When to Differentiate State |0> From State |1>

In the lesson Quantum machine learning in the NISQ era, we mentioned that high precision quantum computers must work because quantum algorithms build on precise manipulations of continuously varying parameters. Therefore, even the noise caused by heat can ruin the computation.

This is problematic because the computers we can build thus far are essentially expensive electric heaters that perform a small amount of computation as a side effect.

Our computers operate in a way that depends on the intentional loss of some information.

The $and$ operator returns an output of 1 if both input values are 1. In all other cases, we get a 0. Given the output of 0, we have no way of knowing what the input was.

In the process of performing such an operator, the computer destructively overwrites its input. Then, it physically destroys the old information by pushing it out into the computer’s thermal environment. Thus, it becomes entropy that manifests as heat.

Quantum computers operate at shallow temperatures below 1 kelvin or -273°C. As a result, quantum computers must be very energy efficient, not because energy is a valuable resource, but because any loss of energy inevitably overheats the computer.

It’s possible to carry out computations without losing information and thus, without producing heat. This is known as reversible computation.

Enabling our $H$-operator to distinguish between the input states $|0\rangle$ and $|1\rangle$ ...