Algorithmic Shadow Spectroscopy Article Swipe
Hans Hon Sang Chan
,
Richard J. Meister
,
Matthew L. Goh
,
Bálint Koczor
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.11036
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2212.11036
We present shadow spectroscopy as a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits) beyond performing time evolution and measurements. The approach builds on the fundamental feature that every observable property of a quantum system must evolve according to the same harmonic components: we can reveal them by post-processing classical shadows of time-evolved quantum states to extract a large number of time-periodic signals $N_o\propto 10^8$, whose frequencies correspond to Hamiltonian energy differences with Heisenberg-limited precision. We provide strong analytical guarantees that (a) quantum resources scale as $O(\log N_o)$, while the classical computational complexity is linear $O(N_o)$, (b) the signal-to-noise ratio increases with the number of processed signals as $\propto \sqrt{N_o}$, and (c) spectral peak positions are immune to reasonable levels of noise. We demonstrate our approach on model spin systems and the excited state conical intersection of molecular CH$_2$ and verify that our method is indeed intuitively easy to use in practice, robust against gate noise, amiable to a new type of algorithmic-error mitigation technique, and uses orders of magnitude fewer number of shots than typical near-term quantum algorithms -- as low as 10 shots per timestep is sufficient. Finally, we measured a high-quality, experimental shadow spectrum of a spin chain on readily-available IBM quantum computers, achieving the same precision as in noise-free simulations without using any advanced error mitigation, and verified scalability in tensor-network simulations of up to 100-qubit systems.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2212.11036
- https://arxiv.org/pdf/2212.11036
- OA Status
- green
- Cited By
- 7
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4312108052
All OpenAlex metadata
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https://openalex.org/W4312108052Canonical identifier for this work in OpenAlex
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https://doi.org/10.48550/arxiv.2212.11036Digital Object Identifier
- Title
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Algorithmic Shadow SpectroscopyWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
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2022-12-21Full publication date if available
- Authors
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Hans Hon Sang Chan, Richard J. Meister, Matthew L. Goh, Bálint KoczorList of authors in order
- Landing page
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https://arxiv.org/abs/2212.11036Publisher landing page
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https://arxiv.org/pdf/2212.11036Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2212.11036Direct OA link when available
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Quantum, Qubit, Algorithm, Quantum computer, Quantum mechanics, Hamiltonian (control theory), Quantum error correction, Physics, Observable, Computer science, Mathematics, Mathematical optimizationTop concepts (fields/topics) attached by OpenAlex
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7Total citation count in OpenAlex
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2025: 1, 2024: 3, 2023: 3Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.systems. | 241 |
| abstract_inverted_index.timestep | 197 |
| abstract_inverted_index.verified | 232 |
| abstract_inverted_index.$O(N_o)$, | 106 |
| abstract_inverted_index.100-qubit | 240 |
| abstract_inverted_index.according | 48 |
| abstract_inverted_index.achieving | 217 |
| abstract_inverted_index.algorithm | 8 |
| abstract_inverted_index.classical | 60, 101 |
| abstract_inverted_index.evolution | 28 |
| abstract_inverted_index.increases | 111 |
| abstract_inverted_index.magnitude | 180 |
| abstract_inverted_index.molecular | 148 |
| abstract_inverted_index.near-term | 187 |
| abstract_inverted_index.positions | 125 |
| abstract_inverted_index.practice, | 162 |
| abstract_inverted_index.precision | 220 |
| abstract_inverted_index.processed | 116 |
| abstract_inverted_index.resources | 22, 94 |
| abstract_inverted_index.algorithms | 189 |
| abstract_inverted_index.analytical | 89 |
| abstract_inverted_index.complexity | 103 |
| abstract_inverted_index.computers, | 216 |
| abstract_inverted_index.correspond | 78 |
| abstract_inverted_index.estimating | 10 |
| abstract_inverted_index.guarantees | 90 |
| abstract_inverted_index.mitigation | 174 |
| abstract_inverted_index.noise-free | 223 |
| abstract_inverted_index.observable | 40 |
| abstract_inverted_index.performing | 26 |
| abstract_inverted_index.precision. | 85 |
| abstract_inverted_index.reasonable | 129 |
| abstract_inverted_index.technique, | 175 |
| abstract_inverted_index.$N_o\propto | 74 |
| abstract_inverted_index.Hamiltonian | 80 |
| abstract_inverted_index.components: | 53 |
| abstract_inverted_index.demonstrate | 134 |
| abstract_inverted_index.differences | 82 |
| abstract_inverted_index.frequencies | 77 |
| abstract_inverted_index.fundamental | 36 |
| abstract_inverted_index.intuitively | 157 |
| abstract_inverted_index.mitigation, | 230 |
| abstract_inverted_index.repetitions | 17 |
| abstract_inverted_index.scalability | 233 |
| abstract_inverted_index.simulations | 224, 236 |
| abstract_inverted_index.sufficient. | 199 |
| abstract_inverted_index.\sqrt{N_o}$, | 120 |
| abstract_inverted_index.experimental | 205 |
| abstract_inverted_index.intersection | 146 |
| abstract_inverted_index.spectroscopy | 3 |
| abstract_inverted_index.time-evolved | 63 |
| abstract_inverted_index.computational | 102 |
| abstract_inverted_index.high-quality, | 204 |
| abstract_inverted_index.measurements. | 30 |
| abstract_inverted_index.time-periodic | 72 |
| abstract_inverted_index.tensor-network | 235 |
| abstract_inverted_index.post-processing | 59 |
| abstract_inverted_index.signal-to-noise | 109 |
| abstract_inverted_index.algorithmic-error | 173 |
| abstract_inverted_index.readily-available | 213 |
| abstract_inverted_index.Heisenberg-limited | 84 |
| abstract_inverted_index.simulator-agnostic | 6 |
| cited_by_percentile_year.max | 97 |
| cited_by_percentile_year.min | 91 |
| countries_distinct_count | 0 |
| institutions_distinct_count | 4 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/7 |
| sustainable_development_goals[0].score | 0.5400000214576721 |
| sustainable_development_goals[0].display_name | Affordable and clean energy |
| citation_normalized_percentile.value | 0.80708175 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |