John - Quantum Equations

Question 1

Main Problems with Classic Computing

Answer 1

• Moore’s Law
• Sequential Processing nature of Von Neumann Computing.

Question 2

What happens when we make transistors smaller

Answer 2

They behave differently, following quantum mechanics laws

Question 3

Sequential Processing

Answer 3

Simple and ubiquitous. Drawback is that instructions are processed sequentially regardless of number of cores/threads. Meaning NP hard problems remain intractable

Question 4

Limit of Classic Computing

Answer 4

Breaking into secure encryption, as RSA encryption uses 4096 bits which is intractable to compute.

Question 5

Examples of intractable problems

Answer 5

Weather simulation, Quantum mechanics modelling, scheduling, optimization and search.

Question 6

Quantum Computing

Answer 6

Computer that uses quantum mechanical phenomena like superposition and entanglement to perform operations on data.

Question 7

Quantum Computer equivalent of bits

Answer 7

quBits, not restricted to 2 states, but any number of states from 0 to 1. quBits can be in multiple states at once through superposition.

Question 8

Quantum Mechanics

Answer 8

Fundamental theory that describes the nature of atoms and subatomic particles.

Objects have characteristics of both particles and waves.

Question 9

Uncertainty Principle

Answer 9

Limits to the precision at which quantities can be measured in Quantum Mechanics.

Question 10

Electrons in atoms do not obey

Answer 10

Classical/Newtonian laws of motion

Question 11

We can make ____ predictions of the future only

Answer 11

probabilistic

Question 12

What do electrons behave like

Answer 12

Photons - not particles or waves

Question 13

Electrons

Answer 13

Dont orbit the nucleus, but are rather found in electron orbitals. This arises from the fact that electrons behave like both waves and particles.

Question 14

Wave functions

Answer 14

can predict where an electron may be at any point in time with a certain probability. This position is called the ‘orbital’

Question 15

Orbitals

Answer 15

can be thought of as probability clouds or probability density functions.

Question 16

Particle-Wave duality

Answer 16

The duality of behaviour acting like both particles and waves. Described probabilistically. An electron has a probability distribution/orbital where it might be found

Question 17

Heisenberg Uncertainty Principle

Answer 17

We cannot know both simultaneously position and speed of a particle

Question 18

The act of observations

Answer 18

Alters the system

Question 19

Quantum Superposition

Answer 19

Particles can be simultaneously in many states at the same time, when observed they collapse to a single state.

Question 20

Quantum Entanglement

Answer 20

Two matter or light particles are entangled, meaning their quantum states are aligned. Even if separated by a large distance, a change in quantum state of one will affect the other.

Question 21

Spin

Answer 21

Can be thought of as intrinsic angular momentum. Fundamental property of electron.

In a magnetic field, an electron can have either up or down state until measured.

Question 22

Example of Quantum Superposition

Answer 22

Schrodingers cat

Question 23

state of a quBit

Answer 23

can be represented as: a0|0⟩ + a1|1⟩ where |a0|2 + |a1|2 = 1, where the coefficients a0 and a1 are complex numbers that specify the probability amplitudes of the corresponding states.

Question 24

To represent the state of n quBits

Answer 24

one requires 2n complex number amplitudes.

Question 25

In a actual quantum computer, quBits can represent

Answer 25

atoms, ions, photons, or electrons and their respective control devices that are working together to act ascomputer memory and aprocessor.

Question 26

Classical Bits

Answer 26

State of n bits specified by a string x in {0,1}n

Question 27

Quantum Bits (quBits)

Answer 27

State is a superposition over 2n possibilities (a0, a1,…, a2n-1), where ai is complex.

Question 28

Problems and Challenges:

Answer 28

• Decoherence
• Cost
• Reliability
• Scaling
• Cooling

Question 29

Decoherence

Answer 29

As the number of quBits increases, the influence of the external environment perturbs the system. This causes states to change in an unpredictable way, rendering the computer useless.

Decoherence represents a challenge for practical realization of quantum computers since such machines are expected to rely heavily on the undisturbed evolution of quantum coherences.

Question 30

First Quantum Algorithm

Answer 30

St Peter algorithm

Question 31

Shor’s Algorithm

Answer 31

An important problem in computing is finding the prime factors of an integer. This is the base of RSA encryption. Using classical encryption the best time we can achieve is super-polynomial, around 2^sqrt(n).

Multiple runs can be performed to increase the probability that the answer is correct. This increases the complexity to n^3 x log(2)(n)

Question 32

Grover’s Algorithm

Answer 32

Algorithm for searching an unsorted database with N entries in O(N^1/2) time and using O(log2(n)) space.

Repetition can decrease the probability of failure.

Only provides a quadratic speedup unlike other quantum algorithms which can provide exponential speedup.

Question 33

Coherence times of a single quBit

Answer 33

• Coherence times of single quBit have increased exponentially to nearly a millisecond.
• Fidelity of state control has reached the level necessary for fault tolerance.
• Entanglement and schemes for quantum memory architectures have been implemented.
• Specialized software can simulate quBits.