QSC

Day 2 (Wednesday 3 April) @ 11:15–12:45

Jonas Helsen (CWI)

Shadow tomography in practice: repeating circuits and estimating means

In this talk, based on joint work with Michael Walter, I want to take a deeper dive into the Huang-Kueng-Preskill shadow tomography protocol. I will adress two problems: (1) whether it is statistically disadvantageous to repeat randomly sampled circuits, and (2) whether the median-of-means estimator can be replaced with a regular mean estimator without losing exponential concentration (which is required for the seemingly magical logarithmic sample complexity of shadow tomography). We will see that in both cases the answer depends strongly on the underlying gateset, even when that gateset is already a 3-design. In particular, in both cases the Clifford group performs poorly while fully Haar random gates perform well. We also consider efficiently constructible circuit families that interpolate between these two behaviours. On the technical side, we lean strongly on Weingarten calculus and its recently developed Clifford counterpart. We give upper and lower bounds for moments of stabilizer state estimators which might be of independent interest.

Sarah Arpin (Leiden University)

Isogeny paths to quantum-resistant cryptography

With the advent of quantum computers, the cryptographic landscape faces unprecedented challenges as traditional standards fall vulnerable to quantum attacks. Mathematicians and cryptographers are called to construct a cryptographic toolkit capable of withstanding both classical and quantum attacks. Isogeny-based cryptography emerged as a compelling newcomer to cryptography, entering the scene in 2006 with a hash function proposed by Charles-Goren-Lauter and cryptographic group actions proposed by Couveignes and Rostovtsev-Stolbunov. In this presentation, we will delve into supersingular elliptic curve isogeny graphs, shedding light on the unique properties that make them powerful objects for constructing versatile cryptographic protocols. 

Sebastian de Bone (TU Delft)

Fault-tolerant channels for distributed quantum computation

In the search for scalable, fault-tolerant quantum computing, distributed quantum computers are promising candidates. In distributed quantum computers, small quantum devices are connected with entanglement. Next to realizing these distributed structures with multiple nodes on a single chip, these systems can also be extended to large-scale quantum networks. Fault tolerance is naturally achieved by connecting the nodes according to the architecture of, e.g., a two-dimensional topological quantum error-correction code. An example of such an error-correction code is the (toric) surface code.

Carrying out the corresponding error-detection measurements over time can equivalently be interpreted as measuring out the qubits of a three-dimensional cluster state. This equivalence allows one to consider more general fault-tolerant channels. We use this idea to construct fault-tolerant channels for distributed architectures. For several channels, we investigate the resilience against a general type of circuit-level and network noise. For a more specific surface code channel, we perform detailed numerical simulations, employing models developed from experimental characterization of nitrogen-vacancy centers in diamond.

The results highlight the significance of lattice geometry in the design of distributed channels and emphasize the potential for constructing robust and scalable distributed quantum computers.

Joint work with Yves van Montfort, Paul Möller, and David Elkouss