#No clone theorem how to

This post is part of the book: Hands-On Quantum Machine Learning With Python. When we want to use the unique characteristics of quantum computing, such as superposition, entanglement, and interference, we need to learn a new way of solving problems.

#No clone theorem how to

We need to unlearn how to solve a certain type of problem programmatically. It is a serious problem if we continue to think classically. We could measure the clones without collapsing the original qubit. But when we could clone a qubit, we could measure its state indirectly. Measuring a qubit collapses its state of superposition. In fact, the idea of cloning a qubit in an arbitrary state would contradict the underlying concept of superposition. In quantum computing, we simply canвЂ™t use the information stored in a qubit as many times as we want to. But in quantum computing, it is impossible. Even the simplest classical operation, the addition, relies on copying bits. In classical computing, we rely heavily on the ability to copy. Therefore, it is impossible to clone a qubit of an arbitrary state. The only logical conclusion is that G canвЂ™t exist. If the cloning transformation gate G exists, then two terms that are not equal must be equal. WouldnвЂ™t it be good, to create a copy of the qubit before we measure it? We would measure one copy of the qubit while continuing to work with the other copy. But, if you're not allowed to measure the qubit, how could you specify the prior probability? Measuring effectively destroys the qubit superposition. In order to calculate the correct angle, we need to consider the state the qubit is currently in.Д«ut measuring the qubit state collapses it to either 0 or 1. For the gradients of trigonometric functions (such as sine and arcsine) are not constant, the probability an angle represents that starts at the top of the circle (state |0вџ©) is another probability that the same angle represents that starts at the horizontal axis such as the state |+вџ©. But if the qubit is not in the basis state |0вџ© then the same value of Оё represents a different probability change. But we struggled with the problem that Оё is the angle between the vector |П€вџ© and the basis state vector |0вџ©. We got to know the angle Оё and it controls the probability of measuring the qubit as 0 or 1. In a previous post, we learned how to change the measurement probabilities of a qubit by rotating it around the y-axis. This would be particularly useful in quantum computing. We will receive the same output at both ends.ДЄnd, we can use the copies to evaluate the state at different parts of the program at different times. If there is a voltage at a certain time, we interpret it as 1. In electrical engineering, we have wires. In a classical circuit, this is the fan-out operation. In a classical program, we rely on this ability to copy data. The value of the variable doesnвЂ™t matter. We can use the assignment operator to create a copy of a variable.

my_var = 1 copy_of_my_var = my_var print (my_var, copy_of_my_var) LetвЂ™s take one of the simplest operators in classical computing, the assignment. Classical control structures are a dead-end. But this thinking will not let us succeed in quantum computing. And it requires a different kind of programs.Д¬lassically, we think about input, transformational boolean logic, and output. It is a fundamentally different way of computing. But quantum computing does not simply add new features we can use. When starting with quantum computing, weвЂ™re tempted to focus on the possibilities that arise from superposition and entanglement. It seems to know a measurement has taken place and it takes on a state that acknowledges the measured value.

Once you measure one qubit, its entangled fellow instantly jumps to a different state of superposition. Two qubits can share a state of superposition. But when you measure it, the quantum superposition collapses and the qubit is either 0 or 1, as a classical bit. Unless you measure it, the qubit is in a complex linear combination of 0 and 1. Unlike a classical bit, a quantum bit (qubit) is not 0 or 1. It starts with the quantum superposition.