Quantum ComputingFrom Bits to Qubits

Wayne Viers and Josh Lamkins

What is Quantum Computing?

• Quantum computing is the field of research associated with building a quantum computer and creating algorithms to harness its power.

• Building a quantum computer

is not as simple as connecting

processors and memory like

a normal computer.

Types of Quantum Computers

1) Gate Model Quantum Computer•Based on a very familiar approach that traditional computers use.

•Gate model quantum computing creates quantum equivalents of digital logic gates – and puts these gates together to build a quantum computer.

2) Adiabatic Quantum Computer•Relatively robust against environmental interference.

•Allows scientists to leverage existing superconducting integrated circuit technology

•Built using macroscopic-sized qubits fabricated using semiconductor fabrication techniques.

Gate Model Quantum Computer

The Good News:•Crucial for improving our understanding of quantum computing

•Helps in pushing research forward.

The Bad News:•Very difficult to build and scale

•They are extremely susceptible to environmental factors

•Difficult to control and correct for errors

•Despite many years of research, there has been very slow progress made toward the development of anything near commercially useful

Adiabatic Quantum Computing

Adiabatic Quantum computers operate in extreme environments.

•Processor is placed in dilution refrigerator

•Cooled to 150x colder than interstellar space (0.02 Kelvin)

•Shielded to 50,000× less than Earth’s magnetic field

•Placed in a high vacuum: pressure is 10 billion times lower than atmospheric pressure

What is a Bit?• A bit is the basic unit of information in computing and digital

communications.

• Represented in a computer as an electrical signal.

• The most common representation of these values are 0 and 1.

What is a QuBit?• A unit of Quantum information

• Qubits are often made of subatomic particleso Photonso Coherent State of Lighto Electronso Nucleuso Optical Latticeso Josephson Junctiono Singularly Charged Quantum Dot

Pairo Quantum Dot

Representation of a QuBit

• For qubits implemented by electrons, the state is represented by the direction of spin

0 1

Quantum Superposition

• The fundamental principle of quantum mechanics

• A physical system - such as an electron - exists partly in all its particular theoretically possible states simultaneously

• When measured or observed, it gives a result corresponding to only one of the possible configurations

Quantum Parallel Processing• In classical computers, parallel computing is

performed by having several processors linked together, so that each processor performs one computation while the other processors are performing other computations.

• In a quantum computer, a single quantum processor is able to perform multiple computations on its own by utilizing the fact that the qubit (or quantum bit of information) exists in multiple states simultaneously. This gives a quantum computer much greater raw computation ability than a traditional computer (to).

Requirements for a Working QC

•• It must be possible to set all of the qubits to a simple initial state, such as all 0.

• The interactions between qubits must be controllable enough to make quantum logic gates.

• To perform operations using these gates, the decoherence times must be much longer than the gate-operation time (typically milliseconds to seconds).

• There must be some readout capability.

• To link up the computer's circuitry, it must be possible to convert memory qubits into processing qubits, and vice versa.

• It must be possible to move processing qubits accurately between specified locations.

It must be scalable: it needs a set of qubits that can be added to indefinitely.

Deterministic vs. Probabilistic

•Deterministic Algorithmo Given a particular input, a deterministic algorithm will always

produce the same output, with the underlying machine always passing through the same sequence of states

•Probabilistic Algorithmo Any algorithm that works for all practical purposes but has a

theoretical chance of being wrong

• Quantum computers are probabilistic because the final answer is a collapse of all of the quantum states

• One qubit can collapse to any single value from its supposition

Problems/Areas of Improvement

•Observer Effecto Qubits cannot be observed without destroying their state.

•Decoherenceo Decoherence occurs when a system interacts with its

environment in a thermodynamically irreversible way.o Must go to great lengths to create interference free

environment → control pressure, temperature, electromagnetic waves etc.

Decoherence

Uses for Quantum Computers

•Could provide quadratic speedup for searching an unordered database using Grover’s algorithm

•Shor’s algorithm o -O((log N)^3) time integer factorizationo Could be used to break public key

cryptography like RSA

Current Developments

•Quantum Gate Arrayso A series of linear transformations performed on qubits to

make an algorithmo Similar to the structure of a normal computer with logic gateso allows for the transfer of energy between qubitso External forces can easily disrupt these exchanges

Hadamard Gate

Current Developments

•One-way quantum computero A gate-model quantum computer using quantum

gateso Sets up initial entangled resource state pertaining

to problemo Applies logic gates then takes a measurement,

destroying the resource stateo Has a high amount of error, many trials required

Current Developments

•Adiabatic quantum computingo A series of qubits kept at a very low ground state

by cooling them to near zero degrees Kelvin.o A specific transverse field is applied to the qubits

that cause their values to fluctuate.o After the transverse field is switched off, the

solution is measured.o Used in D-Wave

Current Developments“a quantum adiabatic computer does a rapid global search. It starts

with the analogue of tipping water onto a flat landscape — a state in which the qubits are in a perfect quantum superposition of zeroes and ones — then lets the mountains rise slowly, so that the water naturally pools in the best solutions.”

Current Developments

•Topological Quantum Computero Theoretical quantum computer that employs two dimensional

quasiparticles called anyons whose trajectories in space time cross one another to form braids in three dimensional spacetime

o These braids form logic gateso The braids are much more stable than trapped quantum

particleso May be created using semiconductor plates at a temperature

near absolute zero and subjected to strong magnetic fields

Questions?