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Quantum Computing
Group 8
Yasin Hussain | Michael Womack | Cori Beemish | Michael Swanson
What is a Quantum Computer?
● Defined as a computer based on a
computational model which uses quantum
mechanics.
● Which is a subfield of physics that studies
phenomena at the micro level.
Continued
● One method is to compute a probability first and then to interpret it to
describe the nature. The other method is to simulate a probability by using
probabilistic computers.
● When certain computation is performed in quantum computers, similar
computation is simultaneously performed in other world which is connected
with the actual world. The result is obtained by a probability if we try to see
the result of computation, and we can obtain the probability that the result
holds.
The basic unit of information in quantum computers is called a qubit. It is based
on superposition states in which both the states 0 and 1 are overlapped.
Current computers represent information by means of a bit which can have
only one value of 0 and 1. On the other hand, quantum computers use qubits
which can represent more information than in bits.
Qubits
● Classical computing: discrete states
● Simplest quantum system
o expressed as the superposition state consisting of two orthogonal states
● Can take on infinitely many states
o But can also extract single classical bit’s worth of information
● Linear combination of states called superposition state
Quantum Gates and Circuits
● A quantum state transformation that acts on only a small number of
qubits
● Applying sequence of unitary operators to quantum state gives us a
quantum circuit or quantum gate array
● Do not necessarily correspond to physical objects
o Physical: solid state and optical implementations
o NMR and Ion trap implementations, qubits are stationary
particles, gates are operations using magnetic fields or laser
pulses and operate on physical register of qubits
● Unlike classical circuits, quantum circuits “one-shot circuits”
● Single and Multiple qubit gates, Pauli Gates, Hadamard Gates
Quantum Algorithms
● Used to combine unitary operations in a quantum system to achieve
computation goal
● Many developed over past 25 years
● Shor’s Algorithm (1994)
o factorization of large numbers with complexity O((logN)3)
o extremely important for cryptography (makes RSA vulnerable)
o use quantum Fourier Transform (linear transformation on qubits)
 factoring, hidden subgroup problem, discrete logarithms, and order
finding
● Grover’s Algorithm
o Database search algorithm provides quadratic speedup
 linear search from O(N) to O(N1/2)
 speedy database query and statistical analysis, shortest path
Applications
The Quantum Tree: Application of technology
Q-Computing
Breaking codes
Q-Communication
Key-Distribution
Teleportation
Drug Design
Q-Sensors
Oil Exploration
Medicine
Quantum Key Distribution
Alice Wants to Communicate With Bob
1101001
Traditional Message Transmission
CLASSIC CHANNEL
1101001
“Tapping”
1101001
1101001
SOLUTION: QBITS!
FIBER OPTIC CHANNEL
1
0
1
0
RANDOM: HEISENBERG UNCERTAINTY
Channel Components
• Quantum Key distribution is divided into 2 parts:
• Quantum part (lets start here first)
• Classic part (we learned this in data comm!)
Bi-directional
Unidirectional
Quantum Part
• Alice and Bob agree on the polarization types (H/V and D/A)
• Alice randomly picks 0’s and 1’s and puts them into a polarization
machine “black box
0101011101001
Quantum Part
• Bob receives the polarization form of the bits and randomly chooses
a filter to guess the code.
• Regardless of the filter that Bob uses, he can only be wrong 50% of
the time
Quantum Part
• Bob receives the polarization form of the bits and randomly chooses
a filter to guess the code.
• Regardless of the filter that Bob uses, he can only be wrong 50% of
the time
Tapping With Q-bits
Any tampering with the Q-bit results in a state change, and will lead to an increase in errors
Alice’s polarization machine released a 45⁰ spin, but Eve’s tap changed the spin to 180⁰
Classic Part: Verification of Safe Transmission
• Bob compares his bitstring with Alice. If there are significantly more
than 50% errors, they can infer that the code has been compromised
Key Points: Quantum Key Distribution
• Unlike contemporary encoding, quantum key is dynamic
• The first steps in the process do not involve the actual message
• The new key isn’t used unless Bob’s bitstring is ~50% or more error
free
• In order to create the Key from Alice’s and Bob’s bitstrings, the
strings are compared and the correct guesses form the key
1110
1101001
Quantum Teleportation
Quantum Teleportation:
• Entanglement
• 3 explanations
• Instantaneous communication
• Q-bit DNA
• The universe is alive?
So We can teleport people?
• Not quite, but data… why not?
• if we could manipulate the Q-bit at Tx end to equal 0, there would be
an instantaneous complementary response at the Rx of 1!
CLASSIC CHANNEL
So We can teleport people?
• Not quite, but data… why not?
• If we could manipulate the Q-bit at Tx end to equal 0, there would be
an instantaneous complementary response at the Rx of 1!
1101001
0010110
So We can teleport people?
• Not quite, but data… why not?
• If we could manipulate the Q-bit at Tx end to equal 0, there would be
an instantaneous complementary response at the Rx of 1!
1101001
0010110
Quantum Programming
• If/when quantum computers are developed, we will still need an
approach to implement the algorithms so quantum computing can be
leveraged in practical applications.
• 2 forms of implementation:
• Hardware: will require quantum gates… Expensive!
• Software: will require a quantum programming language
• Quantum Computation Language (QCL)
• Will allow us to work with quantum events at an abtract level
• Simulation models
Future of Quantum Computing
● Nuclear Magnetic Resonance (NMR)
o Phenomena that happens when atomic nuclei are immersed in a static
magnetic field and exposed to a second oscillating magnetic field.
● Trapped Ion Quantum Computer
o A device capable of locking up charged particles with electromagnetic
fields in a very low temperature and in vacuum electromagnetic field.
● Quantum Dots
o The state of an electron locked up in a three-dimensional space,
which can be seen as tiny particles, or nanoparticles.
● Josephson Junction
o The phenomena of the flow of electric current between two pieces of
superconducting material separated by a thin layer of insulating
material.
DiVincenzo’s Five Criteria
1. A scalable physical system with well characterized qubits
2. The ability to initialize the state of the qubits to a simple fiducial state
3. Long relevant decoherence times, much longer than the gate operation
time
4. A “universal” set of quantum gates
5. A qubit-specific measurement capability
Additional Criteria for Quantum Communications
6. The ability to interconvert stationary and flying qubits
7. The ability faithfully to transmit flying qubits between specified locations
Problems of Quantum Computing
● Theoretical Problems
1. Artificial Intelligence and quantum computation
2. Computability of quantum computers
3. Quantum logic and quantum computation
● Practical Problems
1. General architecture of quantum computers
2. New quantum algorithms
3. Use of quantum programming languages
Works Cited
Akama, S. (2015). Elements of Quantum Computing: History, Theories and Engineering Applications.
Springer International Publishing
Mermin, N. D. (2007). Quantum Computer Science: An Introduction. Cambridge: Cambridge University
Press.
Perry, R. T. (2012). Quantum Computing from the Ground Up. Singapore: World Scientific.
Rieffel, E., & Polak, W. (2011). Quantum Computing: A Gentle Introduction. Cambridge, Mass.: The
MIT Press.