Quantum Catalytic Space
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10515150" target="_blank" >RIV/00216208:11320/25:10515150 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.TQC.2025.11" target="_blank" >https://doi.org/10.4230/LIPIcs.TQC.2025.11</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.TQC.2025.11" target="_blank" >10.4230/LIPIcs.TQC.2025.11</a>
Alternative languages
Result language
angličtina
Original language name
Quantum Catalytic Space
Original language description
Space complexity is a key field of study in theoretical computer science. In the quantum setting there are clear motivations to understand the power of space-restricted computation, as qubits are an especially precious and limited resource. Recently, a new branch of space-bounded complexity called catalytic computing has shown that reusing space is a very powerful computational resource, especially for subroutines that incur little to no space overhead. While quantum catalysis in an information theoretic context, and the power of "dirty" qubits for quantum computation, has been studied over the years, these models are generally not suitable for use in quantum space-bounded algorithms, as they either rely on specific catalytic states or destroy the memory being borrowed. We define the notion of catalytic computing in the quantum setting and show a number of initial results about the model. First, we show that quantum catalytic logspace can always be computed quantumly in polynomial time; the classical analogue of this is the largest open question in catalytic computing. This also allows quantum catalytic space to be defined in an equivalent way with respect to circuits instead of Turing machines. We also prove that quantum catalytic logspace can simulate log-depth threshold circuits, a class which is known to contain (and believed to strictly contain) quantum logspace, thus showcasing the power of quantum catalytic space. Finally we show that both unitary quantum catalytic logspace and classical catalytic logspace can be simulated in the one-clean qubit model.
Czech name
—
Czech description
—
Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA24-10306S" target="_blank" >GA24-10306S: New challenges in streaming, online, and combinatorial algorithms</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Leibniz International Proceedings in Informatics, LIPIcs
ISBN
978-3-95977-392-8
ISSN
1868-8969
e-ISSN
1868-8969
Number of pages
24
Pages from-to
1-24
Publisher name
Schloss Dagstuhl, Leibniz-Zentrum für Informatik
Place of publication
Wadern
Event location
Bengaluru
Event date
Sep 15, 2025
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
—