B.1.a
Bases
In quantum mechanics certain physical quantities are quantized, such as the
energy of an electron in an atom. Therefore an atom might be in certain
C. QUANTUM INFORMATION
C
99
Quantum information
C.1
Qubits
C.1.a
Single qubits
Just as the bits 0 and 1 are represented by distinct physical states in a conventional computer, so the quantum bits (or qubits) 0i and 1i are represented
by distinct quantum
Quantum computation
104
21
CHAPTER III. QUANTUM COMPUTATION
!
!"'
!
"
!
"#$
!
"
! $!% "
"%$
!
"
! "# "
"&$
! &"# "
"'$
"($
!
"
! !$!% "
!
")$
!
"
! !"# "
!
Figure 1.6. On the left are some standard single and multiple bit gates, while on the right is the
46
CHAPTER II. PHYSICS OF COMPUTATION
C
Reversible computing
C.1
Reversible computing as a solution
Notice that the key quantity FE in Eqn. II.1 depends on the energy dissipated
as heat.17 The 100kB T limit depends on the energy in the signal (necessary
t
Chapter III
Quantum Computation
These lecture notes are exclusively for the use of students in Prof. MacLennans Unconventional Computation course. c 2016, B. J. MacLennan, EECS,
University of Tennessee, Knoxville. Version of August 24, 2016.
A
Mathematica
Chapter I
Introduction
These lecture notes are exclusively for the use of students in Prof. MacLennans Unconventional Computation course. c 2016, B. J. MacLennan, EECS,
University of Tennessee, Knoxville. Version of August 16, 2016.
A
What is unconvention
Chapter I
Introduction
These lecture notes are exclusively for the use of students in Prof. MacLennans Unconventional Computation course. c 2013, B. J. MacLennan, EECS,
University of Tennessee, Knoxville. Version of August 21, 2013.
These lecture notes ar
Chapter II
Physics of Computation
These lecture notes are exclusively for the use of students in Prof. MacLennans Unconventional Computation course. c 2013, B. J. MacLennan, EECS,
University of Tennessee, Knoxville. Version of August 27, 2013.
A
Energy di
34
CHAPTER II. PHYSICS OF COMPUTATION
B
Thermodynamics of computation
B.1
Von NeumannLandaur Principle
1. Entropy: A quick introduction/review of the entropy concept. We
will look at it in more detail soon (Sec. B.4).
2. Information content: The informat
Chapter IV
Molecular Computation
These lecture notes are exclusively for the use of students in Prof. MacLennans Unconventional Computation course. c 2013, B. J. MacLennan, EECS,
University of Tennessee, Knoxville. Version of November 13, 2013.
A
A.1
Basi
198
H
CHAPTER III. QUANTUM COMPUTATION
Quantum probability in cognition
This lecture is based on Emmanuel M. Pothos and Jerome R. Busemeyer,
Can quantum probability provide a new direction for cognitive modeling?
Behavioral and Brain Sciences, forthcoming
188
G
CHAPTER III. QUANTUM COMPUTATION
Physical realizations
The principal source for this lecture is NC, ch. 7.
G.1
Basic criteria
1. We can outline a fundamental set of requirements for any practical
physical realization of quantum computing.
2. (a) Sca
F. UNIVERSAL QUANTUM COMPUTERS
F
177
Universal quantum computers
1. Power: A natural question is: What is the power of a quantum computer?
Is it superTuring or subTuring?
2. E ciency: Another question is: What is its e ciency?
Can it solve NP problems e
172
E
CHAPTER III. QUANTUM COMPUTATION
AbramsLloyd theorem
This lecture is based on Daniel S. Abrams and Seth Lloyd (1998), Nonlinear
quantum mechanics implies polynomialtime solution for NPcomplete and
#P problems. Phys. Rev. Lett. 81, 39923995 (1998)
132
Quantum
33
CHAPTER III. QUANTUM algorithms
COMPUTATION
Figure 1.19. Quantum circuit implementing Deutschs algorithm.
Figure III.22: Quantum circuit for Deutsch algorithm. [g. from NC]
is sent through two Hadamard gates to give
0i + 1i 0i 1i
p
p

C. QUANTUM INFORMATION
101
C
C.1
C.1.a
Quantum information
Qubits
Single qubits
1. Qubit: Just as the bits 0 and 1 are represented by distinct physical states, so the quantum bits (or qubits) 0i and 1i are represented by distinct quantum states. 2. Comp
80
CHAPTER III. QUANTUM COMPUTATION
Figure III.1: Probability density of rst six hydrogen orbitals. The main
quantum number (n = 1, 2, 3) and the angular momentum quantum number
(` = 0, 1, 2 = s, p, d) are shown. (The magnetic quantum number m = 0 in
thes
Chapter III
Quantum Computation
These lecture notes are exclusively for the use of students in Prof. MacLennans Unconventional Computation course. c 2013, B. J. MacLennan, EECS,
University of Tennessee, Knoxville. Version of September 6, 2013.
A
Mathemati
C. REVERSIBLE COMPUTING
C
49
Reversible computing
C.1
Reversible computing as solution
This section is based on Frank (2005).
C.1.a
Possible solution
1. Notice that the key quantity FE in Eqn. II.1 depends on the energy
dissipated as heat.
2. The 100kB T
The key to both dense coding and teleportation is the use of entangled particles. The
initial set up is the same for both processes. Alice and Bob wish to communicate. Each is
sent one of the entangled particles making up an EPR pair,
0
C.
1
= p (00i + 