# Decoherence

Of course, there is a catch or two to all of this glorious quantum future: perfect quantum computers are very hard to build.

Any tiny
imperfection in our ability to control or measure the qubits, or any
unintended interaction between the qubits and the outside environment,
damages the quantum state. This *decoherence* not only affects
whether our qubit is zero or one, it also affects the phase of the
qubit, and our ability to properly create the interference that is
vital to the operation of quantum algorithms.

## Control

The technology necessary to control and measure individual electrons, atoms, or photons must be precise and sensitive. Often, it must also be complex; signals that control a superconducting qubit might be carefully constructed pulses of microwave radiation, those that control individual atoms might be precisely timed pulses of laser light. For example, if the laser is left on a smidgen too long, the single-qubit rotation may go a little too far; instead of an intended rotation, you might get instead.

This results in a certain probability of an error if you measure the qubit right away, or worse, the error in one qubit can propagate to other qubits as you continue on with your algorithm.

## Isolation

Qubits must be properly isolated from the outside environment: given
that we use light, or microwaves, or magnetic fields to control
qubits, any stray signals can damage our state. The basic way to
isolate something from radio waves is to put it inside a *Faraday
cage*, a shell of conductive metal that absorbs the signal. Even with
our best effort, though, some radio waves can leak through, and
some quantum systems are so sensitive that interference caused by
electric trains running a kilometer away from the laboratory can be
detected!

Without proper isolation from the environment, it is also possible information leaks out of the system, causing our qubits to be measured inadvertently by the environment, or become entangled with the environment. In the worst case, this will destroy the superposition or entanglement of our qubits, leaving us with nothing but noisy, random classical data.

Different physical technologies for making the qubits require
different control technology and hence are susceptible to different
interference from the outside. Fundamentally, it’s a tradeoff: qubits
that are easy to control *intentionally* are also easily affected
*unintentionally*.

## Getting the Vocabulary Right: Pure and Mixed States

Getting the vocabulary right when dealing with errors will keep the confusion to a minimum. Physicists always mean something precise when they use a particular word, but these meanings do not always line up exactly with daily use.

We have talked already about *superposition* states and *entangled*
states. Until this discussion of decoherence, everything we have
talked about has assumed that the quantum computer works perfectly.
Without errors, all of the states we have presented are *pure* states.
A state that might have errors, on the other hand, is called a *mixed*
state. Note that it’s very tempting to call a superposition or an
entangled state “mixed”, but that’s incorrect use of the term.

Mixed states are described, in part, in terms of their *fidelity*.
The fidelity of a quantum state is the probability that the state we
have created is identical to the state we *think* we have created,
regardless of whether that state is a simple state such as
or a superposition such as .

The fidelity is a number between 0.0 and 1.0.
implies that our quantum computer works perfectly. For a single
qubit, means that the state has a probability of
being the state we expect, and a probability of being the
wrong state; its state is completely random. Such a state is referred
to as *completely mixed*.

For more than two qubits, is the probability that *all* of them
are behaving the way we expect, based on the algorithm we’ve run so
far. For two qubits, the completely mixed state is , for
three qubits, it’s , and so on.

We will talk more about decoherence and error correction later in the course.

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