scholarly journals On the Noether charge and the gravity duals of quantum complexity

2018 ◽  
Vol 2018 (8) ◽  
Author(s):  
Zhong-Ying Fan ◽  
Minyong Guo
Keyword(s):  
Quantum Complexity ◽  
Gravity Duals

scholarly journals The power of quantum complexity

2021 ◽  
Vol 64 (3) ◽  
pp. 15-17
Author(s):  
Don Monroe
Keyword(s):  
Quantum Mechanics ◽  
Quantum Complexity ◽  
Mathematics And Physics

A theorem about computations that exploit quantum mechanics challenges longstanding ideas in mathematics and physics.

scholarly journals Geometry of quantum complexity

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
Roberto Auzzi ◽  
Stefano Baiguera ◽  
G. Bruno De Luca ◽  
Andrea Legramandi ◽  
Giuseppe Nardelli ◽  
...  
Keyword(s):  
Quantum Complexity

scholarly journals Sparse Sachdev-Ye-Kitaev model, quantum chaos, and gravity duals

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
Antonio M. García-García ◽  
Yiyang Jia ◽  
Dario Rosa ◽  
Jacobus J. M. Verbaarschot
Keyword(s):  
Quantum Chaos ◽  
Kitaev Model ◽  
Gravity Duals

scholarly journals Chern-Simons Theories and Wrapped M-Branes in Their Gravity Duals

2009 ◽  
Vol 121 (5) ◽  
pp. 915-940 ◽  
Author(s):  
Y. Imamura ◽  
S. Yokoyama
Keyword(s):  
Chern Simons ◽  
Gravity Duals

scholarly journals The Jones polynomial: quantum algorithms and applications in quantum complexity theory

2008 ◽  
Vol 8 (1&2) ◽  
pp. 147-180
Author(s):  
P. Wocjan ◽  
J. Yard
Keyword(s):  
Quantum Computation ◽  
Braid Group ◽  
Quantum Algorithms ◽  
Primitive Root ◽  
Jones Polynomial ◽  
Tutte Polynomial ◽  
Roots Of Unity ◽  
Complete Problems ◽  
Primitive Roots ◽  
Quantum Complexity

We analyze relationships between quantum computation and a family of generalizations of the Jones polynomial. Extending recent work by Aharonov et al., we give efficient quantum circuits for implementing the unitary Jones-Wenzl representations of the braid group. We use these to provide new quantum algorithms for approximately evaluating a family of specializations of the HOMFLYPT two-variable polynomial of trace closures of braids. We also give algorithms for approximating the Jones polynomial of a general class of closures of braids at roots of unity. Next we provide a self-contained proof of a result of Freedman et al.\ that any quantum computation can be replaced by an additive approximation of the Jones polynomial, evaluated at almost any primitive root of unity. Our proof encodes two-qubit unitaries into the rectangular representation of the eight-strand braid group. We then give QCMA-complete and PSPACE-complete problems which are based on braids. We conclude with direct proofs that evaluating the Jones polynomial of the plat closure at most primitive roots of unity is a \#P-hard problem, while learning its most significant bit is PP-hard, circumventing the usual route through the Tutte polynomial and graph coloring.

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