4 Search Results for "Takahashi, Yasuhiro"

Document
DOI: 10.4230/LIPIcs.TQC.2023.9
Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection

Authors: Ryo Hiromasa, Akihiro Mizutani, Yuki Takeuchi, and Seiichiro Tani

Published in: LIPIcs, Volume 266, 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)

Abstract
We define rewinding operators that invert quantum measurements. Then, we define complexity classes RwBQP, CBQP, and AdPostBQP as sets of decision problems solvable by polynomial-size quantum circuits with a polynomial number of rewinding operators, cloning operators, and adaptive postselections, respectively. Our main result is that BPP^PP ⊆ RwBQP = CBQP = AdPostBQP ⊆ PSPACE. As a byproduct of this result, we show that any problem in PostBQP can be solved with only postselections of outputs whose probabilities are polynomially close to one. Under the strongly believed assumption that BQP ⊉ SZK, or the shortest independent vectors problem cannot be efficiently solved with quantum computers, we also show that a single rewinding operator is sufficient to achieve tasks that are intractable for quantum computation. In addition, we consider rewindable Clifford and instantaneous quantum polynomial time circuits.
Cite as

Ryo Hiromasa, Akihiro Mizutani, Yuki Takeuchi, and Seiichiro Tani. Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection. In 18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 266, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{hiromasa_et_al:LIPIcs.TQC.2023.9,
  author =	{Hiromasa, Ryo and Mizutani, Akihiro and Takeuchi, Yuki and Tani, Seiichiro},
  title =	{{Rewindable Quantum Computation and Its Equivalence to Cloning and Adaptive Postselection}},
  booktitle =	{18th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2023)},
  pages =	{9:1--9:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-283-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{266},
  editor =	{Fawzi, Omar and Walter, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2023.9},
  URN =		{urn:nbn:de:0030-drops-183193},
  doi =		{10.4230/LIPIcs.TQC.2023.9},
  annote =	{Keywords: Quantum computing, Postselection, Lattice problems}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.83
Classically Simulating Quantum Circuits with Local Depolarizing Noise

Authors: Yasuhiro Takahashi, Yuki Takeuchi, and Seiichiro Tani

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
We study the effect of noise on the classical simulatability of quantum circuits defined by computationally tractable (CT) states and efficiently computable sparse (ECS) operations. Examples of such circuits, which we call CT-ECS circuits, are IQP, Clifford Magic, and conjugated Clifford circuits. This means that there exist various CT-ECS circuits such that their output probability distributions are anti-concentrated and not classically simulatable in the noise-free setting (under plausible assumptions). First, we consider a noise model where a depolarizing channel with an arbitrarily small constant rate is applied to each qubit at the end of computation. We show that, under this noise model, if an approximate value of the noise rate is known, any CT-ECS circuit with an anti-concentrated output probability distribution is classically simulatable. This indicates that the presence of small noise drastically affects the classical simulatability of CT-ECS circuits. Then, we consider an extension of the noise model where the noise rate can vary with each qubit, and provide a similar sufficient condition for classically simulating CT-ECS circuits with anti-concentrated output probability distributions.
Cite as

Yasuhiro Takahashi, Yuki Takeuchi, and Seiichiro Tani. Classically Simulating Quantum Circuits with Local Depolarizing Noise. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 83:1-83:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{takahashi_et_al:LIPIcs.MFCS.2020.83,
  author =	{Takahashi, Yasuhiro and Takeuchi, Yuki and Tani, Seiichiro},
  title =	{{Classically Simulating Quantum Circuits with Local Depolarizing Noise}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{83:1--83:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.83},
  URN =		{urn:nbn:de:0030-drops-127533},
  doi =		{10.4230/LIPIcs.MFCS.2020.83},
  annote =	{Keywords: Classical Simulation, Quantum Circuit, Local Depolarizing Noise}
}
Document
DOI: 10.4230/LIPIcs.CCC.2019.21
Average-Case Quantum Advantage with Shallow Circuits

Authors: François Le Gall

Published in: LIPIcs, Volume 137, 34th Computational Complexity Conference (CCC 2019)

Abstract
Recently Bravyi, Gosset and König (Science 2018) proved an unconditional separation between the computational powers of small-depth quantum and classical circuits for a relation. In this paper we show a similar separation in the average-case setting that gives stronger evidence of the superiority of small-depth quantum computation: we construct a computational task that can be solved on all inputs by a quantum circuit of constant depth with bounded-fanin gates (a "shallow" quantum circuit) and show that any classical circuit with bounded-fanin gates solving this problem on a non-negligible fraction of the inputs must have logarithmic depth. Our results are obtained by introducing a technique to create quantum states exhibiting global quantum correlations from any graph, via a construction that we call the extended graph. Similar results have been very recently (and independently) obtained by Coudron, Stark and Vidick (arXiv:1810.04233}), and Bene Watts, Kothari, Schaeffer and Tal (STOC 2019).
Cite as

François Le Gall. Average-Case Quantum Advantage with Shallow Circuits. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{legall:LIPIcs.CCC.2019.21,
  author =	{Le Gall, Fran\c{c}ois},
  title =	{{Average-Case Quantum Advantage with Shallow Circuits}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Shpilka, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.21},
  URN =		{urn:nbn:de:0030-drops-108432},
  doi =		{10.4230/LIPIcs.CCC.2019.21},
  annote =	{Keywords: Quantum computing, circuit complexity, constant-depth circuits}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.57
Power of Uninitialized Qubits in Shallow Quantum Circuits

Authors: Yasuhiro Takahashi and Seiichiro Tani

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
We study the computational power of shallow quantum circuits with O(log n) initialized and n^{O(1)} uninitialized ancillary qubits, where n is the input length and the initial state of the uninitialized ancillary qubits is arbitrary. First, we show that such a circuit can compute any symmetric function on n bits that is classically computable in polynomial time. Then, we regard such a circuit as an oracle and show that a polynomial-time classical algorithm with the oracle can estimate the elements of any unitary matrix corresponding to a constant-depth quantum circuit on n qubits. Since it seems unlikely that these tasks can be done with only O(log n) initialized ancillary qubits, our results give evidences that adding uninitialized ancillary qubits increases the computational power of shallow quantum circuits with only O(log n) initialized ancillary qubits. Lastly, to understand the limitations of uninitialized ancillary qubits, we focus on near-logarithmic-depth quantum circuits with them and show the impossibility of computing the parity function on n bits.
Cite as

Yasuhiro Takahashi and Seiichiro Tani. Power of Uninitialized Qubits in Shallow Quantum Circuits. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 57:1-57:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{takahashi_et_al:LIPIcs.STACS.2018.57,
  author =	{Takahashi, Yasuhiro and Tani, Seiichiro},
  title =	{{Power of Uninitialized Qubits in Shallow Quantum Circuits}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{57:1--57:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.57},
  URN =		{urn:nbn:de:0030-drops-84907},
  doi =		{10.4230/LIPIcs.STACS.2018.57},
  annote =	{Keywords: quantum circuit complexity, shallow quantum circuit, uninitialized qubit}
}
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