Quantum gates SALEEL AHAMMAD SALEEL

Introduction

Logic gate A logic gate is an idealized or physical device a Boolean function, that is, it performs a logical operation on one or more logic inputs and implementing produces a single logic output.

Quantum Gates a quantum gate (or quantum logic gate) is a basic quantum circuit operating on a small number of qubits. They are the building blocks of quantum circuits, like classical logic gates are for conventional digital circuits. quantum bit (qubit) is a unit of quantum information—the quantum analogue of the classical bit—with additional dimensions associated to the quantum properties of a physical atom.

Why Quantum gate Quantum Gates are similar to classical gates, but do not have a degenerate output. i.e. their original input state can be derived from their output state, uniquely. They must be reversible. This means that a deterministic computation can be performed on a quantum computer only if it is reversible. Luckily, it has been shown that any deterministic computation can be made reversible.

AND gate A B C In these 3 cases, information is being destroyed Due to the nature of quantum physics, the destruction of information in a gate will cause heat to be evolved which can destroy the superposition of qubits. Example.

Explanation

Quantum States For quantum computing we need only deal with finite quantum systems, and it suffices to consider only finite dimensional complex vector spaces with inner product. A quantum bit (qubit) is a unit vector in a one- dimensional complex vector space. We will use Bra/Ket (invented by Dirac) to represent these unit vectors. |0> = 1010 |1> = 0101

A physical implementation of a qubit could use the two energy levels of an atom. An excited state representing |1> and a ground state representing |0>. Excited State Ground State Nucleus Light pulse of frequency for time interval t Electron State |0>State |1> Qbit representation

Super position A single qubit can be forced into a superposition of the two states denoted by the addition of the state vectors: |  > =  |0> +  |1> Where  and  are complex numbers and |  | + |  | = A qubit in superposition is in both of the states |1> and |0 at the same time

Quantum Gates One-Input gate: Hadamard Maps    1/  2   + 1/  2   and    1/  2   – 1/  2  . Ignoring the normalization factor 1/  2, we can write  x   (-1)x  x  –  –  x  One-Input gate: Phase shift H 

Quantum Gates - Controlled NOT A gate which operates on two qubits is called a Controlled- NOT (CN) Gate. If the bit on the control line is 1, invert the bit on the target line. A - Target B - Control InputOutput Note: The CN gate has a similar behavior to the XOR gate with some extra information to make it reversible A’ B’

The CCN gate has been shown to be a universal reversible logic gate as it can be used as a NAND gate. A - Target B - Control 1 C - Control 2 InputOutput A’ B’ C’ When our target input is 1, our target output is a result of a NAND of B and C. Controlled Controlled NOT

New Frontiers Quantum Computer Quantum Mechanics Quantum Logic Quantum computers Quantum Programming

Nuclear spins 5-spin molecule synthesized Pathway to 7-9 qubits First demonstration of a fast 5-qubit algorithm

Quantum information is radically different to its classical counterpart. This is because the superposition principle allows for many possible states. Our inability to measure every property we might like leads to information security, but generalised measurements allow more possibilities than the more familiar von Neumann measurements. Summary

Entanglement is the quintessential quantum property. It allows us to teleport quantum information AND it underlies the speed-up of quantum algorithms Entanglement is the quintessential quantum property. It allows us to teleport quantum information AND it underlies the speed-up of quantum algorithms.. Quantum information technology will radically change all information processing and much else besides!