Understanding PWM modulation in Electric drives

 

Quantum computing

 Quantum computers function on the basis of Quantum mechanics, that describes the behavior of very small particles providing the basis for a new paradigm of computing. The Computer technology has developed so greatly over the many years, from a stage where the earlier computers were huge, expensive, to the stage especially today’s computers dramatically became smaller, cheaper, more efficient, and more powerful. It is the result of improvements in hardware, software, and architecture. Today’s palm size computers that fit in one’s pocket, have much computational power as the fastest supercomputers of 20 years ago. Let say the present classical super computer if it could solve a tough problem in 10000 years, the same problem is solved by the  quantum computer in milli seconds. This is the computing power capacity of quantum computers.

In a classical computer, we input the data from a key- board or other input devices and the signal is sent to the I/O port of the computer, which is then stored in the memory, then fed into the microprocessor, and the result is stored in the memory before it is printed or it is displayed on the screen. Thus information travels around the circuit.

In contrast in quantum computers, the information s stored in a register, external fields such as oscillating magnetic fields, electric fields or laser beams are applied to produce gate operations on the register. These external fields are designed so that they produce desired gate operation, i.e., unitary matrix acting on a particular set of qubits. Therefore the information sits in the register and they are updated each time the gate operation acts on the register.

The distinctions between classical computation and quantum computation is that the classical computer is based upon digital processing whereas quantum computer is based  on hybrid (digital + analogue) processing.

The main component of Quantum computers is qubits where as classical computer uses bits. A bit is a transistor that can only be on or off, or zero or one state. A qubit, or quantum bit, is the basic unit of information used to encode data in quantum computing. The types of qubits  that are used are superconducting qubits, trapped ions qubits, and photons. It is also a transistor  having the  states called quantum states  both zero and one simultaneously called superposition and the quantum states so called are called as  computational states  read as ket0: |0>  and ket 1 |1) can exit simultaneously, this property is called Superposition. The quantum computers use the principles of superposition, entanglement, and quantum interference.

The quantum computation is that the computer prepares the superposition of computational states and then a quantum circuit or called  a quantum gate which is prepared by the user uses these operations to generate entanglement, leading to an interface between the different states. All these operations are controlled by the special algorithm used in quantum computers. This is the working of quantum computer. Quantum entanglement is a phenomenon in which two qubits intertwine in such a way that the state of one particle cannot be described independently of the state of the other, regardless of the distance between them. Entangled qubits transfer information across even lightyears instantaneously, faster than the speed of light. The qubits transfer the data much faster than light  thus the quantum entanglement increase the power of quantum circuits. When two qubits are entangled, they both exist in a superposition until either is measured. Once observed, the quantum superposition of both is collapsed.

Quantum gates are the fundamental building blocks of quantum computation, playing a crucial role in manipulating and controlling the behavior of qubits, the basic units of quantum information. A quantum gate is a mathematical operation that transforms the state of one or more qubits, similar to how logic gates manipulate bits in classical computing. Quantum gates can be thought of as the “instructions” that are executed on a quantum computer.

The quantum gate is the single-qubit gate, multiple qubit gates . The single qubit gates operates on a single qubit and performs a specific operation, such as rotation or phase shift. Examples of single-qubit gates include the Hadamard gate (H), Pauli-X gate (X)  known as the bit-flip gate and Pauli-Y gate (Y) which rotates a qubit around the Y-axis . These gates are represented by 2×2 unitary matrices, which describe how the qubit’s state is transformed. The Hadamard gate is a fundamental single-qubit gate that creates a superposition of the two computational basis states. This gate can be represented by the matrix [1/√2 1/√2; 1/√2 -1/√2], where the rows and columns correspond to the computational basis states |0and |1.

The Multi-qubit gates operate on two or more qubits and perform operations that involve entanglement between the qubits. Examples of multi-qubit gates include the controlled-NOT gate (CNOT) and the Toffoli gate. These gates are represented by larger unitary matrices, which describe how the states of multiple qubits are transformed.

To manipulate and control qubits, various techniques such as quantum error correction codes, dynamical decoupling, and optimal control theory are employed. For instance, a Hadamard gate applies a 180-degree rotation around the x-axis, while a CNOT gate performs an entanglement operation between two qubits. These gates can be combined to form more complex quantum circuits that enable various quantum computations.

One logical qubit is encoded using seven physical qubits.

|0> = |0000000i>+ |1111000> + j1100110> + |1010101> + |0011110> + }0101101> + |0110011> + |1001011>

Smallest code that allows the logical gates is : H;CNOT;X; Z;Y ; S

This is the quantum logic gate or circuit used in teleportation problem

Popular quantum computing Algorithum and their solutions are Grover’s algorithum  , Shor’s algorithums