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Quantum Depth in the Random Oracle Model

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Název: Quantum Depth in the Random Oracle Model
Autoři: Arora, Atul Singh, Coladangelo, Andrea, Coudron, Matthew, Gheorghiu, Alexandru, 1990, Singh, Uttam, Waldner, Hendrik
Zdroj: 55th Annual ACM Symposium on Theory of Computing, STOC 2023, Orlando, USA Proceedings of the Annual ACM Symposium on Theory of Computing. :1111-1124
Témata: proof of quantum depth, random oracle model, Hybrid classical-quantum models of computation
Popis: We give a comprehensive characterisation of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a random oracle: (a) BPPQNCBPP BQP. This refutes Jozsa's conjecture in the random oracle model. As a result, this gives the first instantiatable separation between the classes by replacing the oracle with a cryptographic hash function, yielding a resolution to one of Aaronson's ten semi-grand challenges in quantum computing. (b) BPPQNC QNCBPP and QNCBPP BPPQNC. This shows that there is a subtle interplay between classical computation and shallow quantum computation. In fact, for the second separation, we establish that, for some problems, the ability to perform adaptive measurements in a single shallow quantum circuit, is more useful than the ability to perform polynomially many shallow quantum circuits without adaptive measurements. We also show that BPPQNC and BPPQNC are both strictly contained in BPPQNCBPP. (c) There exists a 2-message proof of quantum depth protocol. Such a protocol allows a classical verifier to efficiently certify that a prover must be performing a computation of some minimum quantum depth. Our proof of quantum depth can be instantiated using the recent proof of quantumness construction by Yamakawa and Zhandry.
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Přístupová URL adresa: https://research.chalmers.se/publication/536510
https://research.chalmers.se/publication/536510/file/536510_Fulltext.pdf
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  Data: Quantum Depth in the Random Oracle Model
– Name: Author
  Label: Authors
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  Data: <searchLink fieldCode="AR" term="%22Arora%2C+Atul+Singh%22">Arora, Atul Singh</searchLink><br /><searchLink fieldCode="AR" term="%22Coladangelo%2C+Andrea%22">Coladangelo, Andrea</searchLink><br /><searchLink fieldCode="AR" term="%22Coudron%2C+Matthew%22">Coudron, Matthew</searchLink><br /><searchLink fieldCode="AR" term="%22Gheorghiu%2C+Alexandru%22">Gheorghiu, Alexandru</searchLink>, 1990<br /><searchLink fieldCode="AR" term="%22Singh%2C+Uttam%22">Singh, Uttam</searchLink><br /><searchLink fieldCode="AR" term="%22Waldner%2C+Hendrik%22">Waldner, Hendrik</searchLink>
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  Data: <i>55th Annual ACM Symposium on Theory of Computing, STOC 2023, Orlando, USA Proceedings of the Annual ACM Symposium on Theory of Computing</i>. :1111-1124
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  Data: <searchLink fieldCode="DE" term="%22proof+of+quantum+depth%22">proof of quantum depth</searchLink><br /><searchLink fieldCode="DE" term="%22random+oracle+model%22">random oracle model</searchLink><br /><searchLink fieldCode="DE" term="%22Hybrid+classical-quantum+models+of+computation%22">Hybrid classical-quantum models of computation</searchLink>
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  Label: Description
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  Data: We give a comprehensive characterisation of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a random oracle: (a) BPPQNCBPP BQP. This refutes Jozsa's conjecture in the random oracle model. As a result, this gives the first instantiatable separation between the classes by replacing the oracle with a cryptographic hash function, yielding a resolution to one of Aaronson's ten semi-grand challenges in quantum computing. (b) BPPQNC QNCBPP and QNCBPP BPPQNC. This shows that there is a subtle interplay between classical computation and shallow quantum computation. In fact, for the second separation, we establish that, for some problems, the ability to perform adaptive measurements in a single shallow quantum circuit, is more useful than the ability to perform polynomially many shallow quantum circuits without adaptive measurements. We also show that BPPQNC and BPPQNC are both strictly contained in BPPQNCBPP. (c) There exists a 2-message proof of quantum depth protocol. Such a protocol allows a classical verifier to efficiently certify that a prover must be performing a computation of some minimum quantum depth. Our proof of quantum depth can be instantiated using the recent proof of quantumness construction by Yamakawa and Zhandry.
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        Value: 10.1145/3564246.3585153
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      – TitleFull: Quantum Depth in the Random Oracle Model
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            NameFull: Singh, Uttam
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              Type: published
              Y: 2023
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            – TitleFull: 55th Annual ACM Symposium on Theory of Computing, STOC 2023, Orlando, USA Proceedings of the Annual ACM Symposium on Theory of Computing
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