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We consider the problem of simulating dynamics of classical nonlinear dissipative systems with N>>1 degrees of freedom. To make the problem tractable for quantum computers, we add a weak Gaussian noise to the equation of motion and the initial state. Our main result is an end-to-end quantum algorithm for simulating the noisy dynamics of nonlinear systems satisfying certain sparsity and divergence-free conditions. For any constant nonzero noise rate, the quantum runtime scales polynomially with log(N), evolution time, inverse error tolerance, and the relative strength of nonlinearity and dissipation.

In this talk, I will explore the fascinating landscape of minimal assumptions in quantum cryptography—how little we need to assume to build secure quantum protocols. We will cover key cryptographic primitives including quantum encryption, signatures, and money, and show how these primitives imply the existence of one-way puzzles, a quantum analogue of classical one-way functions. I will also highlight the utility of one-way puzzles and discuss concrete assumptions that enable their realization, revealing intriguing connections with quantum advantage.

In distributed quantum information processing, the parties are often limited to performing local operations and classical communication (LOCC). The class of LOCC is notoriously difficult to analyze, and typically one considers the larger class of so-called separable (SEP) operations, which has a nicer mathematical structure. Finding separable but non-LOCC maps is a challenging endeavor, with most known examples involving the task of state discrimination. In this talk, I will describe an approach for constructing SEP but non-LOCC channels based on the resource theory of quantum coherence. This further highlights the value of studying general resource theories within quantum information theory. This is joint work with Ludovico Lami.

In this talk, I will discuss quantum diagonalization methods, based on subspaces obtained from quantum computers, which overcome the scaling limitations of variational algorithms and enabled realistic chemistry computations of up to 77 qubits on a quantum centric supercomputing architecture, using a Heron quantum processor and the RIKEN supercomputer Fugaku. Merging these ideas with Krylov quantum subspaces, I will present a ground state algorithm with convergence similar to phase estimation and robustness to noise, which led to an experimental demonstration for lattice ground state problems obtained with Heron processors and the supercomputer Frontier.