Quantum-mechanical computers and uncomputability

Details Quantum-mechanical computers and uncomputability Quantum-mechanical computers and uncomputability

Aug 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phrvl..71..943l&link_type=abstract

Physical Review Letters, Volume 71, Issue 6, August 9, 1993, pp.943-946

Computer Science

Information Theory

9

Information Theory And Communication Theory, Quantum Mechanics

Scientific paper

The time evolution operator for any quantum-mechanical computer is diagonalizable, but to obtain the diagonal decomposition of a program state of the computer is as hard as actually performing the computation corresponding to the program. In particular, if a quantum-mechanical system is capable of universal computation, then the diagonal decomposition of program states is uncomputable. As a result, in a universe in which local variables support universal computation, a quantum-mechanical theory for that universe that supplies its spectrum cannot supply the spectral decomposition of the computational variables. A ``theory of everything'' can be simultaneously correct and fundamentally incomplete.

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