the shifting paradigm of quantum computing
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The Shifting Paradigm of Quantum Computing. Presented at the Nov 2005 Annual Dallas Mensa Gathering By Douglas Matzke, Ph.D. [email protected] http://www.QuantumDoug.com. Abstract. - PowerPoint PPT PresentationTRANSCRIPT
The Shifting Paradigm of Quantum Computing
Presented at the Nov 2005
Annual Dallas Mensa Gathering
By Douglas Matzke, Ph.D.
http://www.QuantumDoug.com
DJM Nov 25, 2005
Abstract
Quantum computing has shown to efficiently solve problems that classical computers are unable to solve. Quantum computers represent information using phase states in high dimensional spaces, which produces the two fundamental quantum properties of superposition and entanglement.
This talk introduces these concepts in plain-speak and discusses how this leads to a paradigm shift of thinking "outside the classical computing box".
DJM Nov 25, 2005
Biography
Doug Matzke has been researching the limits of computing for over twenty years. These interests led him to investigating the area of quantum computing and earning a Ph.D. in May 2001. In his thirty year career, he has hosted two workshops on physics and computation (PhysComp92 and (PhysComp94), he has contributed to 15 patent disclosures and over thirty papers/talks (see his papers on QuantumDoug.com). He is an enthusiastic and thought provoking speaker.
DJM Nov 25, 2005
Outline Classical Bits
Distinguishability Mutual Exclusion
Quantum Bits – Qubits Orthogonal Phase States Superposition Measurement Noise – Pauli Spin Matrices
Quantum Registers Entanglement
Entangled Bits – Ebits Bell and Magic States
Quantum Algorithms Shor’s algorithm Grover’s Algorithm
Quantum Communication Quantum Cryptography
Summary
DJM Nov 25, 2005
Classical Information
Distinguishability Definition: Individual items are identifiable
Coins, photons, electrons etc are not distinguishable Groups of objects described using statistics
Mutual Exclusion (mutex) Definition: Some state excludes another state
Coin lands on heads or tails but not both Faces point in opposite directions in vector notation
+ -
DJM Nov 25, 2005
Coin Demonstration: Act ISetup:
Person stands with both hands behind back
Act I part A: Person shows hand containing a coin then hides it again
Act I part B: Person again shows a coin (indistinguishable from 1st)
Act I part C: Person asks: “How many coins do I have?”
Represents one bit: either has 1 coin or has >1 coin
DJM Nov 25, 2005
Coin Demonstration (cont)
Act II: Person holds out hand showing two identical coins
Received one bit since ambiguity resolved!
Act III: Asks: “Where did the bit of information come from?”
Answer: Simultaneous presence of the 2 coins!
DJM Nov 25, 2005
Space and Time Ideas
Co-occurrence means states exist exactly simultaneously: Spatial prim. with addition operator
Co-exclusion means a change occurred due to an operator: Temporal with multiply operator
* see definitions in my dissertation but originated with Manthey
DJM Nov 25, 2005
Quantum Bits – Qubits
+
-
-
+
Classical bit states: Mutual Exclusive
Quantum bit states: Orthogonal
180°90°
Qubits states are called spin ½
State1
State0
State1
State0
DJM Nov 25, 2005
Phases & Superposition
-
+
90°
State1
State0
(C0 State0 + C1 State1)
0 1
1
2c c
= 45°
21 i ic p Unitarity Constraint is
C0
C1
10 0
0state
0
1 11
state
DJM Nov 25, 2005
Unitary Qubit Operators
Gate Symbolic Matrix Circuit Exists
Identity
Not (Pauli-X)
Shift (Pauli-Z)
Rotate
Hadamard -Superposition
cos sin
sin cos
1
0 1
1 0
1 11
1 12H
0 *
*H
*
3
1 0
0 1
H
θ
X
Z
0 1
1 *
3 *
0
1 0
0 1
01
11
31
1
1 H
DJM Nov 25, 2005
Matrices 101a b
c d
*a b a b
c d c d
1
0 1 1 0*1 1*0 0* 0
1 0 0 1*1 0*0 1
00 0 0
0
1 1 1 1*1 1*0 1* 0
1 1 0 1*1 1*0 1
cH c c c
c
0 1 2
0.707
c
DJM Nov 25, 2005
Trine States
33120
0 1 1
0 1 0 1 2
0 1 0
1
0 0 1
0 1 0 1
0 1 0
Tr
Tr c c T
Tr c c c c T
Tr c c T
0 1 2c 1 3 2c
0 1 4p 1 3 4p
T0
T1
T2
120°
120°
120°
DJM Nov 25, 2005
Quantum Noise Pauli Spin Matrices
Label Symbolic Matrix Description
Identity
Bit Flip
Phase Flip
Both Flips
1
1
0 1
1 0
3 1 1
0 0 0
2
2
0 1
1 0
i
i
1 * 1
0 1
1 0
3 * 3
1 0
0 1
0 * 0
1 01
0 1
2 * 2
0
0
i
i
DJM Nov 25, 2005
Quantum Measurement
0 1
1
2c c
C0
C1
0 10 1c c
1
0
Probability of state is pi = ci2 and p1 = 1- p0ic i
When
then 0 1
1
2p p
or 50/50 random!
