Thrifty shadow estimation: re-using quantum circuits and bounding tails Article Swipe
Jonas Helsen
,
Michael Walter
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.06240
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.06240
Shadow estimation is a recent protocol that allows estimating exponentially many expectation values of a quantum state from ``classical shadows'', obtained by applying random quantum circuits and computational basis measurements. In this paper we study the statistical efficiency of this approach in light of near-term quantum computing. We propose a more practical variant of the protocol, thrifty shadow estimation, in which quantum circuits are reused many times instead of having to be freshly generated for each measurement. We show that reuse is maximally effective when sampling Haar random unitaries, and maximally ineffective when sampling from the Clifford group, i.e., one should not reuse circuits when performing shadow estimation with the Clifford group. We provide an efficiently simulable family of quantum circuits that interpolates between these extremes, which we believe should be used instead of the Clifford group. Finally, we consider tail bounds for shadow estimation and discuss when median-of-means estimation can be replaced with standard mean estimation.
Related Topics
Concepts
Shadow (psychology)
Computer science
Bounding overwatch
Quantum
Quantum circuit
Electronic circuit
Algorithm
Theoretical computer science
Mathematics
Applied mathematics
Quantum computer
Mathematical optimization
Quantum error correction
Artificial intelligence
Quantum mechanics
Physics
Psychology
Psychotherapist
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2212.06240
- https://arxiv.org/pdf/2212.06240
- OA Status
- green
- Cited By
- 3
- References
- 21
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4311553408
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4311553408Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2212.06240Digital Object Identifier
- Title
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Thrifty shadow estimation: re-using quantum circuits and bounding tailsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2022Year of publication
- Publication date
-
2022-12-12Full publication date if available
- Authors
-
Jonas Helsen, Michael WalterList of authors in order
- Landing page
-
https://arxiv.org/abs/2212.06240Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2212.06240Direct link to full text PDF
- 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://arxiv.org/pdf/2212.06240Direct OA link when available
- Concepts
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Shadow (psychology), Computer science, Bounding overwatch, Quantum, Quantum circuit, Electronic circuit, Algorithm, Theoretical computer science, Mathematics, Applied mathematics, Quantum computer, Mathematical optimization, Quantum error correction, Artificial intelligence, Quantum mechanics, Physics, Psychology, PsychotherapistTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
3Total citation count in OpenAlex
- Citations by year (recent)
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2024: 1, 2023: 1, 2022: 1Per-year citation counts (last 5 years)
- References (count)
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21Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.that | 6, 79, 121 |
| abstract_inverted_index.this | 31, 39 |
| abstract_inverted_index.used | 131 |
| abstract_inverted_index.when | 84, 92, 104, 147 |
| abstract_inverted_index.with | 108, 153 |
| abstract_inverted_index.basis | 28 |
| abstract_inverted_index.i.e., | 98 |
| abstract_inverted_index.light | 42 |
| abstract_inverted_index.paper | 32 |
| abstract_inverted_index.reuse | 80, 102 |
| abstract_inverted_index.state | 16 |
| abstract_inverted_index.study | 34 |
| abstract_inverted_index.these | 124 |
| abstract_inverted_index.times | 66 |
| abstract_inverted_index.which | 60, 126 |
| abstract_inverted_index.Shadow | 0 |
| abstract_inverted_index.allows | 7 |
| abstract_inverted_index.bounds | 141 |
| abstract_inverted_index.family | 117 |
| abstract_inverted_index.group, | 97 |
| abstract_inverted_index.group. | 111, 136 |
| abstract_inverted_index.having | 69 |
| abstract_inverted_index.random | 23, 87 |
| abstract_inverted_index.recent | 4 |
| abstract_inverted_index.reused | 64 |
| abstract_inverted_index.shadow | 57, 106, 143 |
| abstract_inverted_index.should | 100, 129 |
| abstract_inverted_index.values | 12 |
| abstract_inverted_index.believe | 128 |
| abstract_inverted_index.between | 123 |
| abstract_inverted_index.discuss | 146 |
| abstract_inverted_index.freshly | 72 |
| abstract_inverted_index.instead | 67, 132 |
| abstract_inverted_index.propose | 48 |
| abstract_inverted_index.provide | 113 |
| abstract_inverted_index.quantum | 15, 24, 45, 61, 119 |
| abstract_inverted_index.thrifty | 56 |
| abstract_inverted_index.variant | 52 |
| abstract_inverted_index.Clifford | 96, 110, 135 |
| abstract_inverted_index.Finally, | 137 |
| abstract_inverted_index.applying | 22 |
| abstract_inverted_index.approach | 40 |
| abstract_inverted_index.circuits | 25, 62, 103, 120 |
| abstract_inverted_index.consider | 139 |
| abstract_inverted_index.obtained | 20 |
| abstract_inverted_index.protocol | 5 |
| abstract_inverted_index.replaced | 152 |
| abstract_inverted_index.sampling | 85, 93 |
| abstract_inverted_index.standard | 154 |
| abstract_inverted_index.effective | 83 |
| abstract_inverted_index.extremes, | 125 |
| abstract_inverted_index.generated | 73 |
| abstract_inverted_index.maximally | 82, 90 |
| abstract_inverted_index.near-term | 44 |
| abstract_inverted_index.practical | 51 |
| abstract_inverted_index.protocol, | 55 |
| abstract_inverted_index.simulable | 116 |
| abstract_inverted_index.computing. | 46 |
| abstract_inverted_index.efficiency | 37 |
| abstract_inverted_index.estimating | 8 |
| abstract_inverted_index.estimation | 1, 107, 144, 149 |
| abstract_inverted_index.performing | 105 |
| abstract_inverted_index.shadows'', | 19 |
| abstract_inverted_index.unitaries, | 88 |
| abstract_inverted_index.``classical | 18 |
| abstract_inverted_index.efficiently | 115 |
| abstract_inverted_index.estimation, | 58 |
| abstract_inverted_index.estimation. | 156 |
| abstract_inverted_index.expectation | 11 |
| abstract_inverted_index.ineffective | 91 |
| abstract_inverted_index.statistical | 36 |
| abstract_inverted_index.interpolates | 122 |
| abstract_inverted_index.measurement. | 76 |
| abstract_inverted_index.computational | 27 |
| abstract_inverted_index.exponentially | 9 |
| abstract_inverted_index.measurements. | 29 |
| abstract_inverted_index.median-of-means | 148 |
| cited_by_percentile_year.max | 94 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.69162405 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |