CNOT circuits need little help to implement arbitrary Hadamard-free Clifford transformations they generate Article Swipe
Dmitri Maslov
,
Willers Yang
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1038/s41534-023-00760-2
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1038/s41534-023-00760-2
A Hadamard-free Clifford transformation is a circuit composed of quantum Phase (P), CZ, and CNOT gates. It is known that such a circuit can be written as a three-stage computation, -P-CZ-CNOT-, where each stage consists only of gates of the specified type. In this paper, we focus on the minimization of circuit depth by entangling gates, corresponding to the important time-to-solution metric and the reduction of noise due to decoherence. We consider two popular connectivity maps: Linear Nearest Neighbor (LNN) and all-to-all. First, we show that a Hadamard-free Clifford operation can be implemented over LNN in depth 5 n , i.e., in the same depth as the -CNOT- stage alone. This allows us to implement arbitrary Clifford transformation over LNN in depth no more than 7 n − 4, improving the best previous upper bound of 9 n . Second, we report heuristic evidence that on average a random uniformly distributed Hadamard-free Clifford transformation over n > 6 qubits can be implemented with only a tiny additive overhead over all-to-all connected architecture compared to the best-known depth-optimized implementation of the -CNOT- stage alone. This suggests the reduction of the depth of Clifford circuits from $$2n\,+\,O({\log }^{2}(n))$$ to $$1.5n\,+\,O({\log }^{2}(n))$$ over unrestricted architectures.
Related Topics
Concepts
Hadamard transform
Controlled NOT gate
Quantum computer
Algorithm
Computer science
Transformation (genetics)
Quantum circuit
Quantum gate
Physics
Quantum mechanics
Quantum
Quantum error correction
Chemistry
Biochemistry
Gene
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1038/s41534-023-00760-2
- https://www.nature.com/articles/s41534-023-00760-2.pdf
- OA Status
- gold
- Cited By
- 8
- References
- 19
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4387187848
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4387187848Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1038/s41534-023-00760-2Digital Object Identifier
- Title
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CNOT circuits need little help to implement arbitrary Hadamard-free Clifford transformations they generateWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
-
2023Year of publication
- Publication date
-
2023-09-29Full publication date if available
- Authors
-
Dmitri Maslov, Willers YangList of authors in order
- Landing page
-
https://doi.org/10.1038/s41534-023-00760-2Publisher landing page
- PDF URL
-
https://www.nature.com/articles/s41534-023-00760-2.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/s41534-023-00760-2.pdfDirect OA link when available
- Concepts
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Hadamard transform, Controlled NOT gate, Quantum computer, Algorithm, Computer science, Transformation (genetics), Quantum circuit, Quantum gate, Physics, Quantum mechanics, Quantum, Quantum error correction, Chemistry, Biochemistry, GeneTop concepts (fields/topics) attached by OpenAlex
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8Total citation count in OpenAlex
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2025: 3, 2024: 3, 2023: 1, 2022: 1Per-year citation counts (last 5 years)
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19Number of works referenced by this work
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.the | 40, 49, 59, 64, 103, 107, 131, 175, 180, 186, 189 |
| abstract_inverted_index.two | 73 |
| abstract_inverted_index.− | 128 |
| abstract_inverted_index.> | 157 |
| abstract_inverted_index.(P), | 12 |
| abstract_inverted_index.CNOT | 15 |
| abstract_inverted_index.This | 111, 184 |
| abstract_inverted_index.best | 132 |
| abstract_inverted_index.each | 33 |
| abstract_inverted_index.from | 194 |
| abstract_inverted_index.more | 124 |
| abstract_inverted_index.only | 36, 164 |
| abstract_inverted_index.over | 94, 119, 155, 169, 264 |
| abstract_inverted_index.same | 104 |
| abstract_inverted_index.show | 85 |
| abstract_inverted_index.such | 21 |
| abstract_inverted_index.than | 125 |
| abstract_inverted_index.that | 20, 86, 145 |
| abstract_inverted_index.this | 44 |
| abstract_inverted_index.tiny | 166 |
| abstract_inverted_index.with | 163 |
| abstract_inverted_index.(LNN) | 80 |
| abstract_inverted_index.Phase | 11 |
| abstract_inverted_index.bound | 135 |
| abstract_inverted_index.depth | 53, 97, 105, 122, 190 |
