Preface – This post is part of the Quantum Computing series.

## Classical Mechanics

Classical mechanics is the branch of physics that deals with the motion of macroscopic objects, such as cars, planets, and baseballs. It is based on the principles of Newtonian mechanics, which were first formulated by Sir Isaac Newton in the 17th century.

## Quantum Mechanics

Quantum mechanics, on the other hand, is the branch of physics that deals with the behavior of subatomic particles, such as electrons and photons. It is based on the principles of quantum theory, which were first developed in the early 20th century.

## Difference between Classical mechanics and Quantum Mechanics

The main difference between classical mechanics and quantum mechanics is the scale at which they are applied. Classical mechanics is used to describe the motion of objects that are large enough to be seen with the naked eye, while quantum mechanics is used to describe the behavior of particles that are too small to be seen, even with a microscope.

Another key difference between the two is the way they describe the behavior of objects. Classical mechanics uses the language of calculus to describe the motion of objects, while quantum mechanics uses the language of wave-particle duality to describe the behavior of particles. This means that classical mechanics is deterministic, meaning that if you know the position and velocity of an object at a given time, you can predict its future motion with perfect accuracy. Quantum mechanics, on the other hand, is probabilistic, meaning that you can only predict the probability of an event occurring, rather than the exact outcome.

There are a few other important differences between classical mechanics and quantum mechanics.

One is that classical mechanics is based on the idea of realism, which means that objects have definite properties, such as position and velocity, that exist independently of whether they are being observed. Quantum mechanics, on the other hand, is based on the idea of uncertainty, which means that the properties of particles are only defined when they are being measured. This means that, according to quantum mechanics, the act of observation can affect the outcome of an experiment.

Another difference is that classical mechanics is a deterministic theory, which means that given the initial conditions of a system, the future evolution of that system can be predicted with perfect accuracy. Quantum mechanics, however, is a probabilistic theory, which means that the future evolution of a system can only be predicted in terms of probabilities.

Finally, classical mechanics is a classical theory, which means that it is based on the concept of continuous quantities, such as position and velocity. Quantum mechanics, on the other hand, is a quantum theory, which means that it is based on the concept of discrete quantities, such as quanta of energy. This means that, according to quantum mechanics, the smallest possible unit of a physical quantity, such as energy or angular momentum, is not a continuous value, but a discrete one.

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