Classical and Quantum Computation

By Song Yuan Yan. 2015

951 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/523eca64dc8726197551186fd21b68ed84a2599e

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

In Computational Theory and Mathematics

Citations in the corpus

Grand Unification of Quantum Algorithms (2021, methodology): “[32] Alexei Yu Kitaev, Alexander Shen, Mikhail N Vyalyi, and Mikhail N Vyalyi.”
Harnessing the Power of the Second Quantum Revolution (2020, methodology): “According to the Solovay-Kitaev theorem, any U ∈ SU ( d ) in the continuum of unitary matrices can be eﬃciently approximated by a ﬁnite sequence in the discrete gate set of universal single-qudit maps [109,110].”
Self-Consistent Quantum Process Tomography (2012, neutral): “In B) we ﬁx the depolarizing strength at E dep = 10 − 3 and vary the set of gates used for SPAM over four sets of gates of diﬀering order. reconstructed gate and the identity by a diamond norm distance [28], which is calculated through the semideﬁ-nite programming technique in [29].”
Error bounds for approximations with deep ReLU networks (2016, neutral): “…network, a deep one can be viewed as a long sequence of non-commutative transformations, which is a natural setting for high expressiveness (cf. the well-known Solovay-Kitaev theorem on fast approximation of arbitrary quantum operations by sequences of non-commutative gates, see Kitaev et al.…”
Roads towards fault-tolerant universal quantum computation (2016, positive): “Obtaining a fault-tolerant logical T gate is only a partial goal as Cliﬀord+ T gates are then used to synthesize other logical gates needed in quantum algorithms 34–37 .”
Quantum computation vs. firewalls (2013, neutral): “This subsection is entirely pedagogical and contains no original material, good references are [41–43].”
Halving the cost of quantum addition (2017, positive): “However, assuming a “phase gradient register” prepared in the state | k i is available, the phase gradient operation can be performed via addition [16].”
Training Variational Quantum Algorithms Is NP-Hard. (2021, positive): “Notably, finding the ground state energy of a local Hamiltonian is QMA-hard [15, 16].”
Digitized adiabatic quantum computing with a superconducting circuit (2015, background): “Quantum mechanics can help solve complex problems in physics [1], chemistry [2], and machine learning [3], provided they can be programmed in a physical device.”
The Theory of Quantum Information (2018, background): “A different example having a similar character, but not giving as sharp a separation, appears in Kitaev, Shen, and Vyalyi [130].”
Hand-waving and interpretive dance: an introductory course on tensor networks (2016, neutral): “49 6.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.7 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49”
Diagnostics of Mixed-State Topological Order and Breakdown of Quantum Memory (2023, background): “More specifically, the quantum relative entropy quantifies whether errors ruin orthogonality between states [18], and coherent information is known to give robust necessary and sufficient conditions on successful QEC [19–21].”