In this lecture, I will cover theories of adaptation that do and do not explicitly account for phenotypes, in particular regarding distribution of fitness effects of mutations across genotypes and environment.
In the one-way model of measurement based quantum computing, unlike the quantum circuit model, a computation is driven not by unitary gates but by successive adaptive single-qubit measurements on an entangled resource state. So-called flow properties ensure that a one-way computation, described by a measurement pattern, is deterministic overall (up to Pauli corrections on output qubits). Translations between quantum circuits and measurement patterns have been used to show universality of the one-way model, verify measurement patterns, optimise quantum circuits, and more. Yet while it is straightforward to translate a circuit into a measurement pattern, the question of algorithmic "circuit extraction" -- how to translate general measurement patterns with flow to ancilla-free circuits -- had long remained open for all but the simplest type of flow.
In this talk, we will recap the one-way model of quantum computing and then explain how the problem of circuit extraction was resolved using the ZX-calculus as a common language for circuits and measurement patterns. We also discuss applications.
There are well established conjectures about the symmetries of SIC-POVMs, and the number fields needed to construct them. If the dimension is of the form n^2 + 3 there is also an algorithm that allows us to calculate them, making use of Stark units in a subfield of the full number field. The algorithm works in the 72 dimensions where it has been tested.
Joint work with (among others) Markus Grassl and Gary McConnell
The Heisenberg limit (HL) and the standard quantum limit (SQL) are two fundamental quantum metrological limits, which describe the scalings of estimation precision of an unknown parameter with respect to N, the number of one-parameter quantum channels applied. In the first part, we show the HL (1/N) is achievable using quantum error correction (QEC) strategies when the ``Hamiltonian-not-in-Kraus-span'' (HNKS) condition is satisfied; and when HNKS is violated, the SQL (1/N^1/2) is optimal and can be achieved with repeated measurements. In the second part, we identify modified metrological limits for estimating one-parameter qubit channels in settings of restricted controls where QEC cannot be performed. We prove unattainability of the HL and further show a ``rotation-generators-not-in-Kraus-span'' (RGNKS) condition that determines the achievability of the SQL.
