One of the important tasks of a quantum compiler, as discussed in the previous module, is to identify operations in an abstract quantum algorithm which cannot be executed directly, and replace them with sequences of operations which are logically equivalent (having the same effect on the qubits’ states), and are composed of operations which can be executed ‘on-chip’. But how do we know how to make such transformations? In the first lecture, Ben Criger will go over the common mathematical techniques which allow us to express and manipulate quantum circuits.

Main takeaways

• Quantum gates act in a manner similar to classical logic gates. They have inputs and outputs, and can be composed together into more sophisticated circuits.
• Many methods exist for proving the equivalence of two circuits. If the circuits under consideration are small, all methods work. As the circuits become larger, more technical methods are used to reduce the amount of mathematics to something we can handle.