
TY  - JOUR
A1  - Flambaum, V. V. 
T1  - Time Dynamics in Chaotic Many-body Systems: Can Chaos Destroy a Quantum Computer?
JF  - Australian Journal of Physics
JO  - Aust. J.  Phys.
Y1  - 2001
VL  - 53
IS  - 4
SP  - 489
EP  - 497
KW  - 
UR  - https://doi.org/10.1071/PH99091 
N2  - Highly excited many-particle states in quantum systems (nuclei, atoms, quantum dots, spin systems, quantum computers) can be &#8216;chaotic&#8217; superpositions of mean-field basis states (Slater determinants, products of spin or qubit states). This is a result of the very high energy level density of many-body states which can be easily mixed by a residual interaction between particles. We consider the time dynamics of wave functions and increase of entropy in such chaotic systems. As an example, we present the time evolution in a closed quantum computer. A time scale for the entropy S(t) increase is t c &#126;&tgr; 0 /(n log 2 n), where &tgr; 0 is the qubit &#8216;lifetime&#8217;, n is the number of qubits, S(0) = 0 and S(t c )=1. At t &lowbar; t c the entropy is small: S &#126;nt 2 J 2 log 2 (1/t 2 J2 ), where J is the inter-qubit interaction strength. At t &#62; t c the number of &#8216;wrong&#8217; states increases exponentially as 2 S(t) . Therefore, t c may be interpreted as a maximal time for operation of a quantum computer. At t &#62;&#62;t c the system entropy approaches that for chaotic eigenstates. 
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