Lecture 14 - Implementation of Quantum Computing

Announcements:

Monday, 5/6/24 (week 5, lesson 1):

F office hours moved to Th. 11-12 this week!
Take mid-quarter survey to let me know how the class is doing and your ideas for improvement both for this quarter and for future iterations. Anonymous and voluntary!
Read Neutral atom quantum computing papers (3 options) – on Canvas
Read lecture slides on Implementation of quantum computing, pp. 1-12
Fill out presentation topic (choose your specific subtopic!) survey by W, 5/8/24

Last Time

We talked about having a universal set of gates to construct the others out of. We said that cNOT, H, and T are all universal.

We asked if cPHASE, H, and T can construct cNOT, and thus is universal. It turns out it is because we can construct a SWAP operation via:

S W A P = H T^{4} H

As you should verify. As such, then we get that:

c N O T = c P H A S E (0) S W A P_{b o t t o m}

Here the cNOT is equivalent to doing the above circuit. Namely:

(I \otimes H) c P H A S E (0) (I \otimes H) = c N O T

To build a quantum computer we need:

Scalable number of qubits (> $10^{6}$ )
Ability to initialize system
Ability to perform a universal set of quantum gates
1. Single qubit gates (at least three parameters)
2. two-qubit gates (one entangling gate)
Long coherence time
Ability to read out qubit state

![[Physics CPE 345 Quantum Computing Lecture slides Week 6 Implementation of quantum computing 240506.pdf#page=5]]

Some interesting notes:

NMR was cool because different frequencies of atoms in a molecule had different resonant frequencies. Sending in the resonnant frequency put the particle in superposition. However, this wasn't scalable and thus fell out of fashion.
Trapped ion, Neutral Atom, and NMR all use light for this information