Get ready for IonQ’s Trotterization challenge!#

Introduction#

This challenge explores a quantum circuit compresssion scheme enabling accurate quantum time dynamics (QTD) on noisy Near-Intermediate Scale Quantum (NISQ) era devices. Interestingly, the compression scheme is powered by the Yang-Baxter Equation (YBE), which plays an important role in many seemingly unrelated areas of modern mathematics and theoretical physics, including anyonic quantum computing, quantum groups, solvable lattice models, certain conformal field theories, and invariants of knots and \(3\)-manifolds, amongst others.

QTD is a key application of quantum computing. In fact, it largely explains why we started thinking about quantum computers in the first place:

“Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy.”

—Richard Feynman (1981)

Quantum computers can efficiently implement some of the time propagation operators arising in QTD simulations. But today we face a critical issue: the depth of the quantum circuits designed to simulate QTD increases with desired approximation accuracy. This is problematic in the current NISQ era because today’s hardware implements noisy quantum gates, and this constrains the depth of the circuits we can effectively execute on hardware. This motivates the need for a quantum circuit compression scheme!

Instructions#

Complete this challenge by reading through the following pages, answering the relevant exercises, and implementing the necessary functionality. Please respond to exercises by filling out the solution environment in the attached exercises.tex file. We have provided “starter code” in the src directory and your implementations will be graded automatically. Please do not alter any file or function names, or function contracts (method signatures and return values). We recommend that you progress through the challenge sequentially, since Stage \(n + 1\) typically depends on Stage \(n\). In addition, the challenge becomes progressively more difficult and we provide less detailed guidance as you advance through the various stages.

The required functionality is described in the source code documentation and accompanying explanations. Please implement it by replacing the relevant:

#####################
### Fill this in! ###
#####################

blocks as appropriate. Every method features a usage example that serves as a basic unit test. Be sure to use the accompanying XYZEvolutionTestSuite to test your code as you go! We provide various references throughout for further reading.

Challenge

Autograder

References#

[Abo22]

Willie Aboumrad. Quantum computing with anyons: an $F$-matrix and braid calculator. 2022. URL: https://arxiv.org/abs/2212.00831, doi:10.48550/ARXIV.2212.00831.

[MVL03]

Cleve Moler and Charles Van Loan. Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review, 45(1):3–49, 2003. doi:10.1137/s00361445024180.

[PGAG22]

Bo Peng, Sahil Gulania, Yuri Alexeev, and Niranjan Govind. Quantum time dynamics employing the Yang-Baxter equation for circuit compression. Physical Review A, 2022. doi:10.1103/physreva.106.012412.

Indices and tables#