Showing posts with label Quantum Speedup. Show all posts
Showing posts with label Quantum Speedup. Show all posts

Quantum Computing Keywords

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

Table Of Contents
What Are Qubits?
What Is A Universal Quantum Computer?
What Is Quantum Annealing?
What Is Quantum Speedup?
What Is Quantum Edge?
What Is Quantum Supremacy?
What Is A Bloch Sphere?
What Is Coherence in Quantum Computing?
What Is DiVincenzo Criteria?
What Is Quantum Entanglement?
What Is Measurement In Quantum Computing?
What Are Quantum Dots?
What Is Quantum Error Correction?
What Is Quantum Indeterminacy?
What Is Quantum Tunneling?
What Is Superposition?
What Is Teleportation In Quantum Computing?
What Is A Topological Quantum Computer?

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?

Quantum teleportation is a technique that uses entanglement to transmit qubits. 

  • 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

You may also want to read more about Quantum Computing here.

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