dorsal/arxiv
View SchemaTime dynamics in chaotic many-body systems: can chaos destroy a quantum computer?
| Authors | V. V. Flambaum |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9911061 |
| URL | https://arxiv.org/abs/quant-ph/9911061 |
Abstract
Highly excited many-particle states in quantum systems (nuclei, atoms, quantum dots, spin systems, quantum computers) can be ``chaotic'' 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 =t_0/(n log_2{n}), where t_0 is the qubit ``lifetime'', n is the number of qubits, S(0)=0 and S(t_c)=1. At t << t_c the entropy is small: S= n t^2 J^2 log_2(1/t^2 J^2), where J is the inter-qubit interaction strength. At t > t_c the number of ``wrong'' states increases exponentially as 2^{S(t)} . Therefore, t_c may be interpreted as a maximal time for operation of a quantum computer, since at t > t_c one has to struggle against the second law of thermodynamics. At t >>t_c the system entropy approaches that for chaotic eigenstates.
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"abstract": "Highly excited many-particle states in quantum systems (nuclei, atoms,\nquantum dots, spin systems, quantum computers) can be ``chaotic\u0027\u0027\nsuperpositions of mean-field basis states (Slater determinants, products of\nspin or qubit states). This is a result of the very high energy level density\nof many-body states which can be easily mixed by a residual interaction between\nparticles. We consider the time dynamics of wave functions and increase of\nentropy in such chaotic systems.\n As an example we present the time evolution in a closed quantum computer. A\ntime scale for the entropy S(t) increase is t_c =t_0/(n log_2{n}), where t_0 is\nthe qubit ``lifetime\u0027\u0027, n is the number of qubits, S(0)=0 and S(t_c)=1. At t \u003c\u003c\nt_c the entropy is small: S= n t^2 J^2 log_2(1/t^2 J^2), where J is the\ninter-qubit interaction strength. At t \u003e t_c the number of ``wrong\u0027\u0027 states\nincreases exponentially as 2^{S(t)} . Therefore, t_c may be interpreted as a\nmaximal time for operation of a quantum computer, since at t \u003e t_c one has to\nstruggle against the second law of thermodynamics. At t \u003e\u003et_c the system\nentropy approaches that for chaotic eigenstates.",
"arxiv_id": "quant-ph/9911061",
"authors": [
"V. V. Flambaum"
],
"categories": [
"quant-ph",
"chao-dyn",
"cond-mat.mes-hall",
"cond-mat.stat-mech",
"nlin.CD",
"nucl-th",
"physics.atom-ph"
],
"title": "Time dynamics in chaotic many-body systems: can chaos destroy a quantum computer?",
"url": "https://arxiv.org/abs/quant-ph/9911061"
},
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