| abstract_inverted_index.focus | 47 |
| abstract_inverted_index.gates | 38 |
| abstract_inverted_index.i.e., | 101 |
| abstract_inverted_index.known | 19 |
| abstract_inverted_index.maps: | 76 |
| abstract_inverted_index.noise | 67 |
| abstract_inverted_index.stage | 34, 109, 182 |
| abstract_inverted_index.type. | 42 |
| abstract_inverted_index.upper | 134 |
| abstract_inverted_index.where | 32 |
| abstract_inverted_index.-CNOT- | 108, 181 |
| abstract_inverted_index.First, | 83 |
| abstract_inverted_index.Linear | 77 |
| abstract_inverted_index.allows | 112 |
| abstract_inverted_index.alone. | 110, 183 |
| abstract_inverted_index.gates, | 56 |
| abstract_inverted_index.gates. | 16 |
| abstract_inverted_index.metric | 62 |
| abstract_inverted_index.paper, | 45 |
| abstract_inverted_index.qubits | 159 |
| abstract_inverted_index.random | 149 |
| abstract_inverted_index.report | 142 |
| abstract_inverted_index.Nearest | 78 |
| abstract_inverted_index.Second, | 140 |
| abstract_inverted_index.average | 147 |
| abstract_inverted_index.circuit | 7, 23, 52 |
| abstract_inverted_index.popular | 74 |
| abstract_inverted_index.quantum | 10 |
| abstract_inverted_index.written | 26 |
| abstract_inverted_index.Abstract | 0 |
| abstract_inverted_index.Clifford | 3, 89, 117, 153, 192 |
| abstract_inverted_index.Neighbor | 79 |
| abstract_inverted_index.additive | 167 |
| abstract_inverted_index.circuits | 193 |
| abstract_inverted_index.compared | 173 |
| abstract_inverted_index.composed | 8 |
| abstract_inverted_index.consider | 72 |
| abstract_inverted_index.consists | 35 |
| abstract_inverted_index.evidence | 144 |
| abstract_inverted_index.overhead | 168 |
| abstract_inverted_index.previous | 133 |
| abstract_inverted_index.suggests | 185 |
| abstract_inverted_index.<mml:math | 197, 232 |
| abstract_inverted_index.arbitrary | 116 |
| abstract_inverted_index.connected | 171 |
| abstract_inverted_index.heuristic | 143 |
| abstract_inverted_index.implement | 115 |
| abstract_inverted_index.important | 60 |
| abstract_inverted_index.improving | 130 |
| abstract_inverted_index.operation | 90 |
| abstract_inverted_index.reduction | 65, 187 |
| abstract_inverted_index.specified | 41 |
| abstract_inverted_index.uniformly | 150 |
| abstract_inverted_index.<mml:mrow> | 199, 206, 208, 210, 213, 217, 219, 234, 241, 243, 245, 248, 252, 254 |
| abstract_inverted_index.<mml:msup> | 209, 244 |
| abstract_inverted_index.all-to-all | 170 |
| abstract_inverted_index.best-known | 176 |
| abstract_inverted_index.entangling | 55 |
| abstract_inverted_index.</mml:math> | 228, 263 |
| abstract_inverted_index.</mml:mrow> | 212, 215, 221, 223, 224, 226, 227, 247, 250, 256, 258, 259, 261, 262 |
| abstract_inverted_index.</mml:msup> | 216, 251 |
| abstract_inverted_index.all-to-all. | 82 |
| abstract_inverted_index.distributed | 151 |
| abstract_inverted_index.implemented | 93, 162 |
| abstract_inverted_index.three-stage | 29 |
| abstract_inverted_index.}^{2}(n))$$ | 196, 231 |
| abstract_inverted_index.-P-CZ-CNOT-, | 31 |
| abstract_inverted_index.architecture | 172 |
| abstract_inverted_index.computation, | 30 |
| abstract_inverted_index.connectivity | 75 |
| abstract_inverted_index.decoherence. | 70 |
| abstract_inverted_index.minimization | 50 |
| abstract_inverted_index.unrestricted | 265 |
| abstract_inverted_index.<mml:mspace/> | 202, 204, 237, 239 |
| abstract_inverted_index.Hadamard-free | 2, 88, 152 |
| abstract_inverted_index.corresponding | 57 |
| abstract_inverted_index.architectures. | 266 |
| abstract_inverted_index.implementation | 178 |
| abstract_inverted_index.transformation | 4, 118, 154 |
| abstract_inverted_index.depth-optimized | 177 |
| abstract_inverted_index.$$2n\,+\,O({\log | 195 |
| abstract_inverted_index.time-to-solution | 61 |
| abstract_inverted_index.$$1.5n\,+\,O({\log | 230 |
| abstract_inverted_index.<mml:mi>O</mml:mi> | 205, 240 |
| abstract_inverted_index.<mml:mi>n</mml:mi> | 201, 220, 236, 255 |
| abstract_inverted_index.<mml:mn>2</mml:mn> | 200, 214, 249 |
| abstract_inverted_index.<mml:mo>(</mml:mo> | 207, 218, 242, 253 |
| abstract_inverted_index.<mml:mo>)</mml:mo> | 222, 225, 257, 260 |
| abstract_inverted_index.<mml:mo>+</mml:mo> | 203, 238 |
| abstract_inverted_index.<mml:mi>log</mml:mi> | 211, 246 |
| abstract_inverted_index.<mml:mn>1.5</mml:mn> | 235 |
| abstract_inverted_index.xmlns:mml="http://www.w3.org/1998/Math/MathML"> | 198, 233 |
| cited_by_percentile_year.max | 97 |
| cited_by_percentile_year.min | 89 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| citation_normalized_percentile.value | 0.85572402 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |