Halving the cost of quantum algorithms with randomization Article Swipe
John M. Martyn
,
Patrick Rall
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1038/s41534-025-01003-2
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1038/s41534-025-01003-2
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized compiling , a technique that promotes a unitary gate to a quantum channel and enables a quadratic suppression of error (i.e., ϵ → O ( ϵ 2 )) at little to no overhead. Here we integrate randomized compiling into QSP through Stochastic Quantum Signal Processing . Our algorithm implements a probabilistic mixture of polynomials, strategically chosen so that the average evolution converges to that of a target function, with an error quadratically smaller than that of an equivalent individual polynomial. Because nearly all QSP-based algorithms exhibit query complexities scaling as $$O(\log (1/\epsilon ))$$ —stemming from a result in functional analysis—this error suppression reduces their query complexity by a factor that asymptotically approaches 1/2. By the unifying capabilities of QSP, this reduction extends broadly to quantum algorithms, which we demonstrate on algorithms for real and imaginary time evolution, phase estimation, ground state preparation, and matrix inversion.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1038/s41534-025-01003-2
- https://www.nature.com/articles/s41534-025-01003-2.pdf
- OA Status
- gold
- Cited By
- 1
- References
- 53
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4408473044
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4408473044Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1038/s41534-025-01003-2Digital Object Identifier
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Halving the cost of quantum algorithms with randomizationWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2025Year of publication
- Publication date
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2025-03-15Full publication date if available
- Authors
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John M. Martyn, Patrick RallList of authors in order
- Landing page
-
https://doi.org/10.1038/s41534-025-01003-2Publisher landing page
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https://www.nature.com/articles/s41534-025-01003-2.pdfDirect link to full text PDF
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://www.nature.com/articles/s41534-025-01003-2.pdfDirect OA link when available
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Computer science, Randomization, Algorithm, Quantum computer, Quantum, Theoretical computer science, Quantum mechanics, Physics, Medicine, Clinical trial, PathologyTop concepts (fields/topics) attached by OpenAlex
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1Total citation count in OpenAlex
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2025: 1Per-year citation counts (last 5 years)
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53Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.overhead. | 64 |
| abstract_inverted_index.parallel, | 26 |
| abstract_inverted_index.quadratic | 48 |
| abstract_inverted_index.reduction | 174 |
| abstract_inverted_index.technique | 35 |
| abstract_inverted_index.<mml:mrow> | 127, 129, 131, 133, 135 |
| abstract_inverted_index.Processing | 76 |
| abstract_inverted_index.Stochastic | 73 |
| abstract_inverted_index.algorithms | 116, 184 |
| abstract_inverted_index.approaches | 165 |
| abstract_inverted_index.complexity | 159 |
| abstract_inverted_index.equivalent | 109 |
| abstract_inverted_index.evolution, | 190 |
| abstract_inverted_index.functional | 152 |
| abstract_inverted_index.implements | 80 |
| abstract_inverted_index.individual | 110 |
| abstract_inverted_index.inversion. | 198 |
| abstract_inverted_index.polynomial | 12 |
| abstract_inverted_index.processing | 3 |
| abstract_inverted_index.randomized | 31, 68 |
| abstract_inverted_index.systematic | 7 |
| abstract_inverted_index.(1/\epsilon | 123 |
| abstract_inverted_index.</mml:math> | 146 |
| abstract_inverted_index.</mml:mrow> | 139, 141, 142, 144, 145 |
| abstract_inverted_index.algorithms, | 179 |
| abstract_inverted_index.algorithms. | 24 |
| abstract_inverted_index.demonstrate | 182 |
| abstract_inverted_index.estimation, | 192 |
| abstract_inverted_index.polynomial. | 111 |
| abstract_inverted_index.suppression | 49, 155 |
| abstract_inverted_index.—stemming | 147 |
| abstract_inverted_index.capabilities | 170 |
| abstract_inverted_index.complexities | 119 |
| abstract_inverted_index.implementing | 10 |
| abstract_inverted_index.polynomials, | 85 |
| abstract_inverted_index.preparation, | 195 |
| abstract_inverted_index.probabilistic | 82 |
| abstract_inverted_index.quadratically | 103 |
| abstract_inverted_index.strategically | 86 |
| abstract_inverted_index.asymptotically | 164 |
| abstract_inverted_index.transformation | 13 |
| abstract_inverted_index.analysis—this | 153 |
| abstract_inverted_index.<mml:mi>O</mml:mi> | 128 |
| abstract_inverted_index.<mml:mn>1</mml:mn> | 136 |
| abstract_inverted_index.<mml:mo>(</mml:mo> | 130, 134 |
| abstract_inverted_index.<mml:mo>)</mml:mo> | 140, 143 |
| abstract_inverted_index.<mml:mo>/</mml:mo> | 137 |
| abstract_inverted_index.<mml:mi>ϵ</mml:mi> | 138 |
| abstract_inverted_index.<mml:mi>log</mml:mi> | 132 |
| abstract_inverted_index.xmlns:mml="http://www.w3.org/1998/Math/MathML"> | 126 |
| cited_by_percentile_year.max | 95 |
| cited_by_percentile_year.min | 91 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.93323746 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |