English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Non-autonomous dynamical systems appear in a very wide range of interestingapplications, both in classical and quantum dynamics, where in the latter caseit corresponds to having a time-dependent Hamiltonian. However, the quantumsimulation of these systems often needs to appeal to rather complicatedprocedures involving the Dyson series, considerations of time-ordering,requirement of time steps to be discrete and/or requiring multiple measurementsand postselection. These procedures are generally much more complicated thanthe quantum simulation of time-independent Hamiltonians. Here we propose analternative formalism that turns any non-autonomous unitary dynamical systeminto an autonomous unitary system, i.e., quantum system with a time-independentHamiltonian, in one higher dimension, while keeping time continuous. This makesthe simulation with time-dependent Hamiltonians not much more difficult thanthat of time-independent Hamiltonians, and can also be framed in terms of ananalogue quantum system evolving continuously in time. We show how our newquantum protocol for time-dependent Hamiltonians can be performed in aresource-efficient way and without measurements, and can be made possible oneither continuous-variable, qubit or hybrid systems. Combined with a techniquecalled Schrodingerisation, this dilation technique can be applied to thequantum simulation of any linear ODEs and PDEs, and nonlinear ODEs and certainnonlinear PDEs, with time-dependent coefficients.

Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations