General Framework for Randomized Benchmarking Article Swipe
Jonas Helsen
,
Ingo Roth
,
Emilio Onorati
,
Albert H. Werner
,
Jens Eisert
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.17169/refubium-35573
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.17169/refubium-35573
Randomized benchmarking refers to a collection of protocols that in the past decade have become central methods for characterizing quantum gates. These protocols aim at efficiently estimating the quality of a set of quantum gates in a way that is resistant to state preparation and measurement errors. Over the years many versions have been developed, however a comprehensive theoretical treatment of randomized benchmarking has been missing. In this work, we develop a rigorous framework of randomized benchmarking general enough to encompass virtually all known protocols as well as novel, more flexible extensions. Overcoming previous limitations on error models and gate sets, this framework allows us, for the first time, to formulate realistic conditions under which we can rigorously guarantee that the output of any randomized benchmarking experiment is well described by a linear combination of matrix exponential decays. We complement this with a detailed analysis of the fitting problem associated with randomized benchmarking data. We introduce modern signal processing techniques to randomized benchmarking, prove analytical sample complexity bounds, and numerically evaluate performance and limitations. In order to reduce the resource demands of this fitting problem, we introduce novel, scalable postprocessing techniques to isolate exponential decays, significantly improving the practical feasibility of a large set of randomized benchmarking protocols. These postprocessing techniques overcome shortcomings in efficiency of several previously proposed methods such as character benchmarking and linear-cross entropy benchmarking. Finally, we discuss, in full generality, how and when randomized benchmarking decay rates can be used to infer quality measures like the average fidelity. On the technical side, our work substantially extends the recently developed Fourier-theoretic perspective on randomized benchmarking by making use of the perturbation theory of invariant subspaces, as well as ideas from signal processing.
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Metadata
- Type
- article
- Language
- en
- Landing Page
- https://refubium.fu-berlin.de/handle/fub188/35858
- OA Status
- green
- Cited By
- 8
- Related Works
- 20
- OpenAlex ID
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All OpenAlex metadata
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https://openalex.org/W3153692613Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.17169/refubium-35573Digital Object Identifier
- Title
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General Framework for Randomized BenchmarkingWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-01-01Full publication date if available
- Authors
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Jonas Helsen, Ingo Roth, Emilio Onorati, Albert H. Werner, Jens EisertList of authors in order
- Landing page
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https://refubium.fu-berlin.de/handle/fub188/35858Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
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https://refubium.fu-berlin.de/handle/fub188/35858Direct OA link when available
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Benchmarking, Computer science, Generality, Set (abstract data type), Scalability, Psychology, Psychotherapist, Database, Programming language, Marketing, BusinessTop concepts (fields/topics) attached by OpenAlex
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8Total citation count in OpenAlex
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2022: 7, 2021: 1Per-year citation counts (last 5 years)
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20Other works algorithmically related by OpenAlex
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| abstract_inverted_index.ideas | 281 |
| abstract_inverted_index.infer | 245 |
| abstract_inverted_index.known | 83 |
| abstract_inverted_index.large | 202 |
| abstract_inverted_index.order | 175 |
| abstract_inverted_index.prove | 163 |
| abstract_inverted_index.rates | 240 |
| abstract_inverted_index.sets, | 100 |
| abstract_inverted_index.side, | 255 |
| abstract_inverted_index.state | 42 |
| abstract_inverted_index.time, | 108 |
| abstract_inverted_index.under | 113 |
| abstract_inverted_index.which | 114 |
| abstract_inverted_index.work, | 68 |
| abstract_inverted_index.years | 49 |
| abstract_inverted_index.allows | 103 |
| abstract_inverted_index.become | 14 |
| abstract_inverted_index.decade | 12 |
| abstract_inverted_index.enough | 78 |
| abstract_inverted_index.gates. | 20 |
| abstract_inverted_index.linear | 132 |
| abstract_inverted_index.making | 269 |
| abstract_inverted_index.matrix | 135 |
| abstract_inverted_index.models | 97 |
