APS March Meeting 2024
Monday–Friday, March 4–8, 2024;
Minneapolis & Virtual
Session K61: Teaching Quantum Information at All Levels I
3:00 PM–4:48 PM,
Tuesday, March 5, 2024
Room: 208AB
Sponsoring
Units:
FED DQI
Chair: Daniel Claes, University of Nebraska - Lincoln
Abstract: K61.00004 : The Quantum Abacus: A Break-Even Point
4:00 PM–4:12 PM
Abstract
Presenter:
Dan-Adrian German
(Indiana University Bloomington)
Author:
Dan-Adrian German
(Indiana University Bloomington)
In 2017 Terry Rudolph proposed a method of teaching quantum mechanics and quantum computing using only the simple rules of arithmetic to students as early as sixth grade. The method is incredibly effective and in a series of papers we showed how we use it to introduce superposition, phase, interference and entanglement with virtually no mathematical overhead. Furthermore we showed that a complete eight week introductory course (for computer science sophomores) has been built around this approach with the following milestones: quantum gates and circuits, phase kickback, the Deutsch-Josza algorithm, Bernstein-Vazirani and the extended Church-Turing thesis, the GHZ game and quantum teleportation. There is general consensus that the actual mathematics behind quantum computation is an inevitable and desirable destination for our students. But for those students that lack an adequate mathematical background (HS and younger students) one can reliably use Terry's method (i.e., computing with misty states, also referred to as The Quantum Abacus) to communicate a visual and entirely operational understanding of key quantum computing concepts without resorting to complex numbers or matrix multiplication. Here we present concrete evidence that the approach can create a genuine bridge to the actual mathematics behind quantum computation. We start with superdense coding and Grover's algorithm (to illustrate how effective the system is) then we identify an elementary break-even point when creating a W entangled state. Terry's Abacus is based on a paper by Shih that Toffoli plus Hadamard gates are universal. When trying to create the W entangled state we need to accommodate rotations and we must use controlled-Hadamard gates. And this is what allows for a break-even point: a Hadamard gate controlled by the output of another Hadamard gate breaks the ubiquitous symmetry in Terry's system, and from then on one has to carry around (i.e., specify) the actual probability amplitudes in misty states.This means that students can proceed to developing, in parallel, with (extended) misty states and Dirac notation. And after crossing that bridge we have an entirely conventional Quantum Computation course, but the intuition we acquired while computing with misty states remains with us.