How Does a Quantum Computer Function?

[cosmicray]

i am not getting how a quantum computer will work.
what i know is that for input they will use a superposition having states with different amplitudes.Then hermitian or unitary operators will interct with the input superposition to give the output superposition. Then error coding will give an accurate output.

• physically, any interaction will destroy the superposition instantaneously. so how will the physical analog of hermitian or unitary operators will be formed.
• Can superposition be created ??
• where is entanglement supposed to be used here?

 

[jambaugh]

No interactions do not destroy superposition. Example, if you want to rotate a photon's polarization non-destructively pass it through a solution of dextrose. This is a unitary operation thus preserving superpositions of polarizations.

Hermitian operators correspond to measurements. These generally are the final steps in a quantum computation and they are the ones which "destroy" superposition but they also create superpositions as well.

Superposition is just the resolution of a single quantum mode in a different basis. For example a photon measured to be vertically polarized (vs horizontal) is in a superposition of being obliquely polarized at +45deg and -45deg. Likewise a photon polarized at +45deg will be in a superposition of vertical and horizontal polarizations. We can mix in other ways using complex phases so that we can also resolve say either cw circular polarization or ccw circular polarization as superposition of V and H polarization modes (and vis versa).

Thus you create a superposition with respect to one set of basis modes by making a measurement with respect to another set of basis modes. Superposition is not really a property of the quantum system but rather a relationship between different sets of compatible measurements. (compatible = mutually commuting within each of the sets but not between the different sets)

Before trying to understand entanglement in too much detail you should first get very clear on the basics of superposition, unitary evolution, and measurement associated with hermitian observables.

Entanglement involves sharply measuring/preparing an ensemble of a composite quantum system made up of many quantum subsystems in a way which is not compatible with certain individual measurements on anyone sub-system. For example you can determine (,measure,prepare) the total spin of a pair of electrons to be zero (singlet mode) which means each component of spin must be opposite = anti-correlated between the two. But in so doing you "erase" any information about what values any given component of spin will have for anyone of the electrons.

Superposition is part of what makes quantum computation able to improve on classical digital computers but as to how you must look on a case by case basis. Each quantum computation is in a sense custom built for the specific algorithm.

The ability to (theoretically) beat classical digital computers is no great mystery. For many algorithms (such as sorting http://en.wikipedia.org/wiki/Spaghetti_sort" ) there are analogue methods which in theory beat digital methods.

 

[Entropia]

I can understand your confusion about how a quantum computer works. It is a complex and constantly evolving technology, so it is natural to have questions and uncertainties. Let me try to explain some key concepts that will hopefully help clarify things for you.

Firstly, the idea of using superposition to represent input states is correct. In classical computers, information is represented as bits with a value of either 0 or 1. In quantum computers, information is represented as qubits, which can be in a superposition of 0 and 1. This means that a qubit can represent multiple values at the same time, allowing for more complex calculations to be performed.

Hermitian and unitary operators are mathematical operations that act on the input superposition to produce an output superposition. These operators are derived from the principles of quantum mechanics and are used to manipulate and manipulate qubits. They are not physical objects, but rather mathematical representations of how the qubits are being manipulated.

You are correct that any interaction with the qubits will destroy the superposition. This is why quantum computers must be kept in highly controlled and isolated environments to prevent any external interference. However, the hermitian and unitary operators used in quantum computers are carefully designed to minimize the impact of these interactions, allowing for accurate outputs to be obtained.

Entanglement is a key concept in quantum computing and is used to create highly correlated qubit states. This allows for information to be transferred between qubits without physically interacting with them, which is essential for performing complex calculations in a quantum computer.

To answer your question about whether superposition can be created - it cannot be created, but it can be manipulated and measured. Superposition is a fundamental property of quantum systems and cannot be artificially generated.

I hope this helps to clarify some of your questions about quantum computing. It is a fascinating and rapidly advancing field, and there is still much to learn and discover about how it works.