Lecture 13 - Universal Set of Quantum Gates

Friday, 5/3/24 (week 5, lesson 3):

1. Read 5.4.9, 4.1-5 (incl. all subsections)
2. Read David DiVincenzo, “The Physical Implementation of Quantum Computation,” Fortschr. Phys. 48(9-11) (2000) – on Canvas
3. HW 4: 3.3, 5.10, 5.11, 5.12, 5.15, and “2-qubit systems and entanglement” problems on Canvas; due 5/10/24
4. WA 4: 2-qubit systems and entanglement, F, 5/10/24, beginning of class. Upload pdf to Canvas when work is complete. Closed book, equations provided.

Today we are going to primarily talk about how to use a lot of these quantum gates in terms of physical technology.

Some things we use to benchmark a Quantum Circuit are:

• Depth: Number of consecutive quantum gates in the circuit proportional to the time taken to execute the circuit.
• Width: Total number of qubits and classical bits.

We want to reduce each of these quantities as much as possible. Notice also that the depth depends not on how many gates you use, but the longest "gate" path that requires previous gate results to compute. We really want to allow parallel applications of gates where possible, and not using this as a limiting factor.

Quantum Circuits

It has been shown that with a basic set of quantum gates, a universal set of quantum gates, any quantum algorithm can be built. A universal set of gates needs to have one entangling gate as well as single-qubit gates.

There are an infinite number of universal sets of quantum gates. Here is just one example, the CNOT Gate.

We require that we need the Hadamard Gate to "even out" the probabilities, so that entanglement can happen.