### Quantum Computing Keywords

We can start to focus in on qubit modalities by composing a working quantum computing vocabulary:

## What Are Qubits?

### The quantum equivalent of conventional digital bits are qubits (quantum bits).

• The qubits are in a state of superposition and operate on quantum mechanics principles.
• To alter the state of the qubits, we must use quantum mechanics concepts.
• We can measure the state of the qubits at the conclusion of the computation by projecting them into conventional digital bits.

## What Is A Universal Quantum Computer?

### A Quantum Turing Machine, also known as a Universal Quantum Computer, is an abstract machine that is used to simulate the effects of a quantum computer.

• Any quantum algorithm may be described formally as a particular quantum Turing Machine, similar to the conventional Turing Machine.

### Quantum states defined in Hilbert space are used to represent internal states.

• In Hilbert space, the transition function is a collection of unitary matrices.

## What Is Quantum Annealing?

### Quantum Fluctuations are used to discover a heuristic method that finds a global minimum from a limited collection of candidate solutions.

• Quantum Annealing may be used to tackle combinatorial optimization problems having a discrete search space with multiple local minima, such as the traveling salesman problem.
• The system begins with the quantum parallelism superposition of all possible states and evolves using the time-dependent Schrodinger equation.
• The amplitudes of all states may be altered by changing the transverse field (a magnetic field perpendicular to the axis of the qubit), resulting in Quantum Tunneling between them.

### The aim is to maintain the system as near to the Hamiltonian's ground state as possible.

• The system achieves its ground state when the transverse field is eventually switched off, which corresponds to the solution of the optimization issue.
• D-Wave Systems exhibited the first Quantum Annealer in 2011.

## What Is Quantum Speedup?

### This is the best-case situation, in which no classical algorithm can outperform a quantum algorithm.

• There are a few quantum algorithms that have a polynomial speedup in addition to factorization and discrete logarithms.
• Grover's algorithm is one such algorithm.

### There have been reports on simulation methods for physical processes in quantum chemistry and solid-state physics.

• The main ideal problem in polynomial time and an approximation method for Jones polynomial with a polynomial speedup and a solution to Pells' equation have been presented.
• This area is changing.

## What Is Quantum Edge?

### Quantum computers have a computational advantage.

• The idea that quantum computers can execute certain calculations more quickly than traditional computers.

## What Is Quantum Supremacy?

### Quantum computers' prospective capacity to tackle issues that conventional computers can't.

• Decoherence is the process by which the quantum information in a qubit is lost over time as a result of interactions with the environment.
• Quantum Volume is a practical method to track and compare progress toward lower system-wide gate error rates for quantum computing and error correction operations in the near future.
• It's a single-number metric that a concrete protocol can measure with a quantum computer of modest size n <=50 in the near future.

## What Is A Bloch Sphere?

### The Bloch sphere, named after scientist Felix Bloch, is a geometrical representation of the pure state space of a two-level quantum mechanical system (qubit) in quantum mechanics.

• Antipodal points correspond to a pair of mutually orthogonal state vectors on the Bloch sphere, which is a unit sphere.

### The Bloch Sphere's interpretation is as follows:

• The poles represent classical bits, and the notation |0 and |1 is used to denote them.
• Unlike conventional bit representation, where these are the only conceivable states, quantum bits span the whole sphere.
• As a result, quantum bits contain a lot more information, as shown by the Bloch sphere.
• When a qubit is measured, one of the two poles collapses.

Which of the two poles collapses depends on which direction the arrow in the Bloch representation points:

• if the arrow is closer to the north pole, there is a greater chance of collapsing to that pole; similarly,
• if the arrow is closer to the south pole, there is a greater chance of collapsing to that pole.

This adds the concept of probability to the Bloch sphere:

• the angle of the arrow with the vertical axes correlates to that probability.
• If the arrow points to the equator, each pole has a 50/50 probability of collapsing.

## What Is Coherence in Quantum Computing?

### A qubit's coherence is defined as its capacity to sustain superposition across time.

• It is therefore the lack of "decoherence," which is defined as any process that collapses a quantum state into a classical one, such as contact with the environment.

## What Is  DiVincenzo Criteria?

### The DiVincenzo criteria are a set of requirements for building a quantum computer that were originally suggested by theoretical physicist David P. DiVincenzo in his article "The Physical Implementation of Quantum Computation" in 2000.

The DiVincenzo criteria are a collection of 5+2 requirements that must be met by an experimental setup in order to effectively execute quantum algorithms like Grover's search algorithm or Shor factorization.

### To perform quantum communication, such as that utilized in quantum key distribution, the two additional requirements are required.

1 – A physically scalable system with well-defined qubits.

2 – The ability to set the qubits' states to a simple fiducial state.

3 – Long decoherence periods that are relevant.

4 – A set of quantum gates that is “universal.”

5 – A measuring capability unique to qubits.

6 — Interconversion of stationary and flying qubits.

7 – The capacity to reliably transfer flying qubits between two points.