| abstract_inverted_index.modern | 156 |
| abstract_inverted_index.novel, | 88, 187 |
| abstract_inverted_index.output | 121 |
| abstract_inverted_index.reduce | 177 |
| abstract_inverted_index.refers | 2 |
| abstract_inverted_index.sample | 165 |
| abstract_inverted_index.signal | 157, 283 |
| abstract_inverted_index.theory | 274 |
| abstract_inverted_index.average | 250 |
| abstract_inverted_index.bounds, | 167 |
| abstract_inverted_index.central | 15 |
| abstract_inverted_index.decays, | 194 |
| abstract_inverted_index.decays. | 137 |
| abstract_inverted_index.demands | 180 |
| abstract_inverted_index.develop | 70 |
| abstract_inverted_index.entropy | 226 |
| abstract_inverted_index.errors. | 46 |
| abstract_inverted_index.extends | 259 |
| abstract_inverted_index.fitting | 147, 183 |
| abstract_inverted_index.general | 77 |
| abstract_inverted_index.however | 55 |
| abstract_inverted_index.isolate | 192 |
| abstract_inverted_index.methods | 16, 219 |
| abstract_inverted_index.problem | 148 |
| abstract_inverted_index.quality | 28, 246 |
| abstract_inverted_index.quantum | 19, 33 |
| abstract_inverted_index.several | 216 |
| abstract_inverted_index.Finally, | 228 |
| abstract_inverted_index.analysis | 144 |
| abstract_inverted_index.detailed | 143 |
| abstract_inverted_index.discuss, | 230 |
| abstract_inverted_index.evaluate | 170 |
| abstract_inverted_index.flexible | 90 |
| abstract_inverted_index.measures | 247 |
| abstract_inverted_index.missing. | 65 |
| abstract_inverted_index.overcome | 211 |
| abstract_inverted_index.previous | 93 |
| abstract_inverted_index.problem, | 184 |
| abstract_inverted_index.proposed | 218 |
| abstract_inverted_index.recently | 261 |
| abstract_inverted_index.resource | 179 |
| abstract_inverted_index.rigorous | 72 |
| abstract_inverted_index.scalable | 188 |
| abstract_inverted_index.versions | 51 |
| abstract_inverted_index.character | 222 |
| abstract_inverted_index.described | 129 |
| abstract_inverted_index.developed | 262 |
| abstract_inverted_index.encompass | 80 |
| abstract_inverted_index.fidelity. | 251 |
| abstract_inverted_index.formulate | 110 |
| abstract_inverted_index.framework | 73, 102 |
| abstract_inverted_index.guarantee | 118 |
| abstract_inverted_index.improving | 196 |
| abstract_inverted_index.introduce | 155, 186 |
| abstract_inverted_index.invariant | 276 |
| abstract_inverted_index.practical | 198 |
| abstract_inverted_index.protocols | 7, 22, 84 |
| abstract_inverted_index.realistic | 111 |
| abstract_inverted_index.resistant | 40 |
| abstract_inverted_index.technical | 254 |
| abstract_inverted_index.treatment | 59 |
| abstract_inverted_index.virtually | 81 |
| abstract_inverted_index.Overcoming | 92 |
| abstract_inverted_index.Randomized | 0 |
| abstract_inverted_index.analytical | 164 |
| abstract_inverted_index.associated | 149 |
| abstract_inverted_index.collection | 5 |
| abstract_inverted_index.complement | 139 |
| abstract_inverted_index.complexity | 166 |
| abstract_inverted_index.conditions | 112 |
| abstract_inverted_index.developed, | 54 |
| abstract_inverted_index.efficiency | 214 |
| abstract_inverted_index.estimating | 26 |
| abstract_inverted_index.experiment | 126 |
| abstract_inverted_index.previously | 217 |
| abstract_inverted_index.processing | 158 |
| abstract_inverted_index.protocols. | 207 |
| abstract_inverted_index.randomized | 61, 75, 124, 151, 161, 205, 237, 266 |
| abstract_inverted_index.rigorously | 117 |
| abstract_inverted_index.subspaces, | 277 |
| abstract_inverted_index.techniques | 159, 190, 210 |
| abstract_inverted_index.combination | 133 |
| abstract_inverted_index.efficiently | 25 |
| abstract_inverted_index.exponential | 136, 193 |
| abstract_inverted_index.extensions. | 91 |
| abstract_inverted_index.feasibility | 199 |
| abstract_inverted_index.generality, | 233 |
| abstract_inverted_index.limitations | 94 |
| abstract_inverted_index.measurement | 45 |
| abstract_inverted_index.numerically | 169 |
| abstract_inverted_index.performance | 171 |
| abstract_inverted_index.perspective | 264 |
| abstract_inverted_index.preparation | 43 |
| abstract_inverted_index.processing. | 284 |
| abstract_inverted_index.theoretical | 58 |
| abstract_inverted_index.benchmarking | 1, 62, 76, 125, 152, 206, 223, 238, 267 |
| abstract_inverted_index.limitations. | 173 |
| abstract_inverted_index.linear-cross | 225 |
| abstract_inverted_index.perturbation | 273 |
| abstract_inverted_index.shortcomings | 212 |
| abstract_inverted_index.benchmarking, | 162 |
| abstract_inverted_index.benchmarking. | 227 |
| abstract_inverted_index.comprehensive | 57 |
| abstract_inverted_index.significantly | 195 |
| abstract_inverted_index.substantially | 258 |
| abstract_inverted_index.characterizing | 18 |
| abstract_inverted_index.postprocessing | 189, 209 |
| abstract_inverted_index.Fourier-theoretic | 263 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 5 |
| citation_normalized_percentile.value | 0.67425884 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |