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Quantum Computing
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Introduction to Computing
• Is currently done on your laptop today
• Numbers as we commonly use them
are in decimal (base 10) format.
Computers represent them in binary
(base 2).
• Each computational operation is done
one step at a time.
Decimal vs. Binary
103
1000
Decimal Representation
102
101
100
10
100
1
The number 14 1 in the 10’s and 4 in the 1’s
How do we represent this in another base?
Add up all the digits to get the same value.
23
8
Binary Representation
22
21
4
2
14 = 8+4+2 → 1110
20
1
BITS!
Addition Operation
Decimal: 5+4 = 9 Piece of cake in the way we think!
Binary:
Represent 5 as a binary number 0101
Represent 4 as a binary number 0100
Add on a column by column (right to left) basis
1 = 1+0
0 = 0+0
0 = 1+1 with carry
1 = 0+0 + carry
Final binary representation: 1001 (Decimal 9)
+ is one of a set of possible operations a computer can
do. Others are -, *, /. Typically only one operation is
done at a time. – Serial processing
How do we do this?
Shown is an Intel processor
capable of performing
1,000,000,000 (1 billion)
mathematical operations per
second!
It is composed of ~500,000,000
individual Transistors! (Transisitors
have no moving parts and are turned on and
off by electrical signals)
The typical size of a transistor in
the picture is about 0.04mm
0.4mm
How Far can this go?
Scale of transistors rapidly reaching quantum dimensions.
Moore’s Law
109
number of
transistors
108
107
106
105
year
104
1975
1980
1985
1990
1995
2000
2005
•When the integrated microprocessor circuit was first made at Texas Instruments,
Gordon Moore postulated that the number of transistors will doubles every 2 years.
• The blue line shows the prediction.
• The crosses show the actual numbers.
• When the number of transistors goes down, so does the overall dimensions
• Transistor size will approach quantum dimensions in ~6-10 years!
• We had better be ready to embrace a new approach.
Quantum Principles
• Quantum Uncertainty— states that
the position and velocity of a particle are
unknown until observed.
• SUPERPOSITION: there is an equal
probability that something is either in one state
(1) or another (0). Thus, something is in both
states, or between both states at the same
time until observed.
• Quantum Nonlocality—
Entanglement: When two particles share
the same quantum state they are entangled.
This means that two or more particles will
share the same properties: for example, their
spins are related. Even when removed from
each other, these particles will continue to
share the same properties.
Classical
vs.
Quantum
Physics
Classical Physics
Quantum Physics
•
•
Predictable outcomes!
Variables are continuous
•
•
•
•
•
•
Take on finite known values
Always has a known state
Binary numbers in the form of
switches that are on or off!
•
Violate classical laws at a small
scale (~h, Plank’s Constant)
Variables are discrete |0> or |1>
Can be in a superposition of
values (representing all states
simultaneously)
State is intdeterminate until
measured.
Bloch sphere shows all
possible states Superposition
Quantum Binary Systems
Can we represent a binary system (bits) in
quantum rather than classical states?
Why not find a quantum mechanical system where we
can use two ‘states’ to represent our binary numbers?
Qubits can be carried as atoms, ions, photons or
electrons and their respective control devices that are
working together to act as computer memory and a
processor.
Entangled qubits allow multiple numbers to be
represented simultaneously. |000>
Qubit
Quantum bit
Bit VS Qubit
• Classical Bit
• 0 or 1
• 101
Qubit
0 or 1
or 1 and 0
000 001 010
011 100 101
110 111
How Quantum Computers Work
Quantum Computers
Today’s Computers
•
•
•
Turing Machine- theoretical device that
consists of tape of unlimited length that is
divided into little squares. Each square
can either hold a symbol (1 or 0) or be left
blank.
Today's computers work by manipulating
bits that exist in one of two states: a 0 or
a 1.
1 and 0’s are carried and turned on by
states of electrical current
•
Quantum computers aren't limited to two states
like today’s computers. They encode information
as quantum bits, or qubits, which can exist in
superposition.
•
Superposition- quantum computers can
represent both 0 and 1 as well as everything in
between at the same time.
•
Qubits can be carried as atoms, ions, photons
or electrons and their respective control devices
that are working together to act as computer
memory and a processor.
•
Basically, a quantum computer can work on
a million computations at once, while your
desktop PC works on one.
Superposition Numbers
Ψ= 1/√2(|> + |>) can be written as
Ψ= 1/√2(|0> + |1>) This can be expanded
|00> + |01> + |10> + |11>
Look! I just wrote down a binary representation
where the numbers 0, 1, 2, and 3 are
simultaneously represented. This is huge by
comparison to a classical computer.
Physical Realization Quantum
Dot
Quantum Dot (Single Electron Transistor SET)
Use the Electron spin |>, |>
1
|>
A one is spin down 0
|>
A zero is spin up
Manipulate the spin using electric and magnetic fields
•Currently used effectively by Charlie Marcus at Harvard
University.
•Current state of the art, 2 transistors talking to each other
Quantum Dot Now and Later
• Easy to make and operate
• Small in size : we are dealing with ions,
atoms, electrons and photons
• The system falls apart rapidly. That means
that the initial 0 or 1 in the system goes away.
This phenomena is called decoherence and
happens in about 1 microsecond.
• Compare to classical computation where the
transistors can retain their state for years.(for
example, how many of you have USB
memory sticks?)
Physical Realization Trapped Ions
Experiment
Trapped Ion use electron system states:
A binary zero is the lowest level or ground state
A one is a chosen higher level
Manipulate the state using lasers tuned to the
‘transistion’ frequency in Strontium (408nm in the
figure above)
The NIST trapped Ion Storage Group currently holds
the record of 7 qubits
Trapped Ions Now and Later
• Difficult make and operate
• Huge in scale, a full laboratory to make
7 systems
• The system is very stable (many
seconds) but takes a very long time to
impress a 0 or 1 on the system.
• The size and speed make it difficult to
imagine a system like your laptop
Today’s Quantum Computer:
The 16-qubit quantum computer
 2007- Canadian startup company D-Wave demonstrated
a 16-qubit quantum computer (
adiabatic
computer), which solved a sudoku puzzle and other
pattern matching problems.
 The company claims it will produce practical systems by
2008 but skeptics believe practical quantum computers are
still decades away.
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The Future of Quantum Computers
Functional quantum computers will be valuable in
factoring large numbers and be very useful for decoding
and encoding secret information. No information on the
internet would be secure.
Quantum computers could also be used to search large
databases in a fraction of the time that it would take a
conventional computer.
 Other applications could include using quantum
computers to study quantum mechanics, or even to
design other quantum computers.
Photo courtesy © 2007
D-Wave Systems, Inc.
D-Wave's 16-qubit
quantum computer
The University of Rochester
&
Research in Quantum Computing
The U of R works with Cornell, Stanford, Harvard, and Rutgers in a
collaborative effort for The Center for Quantum Information.
Of the nine professors involved, five come from UR:
Carlos R. Stroud, Jr.
Ian A. Walmsley
Joseph H. Eberly
Carlos R. Stroud
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Nicholas P. Bigelow
 At UR, there have been 36 peer-reviewed papers published, 13
manuscripts and 68 presentations given.
Interesting Algorithm
Factoring Prime Numbers
• Prime numbers used in current day
cryptography
• Peter Shor discovered quantum
factoring algorithm
• Quantum time to factor
Olog N  
• Classical time to factor
3
 logN 13 
O2




Peter Shor
Polynomial vs. Exponential time to calculate.

Exponential Speedup using quantum computer!
- Where a classical computer would take 5
trillion years to factor a 5,000 digit number, a
quantum computer could finish in 2 minutes.
- Quantum computation is more powerful than
classical computation because more can be
computed in less time!!
Summary
• Classical computers reaching quantum
scale - need alternative to transistor
technology
• Quantum physics allows interesting but
difficult alternative to computation