Universal Control of Quantum Processes Using Sector-Preserving Channels

Explore the concept of universal coherent control in quantum processes, focusing on sector-preserving channels and the limitations and possibilities they offer. Delve into the theoretical frameworks, experimental mismatches, and innovative protocols for implementing quantum control in various systems such as optical and ion-based setups.

• Quantum processes
• Sector-preserving channels
• Coherent control
• Quantum circuits
• Quantum architectures

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1. Universal control of quantum processes using sector-preserving channels Augustin Vanrietvelde R union de lancement du d fi QIP 19/11/202

2. Giulio Augustin Vanrietvelde Chiribella arXiv: 2106.12463

3. yet in fact it can be achieved but we have to use slightly different resources. Universal coherent control has been proven not to be possible

4. yet in fact it can be achieved but we have to use slightly different resources. Universal coherent control has been proven not to be possible Building on a number of references Formally explaining the mismatch between theory and experiments Relevant to: the creation of modular quantum architectures (realising a quantum if ) the study of indefinite causal order (e.g. the quantum switch) Using the ideas and notations of routed quantum circuits Giulio Chiribella and Hl r Kristj nsson. Quantum Shannon theory with superpositions of trajectories. PRSA: MPES, 475(2225):20180903, May 2019 / arXiv: 1812.05292

5. What is a coherently controlled channel? Can also be defined for noisy channels, with a bit more work

6. The no-go theorem There exists no such that Mateus Ara jo, Adrien Feix, Fabio Costa, and aslav Brukner, Quantum circuits cannot control unknown operations. NJP, 16(9):093026, Sep 2014 / arXiv: 1309.7976

7. The catch There are simple protocols that implement universal coherent controllisation But the resources they use are not exactly channels on S. With optical systems With ions Nicolai Friis, Vedran Dunjko, Wolfgang D r, and Hans J.Briegel. Implementing quantum control for unknown sub-routines. PRA, 89(3), Mar 2014 / arXiv: 1401.8128

8. Sector-preserving channels We take a Hilbert space that is sectorised (i.e. partitioned into sectors): And we consider the channels that preserve them: In particular, we ll look at the case in which has dimension 1 Giulio Chiribella and Hl r Kristj nsson. Quantum Shannon theory with superpositions of trajectories. PRSA: MPES, 475(2225):20180903, May 2019 / arXiv: 1812.05292

9. A mathematical equivalence Sector-preserving on a d+1 system Acting on a d- dimensional system Not only mathematically, but also as physical resources!

10. The yes-please-do-go theorem There exists such that Not only mathematically, but also as resources! ,

11. The control supermap

12. The inverse control supermap satisfies Controlled channels and sp channels of type (1,d) are equivalent as resources

13. The 2-control supermap

14. Outlook Universal coherent control on a d-dim system can be implemented, using sector- preserving channels on a (d+1)-system as resources Can be applied to the design of modular architectures (see also PBS-calculus) Routed supermaps could also be applied to the description of indefinite causal order

15. yet in fact it can be achieved but we have to use slightly different resources. Universal coherent control has been proven not to be possible