# On Quantum Complexity

@inproceedings{Alishahiha2022OnQC, title={On Quantum Complexity}, author={Mohsen Alishahiha}, year={2022} }

The ETH ansatz for matrix elements of a given operator in the energy eigenstate basis results in a notion of thermalization for a chaotic system. In this context for a certain quantity - to be found for a given model - one may impose a particular condition on its matrix elements in the energy eigenstate basis so that the corresponding quantity exhibit linear growth at late times. The condition is to do with a possible pole structure the corresponding matrix elements may have. Based on the…

## 3 Citations

### A universal approach to Krylov State and Operator complexities

- Computer Science
- 2022

A general framework in which both Krylov state and operator complexities can be put on the same footing is presented and it is shown that this framework also encompasses nicely the holographic notions of complexity.

### Tower: data structures in Quantum superposition

- Computer ScienceProc. ACM Program. Lang.
- 2022

This work presents Core Tower, the first language for quantum programming with random-access memory, and provides the first executable implementation of sets that satisfies all three mandated properties of reversibility, history independence, and bounded-time execution.

### Sectional curvatures distribution of complexity geometry

- MathematicsJournal of High Energy Physics
- 2022

In the geometric approach to defining complexity, operator complexity is defined as the distance in the operator space. In this paper, based on the analogy with the circuit complexity, the operator…

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