التفاصيل البيبلوغرافية
| العنوان: |
Approximating Output Probabilities of Shallow Quantum Circuits Which Are Geometrically-Local in Any Fixed Dimension |
| المؤلفون: |
Suchetan Dontha and Shi Jie Samuel Tan and Stephen Smith and Sangheon Choi and Matthew Coudron, Dontha, Suchetan, Tan, Shi Jie Samuel, Smith, Stephen, Choi, Sangheon, Coudron, Matthew |
| بيانات النشر: |
Schloss Dagstuhl – Leibniz-Zentrum für Informatik 2022 |
| نوع الوثيقة: |
Electronic Resource |
| مستخلص: |
We present a classical algorithm that, for any D-dimensional geometrically-local, quantum circuit C of polylogarithmic-depth, and any bit string x ∈ {0,1}ⁿ, can compute the quantity ||² to within any inverse-polynomial additive error in quasi-polynomial time, for any fixed dimension D. This is an extension of the result [Nolan J. Coble and Matthew Coudron, 2021], which originally proved this result for D = 3. To see why this is interesting, note that, while the D = 1 case of this result follows from a standard use of Matrix Product States, known for decades, the D = 2 case required novel and interesting techniques introduced in [Sergy Bravyi et al., 2020]. Extending to the case D = 3 was even more laborious, and required further new techniques introduced in [Nolan J. Coble and Matthew Coudron, 2021]. Our work here shows that, while handling each new dimension has historically required a new insight, and fixed algorithmic primitive, based on known techniques for D ≤ 3, we can now handle any fixed dimension D > 3. Our algorithm uses the Divide-and-Conquer framework of [Nolan J. Coble and Matthew Coudron, 2021] to approximate the desired quantity via several instantiations of the same problem type, each involving D-dimensional circuits on about half the number of qubits as the original. This division step is then applied recursively, until the width of the recursively decomposed circuits in the D^{th} dimension is so small that they can effectively be regarded as (D-1)-dimensional problems by absorbing the small width in the D^{th} dimension into the qudit structure at the cost of a moderate increase in runtime. The main technical challenge lies in ensuring that the more involved portions of the recursive circuit decomposition and error analysis from [Nolan J. Coble and Matthew Coudron, 2021] still hold in higher dimensions, which requires small modifications to the analysis in some places. Our work also includes some simplifications, corrections and clari |
| مصطلحات الفهرس: |
Low-Depth Quantum Circuits, Matrix Product States, Block-Encoding, InProceedings, Text, doc-type:ResearchArticle, publishedVersion |
| DOI: |
10.4230.LIPIcs.TQC.2022.9 |
| URL: |
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2022.9
Is Part Of LIPIcs, Volume 232, 17th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2022) |
| الإتاحة: |
Open access content. Open access content
https://creativecommons.org/licenses/by/4.0/legalcode |
| ملاحظة: |
application/pdf
English |
| أرقام أخرى: |
DEDAG oai:drops-oai.dagstuhl.de:16516
doi:10.4230/LIPIcs.TQC.2022.9
urn:nbn:de:0030-drops-165163
1358731272 |
| المصدر المساهم: |
SCHLOSS DAGSTUHL LEIBNIZ ZENTRUM GMBH
From OAIster®, provided by the OCLC Cooperative. |
| رقم الأكسشن: |
edsoai.on1358731272 |
| قاعدة البيانات: |
OAIster |
