The autoconjugacy of a generalized Collatz map

Many of the 2-adic properties of the 3x+1 map generalize to the analogous mx+r map, where m and r are odd integers. We introduce the corresponding autoconjugacy map, prove some simple properties of it and make some further conjectures in the general setting, including weak versions of the periodicity and divergent trajectories conjectures

Practical randomness amplification and privatisation with implementations on quantum computers

We present an end-to-end and practical randomness amplification and privatisation protocol based on Bell tests. This allows the building of device-independent random number generators which output (near-)perfectly unbiased and private numbers, even if using an uncharacterised quantum device potentially built by an adversary. Our generation rates are linear in the repetition rate of the quantum device and the classical randomness post-processing has quasi-linear complexity - making it efficient on a standard personal laptop. The statistical analysis is also tailored for real-world quantum devices. Our protocol is then showcased on several different quantum computers. Although not purposely built for the task, we show that quantum computers can run faithful Bell tests by adding minimal assumptions. In this semi-device-independent manner, our protocol generates (near-)perfectly unbiased and private random numbers on today's quantum computers.Comment: Important revisions and improvements to v1. inc. new sections, improvements to protocol itself and addition of full technical appendixes. 29+23 pages (15 figures and 2 tables

t|ket> : A retargetable compiler for NISQ devices

We present t|ket>, a quantum software development platform produced by Cambridge Quantum Computing Ltd. The heart of t|ket> is a language-agnostic optimising compiler designed to generate code for a variety of NISQ devices, which has several features designed to minimise the influence of device error. The compiler has been extensively benchmarked and outperforms most competitors in terms of circuit optimisation and qubit routing

Some more weak Hubert spaces

We construct, by a variation of the method used to construct the Tsirelson spaces, a new family of weak Hilbert spaces which contain copies of l₂ inside every subspace