Citation: Reichardt, Ben, et al., "Demonstration of quantum computation and error correction with a tesseract code" (2024) arxiv: 2409.04628
Web: https://arxiv.org/abs/2409.04628
Tags: Hardware, Physical, Error-correcting-codes
This paper gives a fantastic demonstration of a new approach towards fault-tolerant quantum computation on quantinuum's processors.
This new approach is based on the tesseract code. The code is defined so that its qubits live on the vertices of a hypercube. There is a pair of stabilizers for every 3-cube in the tesseract; one consisting of all X and the other of all Z. Since these stabilizers touch the same qubits, we call this code "self-dual". The tesseract code is a [[16, 6, 4]] code. The stabilizers are all of weight 8. This code has been studied before in a rudimentary way in two papers so far, though the interpretation in terms of a tesseract is new and is due to Zhenghan:
> Delfosse, Nicolas, and Ben W. Reichardt. "Short shor-style syndrome sequences." arXiv preprint arXiv:2008.05051 (2020).
> Prabhu, Prithviraj, and Ben W. Reichardt. "Distance-four quantum codes with combined postselection and error correction." Physical Review A 110.1 (2024): 012419.
The most brilliant aspect of this paper is the idea that one should sacrifice two of the logical qubits. This turns the code into a [[16,4,4]] code whose stabilizers are weight 4 instead of weight 8! This code is much easier to implement, and has two dangling qubits which can be used as ancillas when computing, such as when implement the CNOT via two XX measurements. This idea of having dangling qubits which are used as gauge degrees of freedom is a well-known idea in the field, but this application of the idea is new:
> Bombín, Héctor. "Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes." New Journal of Physics 17.8 (2015): 083002.
> Bacon, Dave. "Operator quantum error-correcting subsystems for self-correcting quantum memories." Physical Review A—Atomic, Molecular, and Optical Physics 73.1 (2006): 012340.
The symmetries of the code lead to a lot of natural fault-tolerant gates. There are fault tolerant Pauli gates, as well as other types of gates. The authors conjecture that there is a natural way of implementing all Clifford gates via yet-to-be-defined gadgets, and they hope that there is a not-too-costly way of introducing non-Cliffords as well.
The outcome of the experiment is really breathtaking. The error rate drops significantly, with an improvement factor of 22 in the best performing experiment. These experiments not only apply to state preperation, but also to simple computations! The authors are able to create certain cluster states and apply logical CNOTs with huge gains over raw qubits.
Thus, this is the first ever experiment which demonstrates break-even performance for quantum memory and quantum computation! This result (which just came out a few days ago) paired with google's result (which came out two weeks ago) we seem to have very clear demonstration that error correction theory is working and we are below threshold!