Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2406.03972 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914613424029696 |
|---|---|
| author | Cunningham, Joseph Roland, Jérémie |
| author_facet | Cunningham, Joseph Roland, Jérémie |
| contents | We present a framework for quantum computation, similar to Adiabatic Quantum Computation (AQC), that is based on the quantum Zeno effect. By performing randomised dephasing operations at intervals determined by a Poisson process, we are able to track the eigenspace associated to a particular eigenvalue.
We derive a simple differential equation for the fidelity, leading to general theorems bounding the time complexity of a whole class of algorithms. We also use eigenstate filtering to optimise the scaling of the complexity in the error tolerance $ε$.
In many cases the bounds given by our general theorems are optimal, giving a time complexity of $O(1/Δ_m)$ with $Δ_m$ the minimum of the gap. This allows us to prove optimal results using very general features of problems, minimising the problem-specific insight necessary.
As two applications of our framework, we obtain optimal scaling for the Grover problem (i.e.\ $O(\sqrt{N})$ where $N$ is the database size) and the Quantum Linear System Problem (i.e.\ $O(κ\log(1/ε))$ where $κ$ is the condition number and $ε$ the error tolerance) by direct applications of our theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eigenpath traversal by Poisson-distributed phase randomisation Cunningham, Joseph Roland, Jérémie Quantum Physics Data Structures and Algorithms We present a framework for quantum computation, similar to Adiabatic Quantum Computation (AQC), that is based on the quantum Zeno effect. By performing randomised dephasing operations at intervals determined by a Poisson process, we are able to track the eigenspace associated to a particular eigenvalue. We derive a simple differential equation for the fidelity, leading to general theorems bounding the time complexity of a whole class of algorithms. We also use eigenstate filtering to optimise the scaling of the complexity in the error tolerance $ε$. In many cases the bounds given by our general theorems are optimal, giving a time complexity of $O(1/Δ_m)$ with $Δ_m$ the minimum of the gap. This allows us to prove optimal results using very general features of problems, minimising the problem-specific insight necessary. As two applications of our framework, we obtain optimal scaling for the Grover problem (i.e.\ $O(\sqrt{N})$ where $N$ is the database size) and the Quantum Linear System Problem (i.e.\ $O(κ\log(1/ε))$ where $κ$ is the condition number and $ε$ the error tolerance) by direct applications of our theorems. |
| title | Eigenpath traversal by Poisson-distributed phase randomisation |
| topic | Quantum Physics Data Structures and Algorithms |
| url | https://arxiv.org/abs/2406.03972 |