Results 11 to 20 of about 93,203 (297)
Circuit complexity across a topological phase transition [PDF]
Physical Review Research, 2020 We use Nielsen's geometric approach to quantify the circuit complexity in a one-dimensional Kitaev chain across a topological phase transition. We find that the circuit complexities of both the ground states and nonequilibrium steady states of the Kitaev
Fangli Liu +7 more
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Circuit complexity for free fermions
Journal of High Energy Physics, 2018 We study circuit complexity for free fermionic field theories and Gaussian states. Our definition of circuit complexity is based on the notion of geodesic distance on the Lie group of special orthogonal transformations equipped with a right-invariant ...
Lucas Hackl, Robert C. Myers
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Circuit complexity in quantum field theory [PDF]
Journal of High Energy Physics, 2017 Motivated by recent studies of holographic complexity, we examine the question of circuit complexity in quantum field theory. We provide a quantum circuit model for the preparation of Gaussian states, in particular the ground state, in a free scalar ...
Robert A. Jefferson, Robert C. Myers
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20th Annual Symposium on Foundations of Computer Science (sfcs 1979), 1979 AbstractWe argue that uniform circuit complexity introduced by Borodin is a reasonable model of parallel complexity. Three main results are presented. First, we show that alternating Turing machines are also a surprisingly good model of parallel complexity, by showing that simultaneous size/depth of uniform circuits is the same as space/time of ...
Ruzzo, Walter L.
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Deterministic restrictions in circuit complexity [PDF]
Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96, 1996 We study the complexity of computing Boolean functions using AND, OR and NOT gates. We show that a circuit of depth d with S gates can be made to output a constant by setting O(S1− ) (where (d) = 4−d) of its input values. This implies a superlinear size lower bound for a large class of functions. Using this, we obtain a function computable by a uniform
Chaudhuri, S., Radhakrishnan, J.
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Symmetry, 2022 Motivated by recent studies of circuit complexity in weakly interacting scalar field theory, we explore the computation of circuit complexity in Z2 Even Effective Field Theories (Z2 EEFTs). We consider a massive free field theory with higher-order Wilsonian operators such as ϕ4, ϕ6, and ϕ8.
Kiran Adhikari +8 more
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Quantum circuit complexity and unsupervised machine learning of topological order [PDF]
Nature CommunicationsEnabling the discovery of unknown quantum many-body phases of matter remains a fundamental challenge in machine learning for quantum physics. Here, inspired by the close relationship between Kolmogorov complexity and unsupervised machine learning, we ...
Yanming Che +3 more
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Circuit complexity in interacting QFTs and RG flows
Journal of High Energy Physics, 2018 We consider circuit complexity in certain interacting scalar quantum field theories, mainly focusing on the ϕ 4 theory. We work out the circuit complexity for evolving from a nearly Gaussian unentangled reference state to the entangled ground state of ...
Arpan Bhattacharyya +2 more
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Universal early-time growth in quantum circuit complexity
Journal of High Energy PhysicsWe show that quantum circuit complexity for the unitary time evolution operator of any time-independent Hamiltonian is bounded by linear growth at early times, independent of any choices of the fundamental gates or cost metric.
S. Shajidul Haque +2 more
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Arithmetic Circuit Complexity (Tutorial).
, 2014 Arithmetic Circuits compute polynomial functions over their inputs via a sequence of arithmetic operations (additions, subtractions, multiplications, divisions, etc.). This tutorial will give an overview of arithmetic circuit complexity, focusing on the problem of proving lower bounds for arithmetic circuits.
Kayal, Neeraj
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