Destructive and Probabilistic!!
Concepts of projection and singular operators
DJM Nov 25, 2005
Qubit ModelingQubit Operators: not, Hadamard, rotate & measure gates
Our library in Block Diagram tool by Hyperception
DJM Nov 25, 2005
Quantum Registers Entanglement
Tensor Product is mathematical operator Creates 2q orthogonal dimensions from q qubits: q0 q1 … Unitarity constraint for entire qureg
Separable states Can be created by tensor product Maintained by “coherence” and no noise.
Inseparable states Can’t be directly created by tensor product Concept of Ebit (pieces act as whole) EPR and Bell/Magic states (spooky action at distance) Non-locality/a-temporal quantum phenomena proven as valid
DJM Nov 25, 2005
Qureg Dimensions
0
10 0
0state
0
01 1
1state
1
10 0
0state
1
01 1
1state
1
00 00
0
0
state
0
11 01
0
0
state
0
02 10
1
0
state
0
03 11
0
1
state
= q0 q1
q0
q1
Special kind of linear transformations
DJM Nov 25, 2005
Unitary QuReg Operators
Gate Symbolic Matrix Circuit
Cnot = XOR
Control-not
Cnot2
swap=
cnot*cnot2*cnot
1 0 0 0
0 1 0 0
0 0 0 1
0 0 1 0
*swap
*cnot
2*cnot
1 0 0 0
0 0 0 1
0 0 1 0
0 1 0 0
1 0 0 0
0 0 1 0
0 1 0 0
0 0 0 1
00 01 10 11
x
x=
DJM Nov 25, 2005
Reversible ComputingABC
abc
ABC
abc
F T
2 gates back-to-back gives unity gate: T*T = 1 and F*F = 1
3 in & 3 out
DJM Nov 25, 2005
Reversible Quantum CircuitsGate Symbolic Matrix Circuit
Toffoli = control-control-not
Fredkin=control-swap
Deutsch
1
1
1
1
1
1
0 1
1 0
0
0
*D
*T
*F
1
000 001 010 011 100 101 110 111
1
1
1
1
1
0 1
1 0
1
0
0
1
1
1
1
1
1
cos sin
sin cos
0
0 i
i
23
123 x
x
23
1
D
DJM Nov 25, 2005
Ebits – Entangled Bits EPR (Einstein, Podolsky, Rosen) operator
Bell States
Magic States
0 0 1 0
2 0 3 0
00 11 , 00 11
01 10 , 01 10
B c B c
B c B c
0 0 1 1
2 1 3 0
00 11 , 00 11
01 10 , 01 10
M c M c
M c M c
0 1 2c
1 2c i
H
1B
0 0
0 0
0 0
0 0
0 0
0 0
0 0
0 0
c c
c c
c c
c c
DJM Nov 25, 2005
Step1: Two qubits
Step2: Entangle Ebit
Step3: Separate
Step4: Measure a qubit Other is same if Other is opposite if
EPR – Action at a distance
0 10 , 0
00 11
01 10
? , ?
1, 1
1, 0
answer other
answer other
Linked coins analogy
DJM Nov 25, 2005
Quantum Algorithms Speedup over classical algorithms
Complexity Class: Quantum Polynomial Time Reversible logic gates just mimics classical logic
Requires quantum computer with q>100 qubits Largest quantum computer to date has 7 qubits Problems with decoherence and scalability
Known Quantum Algorithms Shor’s Algorithm – prime factors using QFT Grover’s Algorithm – Search that scales as sqrt(N) No other algorithms found to date after much research
DJM Nov 25, 2005
Quantum Communication
Quantum Encryption Uses fact that measuring qubit destroys state Can be setup to detect intrusion
Quantum Key Distribution Uses quantum encryption to distribute fresh keys Can be setup to detect intrusion
Fastest growing quantum product area Many companies and products In enclosed fiber networks and also open air
DJM Nov 25, 2005
Quantum Mind?
Research with random phase ensembles Ensemble states survive random measurements See paper “Math over Mind and Matter”
Did biology to tap into Quantum Computing? Survival value using fast search We might be extinct if not for quantum mind
Relationship to quantum and consciousness? Movie: “What the Bleep do we know anyhow? Conferences and books
DJM Nov 25, 2005
Summary and Conclusions Quantum concepts extend classical ways of thinking
High dimensional spaces and simultaneity Distinguishability, mutual exclusion, co-occurrence and co-exclusion Reversible computing and unitary transforms Qubits superposition, phase states, probabilities & unitarity constraint Measurement and singular operators Entanglement, coherence and noise Ebits, EPR, Non-locality and Bell/Magic States Quantum speedup for algorithms Quantum ensembles have most properties of qubits
Quantum systems are ubiquitous Quantum computing may also be ubiquitous Biology may have tapped into quantum computing Quantum computing and consciousness may be related