The joint QCDA seminar is a bi-weekly meeting of the QCDA groups where an internal or external speaker presents new results in quantum fault-tolerance or quantum information.

 

Joining the Meetings

The QCDA meeting is open to non-QCDA members. In order to join the QCDA meeting please send an email to Nikolas Breuckmann (n.breuckmann@ucl.ac.uk) to receive the Zoom invitations and links to the recorded talks.

 

Schedule

16th November 2020 (16:00 London time): Nicolas Delfosse

Title: Union-Find decoders for homological product codes

Abstract: Homological product codes are a class of codes that can have improved distance while retaining relatively low stabilizer weight. We show how to build union-find decoders for these codes, using a union-find decoder for one of the codes in the product and a brute force decoder for the other code. We apply this construction to the specific case of the product of a surface code with a small code such as a [[4, 2, 2]] code, which we call an augmented surface code. The distance of the augmented surface code is the product of the distance of the surface code with that of the small code, and the union-find decoder, with slight modifications, can decode errors up to half the distance. We present numerical simulations, showing that while the threshold of these augmented codes is lower than that of the surface code, the low noise performance is improved. Based on join work with Matt Hastings. https://arxiv.org/abs/2009.14226

 

30th November 2020 (16:00 London time): Chinmay Nirkhe

Title: Circuit lower bounds for low-energy states of quantum code Hamiltonians

Abstract: The No Low-energy Trivial States (NLTS) conjecture of Freedman and Hastings (Quantum Information and Computation, 2014) — which posits the existence of a local Hamiltonian with a super-constant circuit lower bound on the complexity of all low-energy states — identifies a fundamental obstacle to the resolution of the quantum PCP conjecture. In this work, we provide new techniques based on entropic and local indistinguishability arguments that prove circuit lower bounds for all the low-energy states of local Hamiltonians arising from quantum error-correcting codes. For local Hamiltonians arising from nearly linear-rate and polynomial-distance LDPC stabilizer codes, we prove super-constant circuit lower bounds for the complexity of all states of energy o(n) (which can be viewed as an almost linear NLTS theorem). Such codes are known to exist and are not necessarily locally-testable, a property previously suspected to be essential for the NLTS conjecture. Curiously, such codes can also be constructed on a two-dimensional lattice, showing that low-depth states cannot accurately approximate the ground-energy in physically relevant systems. https://arxiv.org/abs/2011.02044