Quantum Walk and Quantum Billiards. Towards a better understanding of Quantum Chaos
- URL: http://arxiv.org/abs/1903.05002v2
- Date: Thu, 19 Dec 2024 15:47:23 GMT
- Title: Quantum Walk and Quantum Billiards. Towards a better understanding of Quantum Chaos
- Authors: César Alonso-Lobo, Manuel Martínez-Quesada,
- Abstract summary: This study is based on the quantum billiard already obtained by others authors via a tensor product of two 1-D quantum walks.<n>Chaotic and non chaotic billiards are tested.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum billiards have been simulated so far in many ways, but in this work a new aproximation is considerated. This study is based on the quantum billiard already obtained by others authors via a tensor product of two 1-D quantum walks . Chaotic and non chaotic billiards are tested.
Related papers
- Quantum Checkers: The Development and Analysis of a Quantum Combinatorial Game [1.0225653612678713]
This paper develops and analyses a novel quantum game: quantum checkers (codenamed Cheqqers)<n>The concepts of superposition, entanglement, measurements and interference from quantum mechanics are integrated into the game of checkers by adding new types of legal moves.<n>We provide the initial analysis on the complexity of this game using random agents and a Monte Carlo tree search agent.
arXiv Detail & Related papers (2025-06-06T10:39:28Z) - Reinforcement learning for Quantum Tiq-Taq-Toe [0.0]
We study the combination of quantum computing and reinforcement learning in Quantum Tiq-Taq-Toe.
Quantum games are challenging to represent classically due to their inherent partial observability and the potential for exponential state complexity.
arXiv Detail & Related papers (2024-11-10T11:20:36Z) - Global Phase Helps in Quantum Search: Yet Another Look at the Welded Tree Problem [55.80819771134007]
In this paper, we give a short proof of the optimal linear hitting time for a welded tree problem by a discrete-time quantum walk.
The same technique can be applied to other 1-dimensional hierarchical graphs.
arXiv Detail & Related papers (2024-04-30T11:45:49Z) - Phase transition of a continuous-time quantum walk on the half line [0.0]
Quantum walks are referred to as quantum analogs to random walks in mathematics.
We study a continuous-time quantum walk on the half line and challenge to find a limit theorem for it in this paper.
arXiv Detail & Related papers (2024-03-20T13:21:29Z) - A vertical gate-defined double quantum dot in a strained germanium
double quantum well [48.7576911714538]
Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation.
We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well.
We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
arXiv Detail & Related papers (2023-05-23T13:42:36Z) - Simple Tests of Quantumness Also Certify Qubits [69.96668065491183]
A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical.
We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al., 2022) can in fact do much more.
Namely, the same protocols can be used for certifying a qubit, a building-block that stands at the heart of applications such as certifiable randomness and classical delegation of quantum computation.
arXiv Detail & Related papers (2023-03-02T14:18:17Z) - Hear $π$ from Quantum Galperin Billiards [0.0]
Galperin introduced an interesting method to learn the digits of $pi $ by counting the collisions of two billiard balls and a hard wall.
This paper studies two quantum versions of the Galperin billiards.
arXiv Detail & Related papers (2022-07-31T13:16:54Z) - Effects of Quantum Computing in Security [0.0]
We investigate quantum computing-based attacks and shed light on possible future developments.
The existence of quantum computers up to 65 qubits is known.
arXiv Detail & Related papers (2021-09-27T14:21:40Z) - Long-Time Error-Mitigating Simulation of Open Quantum Systems on Near Term Quantum Computers [38.860468003121404]
We study an open quantum system simulation on quantum hardware, which demonstrates robustness to hardware errors even with deep circuits containing up to two thousand entangling gates.
We simulate two systems of electrons coupled to an infinite thermal bath: 1) a system of dissipative free electrons in a driving electric field; and 2) the thermalization of two interacting electrons in a single orbital in a magnetic field -- the Hubbard atom.
Our results demonstrate that algorithms for simulating open quantum systems are able to far outperform similarly complex non-dissipative algorithms on noisy hardware.
arXiv Detail & Related papers (2021-08-02T21:36:37Z) - Depth-efficient proofs of quantumness [77.34726150561087]
A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover.
In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
arXiv Detail & Related papers (2021-07-05T17:45:41Z) - Quantum walk processes in quantum devices [55.41644538483948]
We study how to represent quantum walk on a graph as a quantum circuit.
Our approach paves way for the efficient implementation of quantum walks algorithms on quantum computers.
arXiv Detail & Related papers (2020-12-28T18:04:16Z) - How to Compute Using Quantum Walks [0.0]
Quantum walks are widely and successfully used to model diverse physical processes.
Quantum walks have also been shown to be universal for quantum computing.
This paper explains the relationship between quantum walks as models and quantum walks as computational tools.
arXiv Detail & Related papers (2020-04-03T01:51:03Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.