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In the accompanying paper of arXiv:2408.13472, we have established the method of characterizing the maximal order of asymptotic unitary designs generated by symmetric local random circuits, and have explicitly specified the order in the cases of $\mathbb{Z}_2$, U(1), and SU(2) symmetries.
E. Noether, Invariante variationsprobleme, Nachr. Ges. Wiss. Gottingen 1918
1918
Earlier work this paper cites.
Y. Nambu, Axial vector current conservation in weak interactions, Phys. Rev. Lett. 4
1960
Earlier work this paper cites.
Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. i, Phys. Rev. 122
1961
Earlier work this paper cites.
J. Goldstone, Field theories with superconductor solutions, Nuovo Cim. 19
1961
Earlier work this paper cites.
P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52
1995
Earlier work this paper cites.
X.-G. Wen, Topological orders and edge excitations in fractional quantum hall states, Advances in Physics 44
1995
Earlier work this paper cites.
D. P. DiVincenzo, Two-bit gates are universal for quantum computation, Phys. Rev. A 51
1995
Earlier work this paper cites.
S. Lloyd, Almost any quantum logic gate is universal, Phys. Rev. Lett. 75
1995
Earlier work this paper cites.
A. M. Steane, Error correcting codes in quantum theory, Phys. Rev. Lett. 77
1996
Earlier work this paper cites.
A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Phys. Rev. A 54
1996
Earlier work this paper cites.
A. Y. Kitaev, Quantum computations: algorithms and error correction, Russ. Math. Surv. 52
1997
Earlier work this paper cites.
M. A. Nielsen and I. Chuang, Quantum Computation and Quantum Information
2000
Earlier work this paper cites.
J. Kempe, D. Bacon, D. P. DiVincenzo, and K. B. Whaley, Encoded universality from a single physical interaction, Quantum Info. Comput. 1
2001
Earlier work this paper cites.
A. W. Knapp, Lie Groups Beyond an Introduction
2002
Earlier work this paper cites.
C. L. Kane and E. J. Mele, Quantum spin hall effect in graphene, Phys. Rev. Lett. 95
2005
Earlier work this paper cites.
J. Emerson, R. Alicki, and K. Życzkowski, Scalable noise estimation with random unitary operators, J. Opt. B: Quantum Semiclass. Opt. 7
2005
Earlier work this paper cites.
C. M. Dawson and M. A. Nielsen, The solovay-kitaev algorithm, Quantum Info. Comput. 6
2006
Cited alongside, same era.
A. W. Sandvik, Evidence for deconfined quantum criticality in a two-dimensional heisenberg model with four-spin interactions, Phys. Rev. Lett. 98
2007
Cited alongside, same era.
Y. Nambu, Nobel lecture: Spontaneous symmetry breaking in particle physics: A case of cross fertilization, Rev. Mod. Phys. 81
2009
Cited alongside, same era.
B. Eastin and E. Knill, Restrictions on transversal encoded quantum gate sets, Phys. Rev. Lett. 102
2009
Cited alongside, same era.
Z.-C. Gu and X.-G. Wen, Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order, Phys. Rev. B 80
2009
Cited alongside, same era.
Y. Bao, S. Choi, and E. Altman, Symmetry enriched phases of quantum circuits, Annals of Physics 435
2021
Later among the works it cites.
A. Lavasani, Y. Alavirad, and M. Barkeshli, Measurement-induced topological entanglement transitions in symmetric random quantum circuits, Nature Phys. 17
2021
Later among the works it cites.
I. Marvian, Restrictions on realizable unitary operations imposed by symmetry and locality, Nature Phys. 18
2022
Later among the works it cites.
J. Haferkamp, Random quantum circuits are approximate unitary t t -designs in depth O ( n t 5 + o ( 1 ) ) O\left(nt^{5+o(1)}\right) , Quantum 6
2022
Later among the works it cites.
R. Morral-Yepes, F. Pollmann, and I. Lovas, Detecting and stabilizing measurement-induced symmetry-protected topological phases in generalized cluster models, Phys. Rev. B 108
2023
Later among the works it cites.
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C. Dankert, R. Cleve, J. Emerson, and E. Livine, Exact and approximate unitary 2-designs and their application to fidelity estimation, Phys. Rev. A 80
2009
Cited alongside, same era.
M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82
2010
Cited alongside, same era.
F. Pollmann, A. M. Turner, E. Berg, and M. Oshikawa, Entanglement spectrum of a topological phase in one dimension, Phys. Rev. B 81
2010
Cited alongside, same era.
X. Chen, Z.-C. Gu, Z.-X. Liu, and X.-G. Wen, Symmetry-protected topological orders in interacting bosonic systems, Science 338
2012
Cited alongside, same era.
F. Dupuis, M. Berta, J. Wullschleger, and R. Renner, One-shot decoupling, Commun. Math. Phys. 328
2014
Cited alongside, same era.
R. Zeier and Z. Zimborás, On squares of representations of compact lie algebras, J. Math. Phys. 56
2015
Cited alongside, same era.
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2016
Cited alongside, same era.
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Later among the works it cites.
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2024
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I. Marvian, Theory of quantum circuits with abelian symmetries, Phys. Rev. Res. 6
2024
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I. Marvian, H. Liu, and A. Hulse, Rotationally invariant circuits: Universality with the exchange interaction and two ancilla qubits, Phys. Rev. Lett. 132
2024
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2024
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2024
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S. N. Hearth, M. O. Flynn, A. Chandran, and C. R. Laumann, Unitary k k -designs from random number-conserving quantum circuits, Phys. Rev. X 15
2025
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Y. Mitsuhashi, R. Suzuki, T. Soejima, and N. Yoshioka, Unitary designs of symmetric local random circuits, Phys. Rev. Lett. 134
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