## What Is Quantum Entanglement?

### Quantum entanglement is a unique relationship that exists between two qubits.

• Entanglement may be created in a variety of ways.
• One method is to entangle two qubits by bringing them close together, performing an operation on them, and then moving them apart again.
• You may move them arbitrarily far away from each other after they're entangled, and they'll stay intertwined.

### The results of measurements on these qubits will reflect this entanglement.

• When measured, these qubits will always provide a random result of zero or one, regardless of how far apart they are.

### The first characteristic of entanglement is that it cannot be shared, which allows all of the applications that are derived from it to be created.

• If two qubits are maximally entangled, no other person in the universe may share their entanglement.
• The monogamy of entanglement is the name given to this feature.

### Maximum coordination is the second characteristic of entanglement that gives it its strength.

• When the qubits are measured, this characteristic is shown.
• When two entangled qubits are measured in the same basis, no matter how far apart they are, the result is always the same.
• This result is not predetermined; rather, it is entirely random and determined at the time of measurement.

## What Is Measurement In Quantum Computing?

### The act of seeing a quantum state is known as measurement.

• This observation will provide traditional data, such as a bit.
• It's essential to remember that the quantum state will change as a result of this measurement procedure.

### If the state is in superposition, for example, this measurement will cause it to ‘collapse' into a classical state: zero or one.

• This process of collapsing occurs at random.
• There is no way of knowing what the result will be until the measurement is completed.
• However, the chance of each result may be calculated.

This probability is a prediction about the quantum state that we can test by preparing it many times, measuring it, and calculating the percentage of each result.

## What Are Quantum Dots?

### Quantum dots may be thought of as "manufactured atoms."

• They are semiconductor nanocrystals in which an electron-hole pair may be trapped.
• Because the nanoscale size is equivalent to the wavelength of light, the electron may occupy distinct energy levels, exactly as in an atom.
• The dots may be encased in a photonic crystal cavity and probed with laser light.

## What Is Quantum Error Correction?

### Quantum computers are always in touch with the outside world. This environment has the potential to disrupt the system's computational state, resulting in data loss.

• Quantum error correction compensates for this loss by distributing the system's computational state over multiple qubits in an entangled state.
• Outside classical observers may detect and correct perturbations using this entanglement without having to see the computational state directly, which would collapse it.

## What Is Quantum Indeterminacy?

### The basic condition of existence, backed up by all empirical evidence, in which an isolated quantum system, like as a free electron, does not have fixed characteristics until those attributes are seen in experiments intended to quantify them.

• That is, unless those characteristics are measured, a particle does not have a particular mass, location, velocity, or spin.
• Indeed, the particle does not exist until it is seen in a strict sense.

## What Is Quantum Tunneling?

### Due to the wave-like nature of particles, quantum tunneling is a quantum mechanical phenomenon in which particles have a limited chance of overcoming an energy barrier or transiting through an energy state usually prohibited by classical physics.

• A particle's probability wave reflects the likelihood of locating the particle in a certain place, and there is a limited chance that the particle is on the opposite side of the barrier.

## What Is Superposition?

### Quantum physics' basic premise is superposition.

• It asserts that quantum states, like waves in classical physics, may be joined together – superposed – to produce a new valid quantum state, and that every quantum state can be seen as a linear combination, a sum of other unique quantum states.

## What Is Teleportation In Quantum Computing?

### The following is how teleportation works:

• Initially, Alice and Bob must create an entangled pair of qubits between them.
• Alice next conducts a measurement on the qubit she wishes to transmit as well as the qubit that is entangled with Bob's qubit.
• This measurement compresses the qubits and breaks the entanglement, but it also provides her with two classical outcomes in the form of two classical bits.
• Alice transmits these two traditional bits to Bob over the traditional Internet.
• Bob next applies to his qubit a rectification operation that is based on these two classical bits.
• As a result, he is able to reclaim the qubit that was previously in Alice's control.

It's worth noting that we've now sent a qubit without really utilizing a physical carrier capable of doing so.

To accomplish this, you'll need entanglement, of course.

### It's also worth noting that quantum teleportation doesn't allow for communication faster than the speed of light.

• This is because Bob will not be able to make sense of the qubit she has in her hands until he receives the classical measurement results from Alice.
• The transmission of these traditional measurement results must take a certain length of time.
• This time is also constrained by the speed of light.

## What Is A Topological Quantum Computer?

### A topological quantum computer is a theoretical quantum computer that uses anyons, which are two-dimensional quasiparticles whose world lines intersect to create braided in a three-dimensional spacetime (i.e., one temporal plus two spatial dimensions).

• The logic gates that make up the computer are formed by these strands.
• The benefit of utilizing quantum braiding over trapped quantum particles in a quantum computer is that the former is considerably more stable.
• Small, cumulative perturbations may cause quantum states to decohere and create mistakes in computations, but they have no effect on the topological characteristics of the braiding.
• This is comparable to the work needed to cut a string and reconnect the ends to create a new braid, rather than a ball (representing an ordinary quantum particle in four-dimensional spacetime) colliding with a wall.

In 1997, Alexei Kitaev suggested topological quantum computing.

~ Jai Krishna Ponnappan