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  1. Quantum circuit complexity-a measure of the minimum number of gates needed to implement a given unitary transformation-is a fundamental concept in quantum computation, with widespread applications ranging from determining the running time of quantum algorithms to understanding the physics of black holes.

    Complexity of quantum circuits via sensitivity, magic, and cohere…

    arxiv.org/abs/2204.12051
    arxiv.org/abs/2204.12051
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    What is quantum circuit complexity?
    Quantum circuit complexity, by quantifying the minimal size of any circuit that implements a given unitary, is closely related to computational notions of complexity. The latter quantify the difficulty of solving a given computational task with a quantum computer and determine quantum complexity classes.

    Linear growth of quantum circuit complexity | Nature Physics

    nature.com
    What is a pure state's quantum circuit complexity definable?
    Similarly, a pure state’s quantum circuit complexity definable is the size of the smallest circuit that produces the state from a product state. Quantum circuit complexity, by quantifying the minimal size of any circuit that implements a given unitary, is closely related to computational notions of complexity.

    Linear growth of quantum circuit complexity | Nature Physics

    nature.com
    Does random quantum circuit complexity increase?
    We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity increases. Consider constructing a unitary from Haar-random two-qubit quantum gates. Implementing the unitary exactly requires a circuit of some minimal number of gates - the unitary's exact circuit complexity.

    [2106.05305] Linear growth of quantum circuit complexity - arXiv.org

    arxiv.org
    What is bounding complexity in a random quantum circuit?
    We have proven a prominent physics conjecture proposed by Brown and Susskind for random quantum circuits 4, 14: a local random circuit’s quantum complexity grows linearly in the number of gates until reaching a value exponential in the system size. To prove this conjecture, we have introduced a technique for bounding complexity.

    Linear growth of quantum circuit complexity | Nature Physics

    nature.com
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  3. Nature
    https://www.nature.com/articles/s41567-022-01539-6

    Linear growth of quantum circuit complexity | Nature Physics

  4. arXiv.org
    https://arxiv.org/html/2408.09641v3

    Character Complexity: A Novel Measure for Quantum Circuit Analysis

  5. Nature
    https://www.nature.com/articles/s41567-024-02622-w

    A general theory of quantum codes connecting quantum ... - Nature

  7. Springer
    https://link.springer.com/article/10.1007/s11128-024-04508-5

    Classification and transformations of quantum circuit …

  8. Physical Review Link Manager
    https://link.aps.org/doi/10.1103/PRXQuantum.2.030316

    PRX Quantum 2, 030316 (2021) - Models of Quantum Complexity …

  9. Springer
    https://link.springer.com/article/10.1007/s00220-024-05030-6

    Complexity of Quantum Circuits via Sensitivity, Magic, and …

  10. Nature
    https://www.nature.com/articles/s41534-02…

    Circuit complexity of quantum access models for …

    网页2024年4月23日 · We benchmark the circuit complexity of a given quantum circuit with three quantities: total number of elementary gates, total qubit number (including data qubits and ancillary qubits), and...

  11. arXiv.org
    https://arxiv.org/abs/2106.05305

    [2106.05305] Linear growth of quantum circuit complexity - arXiv.org

  12. arXiv.org
    https://arxiv.org/abs/2208.06306

    [2208.06306] Wasserstein Complexity of Quantum Circuits - arXiv.org

  13. Particle Theory Group
    http://theory.caltech.edu/~preskill/pubs/preskill-2021-complexity.pdf
    [PDF]

    PRX QUANTUM 2, 030316 (2021) - Particle Theory Group