Thu, 05 Jun 2025
14:00
Lecture Room 3

Solving sparse linear systems using quantum computing algorithms

Leigh Lapworth
(Rolls-Royce)
Abstract

The currently available quantum computers fall into the NISQ (Noisy Intermediate Scale Quantum) regime. These enable variational algorithms with a relatively small number of free parameters. We are now entering the FTQC (Fault Tolerant Quantum Computer)  regime where gate fidelities are high enough that error-correction schemes are effective. The UK Quantum Missions include the target for a FTQC device that can perform a million operations by 2028, and a trillion operations by 2035.

 

This talk will present the outcomes from assessments of  two quantum linear equation solvers for FTQCs– the Harrow–Hassidim–Lloyd (HHL) and the Quantum Singular Value Transform (QSVT) algorithms. These have used sample matrices from a Computational Fluid Dynamics (CFD) testcase. The quantum solvers have also been embedded with an outer non-linear solver to judge their impact on convergence. The analysis uses circuit emulation and is used to judge the FTQC requirements to deliver quantum utility.

Tue, 11 Feb 2025
15:30
L4

Equivariant Floer theory for symplectic C*-manifolds

Alexander Ritter
(Oxford)
Abstract
The talk will be on recent progress in a series of joint papers with Filip Živanović, about a large class of non-compact symplectic manifolds, which includes semiprojective toric varieties, quiver varieties, and conical symplectic resolutions of singularities. These manifolds admit a Hamiltonian circle action which is part of a pseudo-holomorphic action of a complex torus. The symplectic form on these spaces is highly non-exact, yet we can make sense of Hamiltonian Floer cohomology for functions of the moment map of the circle action. We showed that Floer theory induces a filtration by ideals on quantum cohomology. I will explain recent progress on equivariant Floer cohomology for these spaces, in which case we obtain a filtration on equivariant quantum cohomology. If time permits, I will also mention a presentation of symplectic cohomology and quantum cohomology for semiprojective toric varities.
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