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Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints
The statistical mechanics of quantum-classical systems with holonomic
constraints is formulated rigorously by unifying the classical Dirac bracket
and the quantum-classical bracket in matrix form.
The resulting Dirac quantum-classical theory, which conserves the holonomic
constraints exactly, is then used to formulate time evolution and statistical
mechanics. The correct momentum-jump approximation for constrained system
arises naturally from this formalism. Finally, in analogy with what was found
in the classical case, it is shown that the rigorous linear response function
of constrained quantum-classical systems contains non-trivial additional terms
which are absent in the response of unconstrained systems.Comment: Submitted to Journal of Chemical Physic
Statistical Constraints on State Preparation for a Quantum Computer
Quantum computing algorithms require that the quantum register be initially
present in a superposition state. To achieve this, we consider the practical
problem of creating a coherent superposition state of several qubits. Owing to
considerations of quantum statistics, this requires that the entropy of the
system go down. This, in turn, has two practical implications: (i) the initial
state cannot be controlled; (ii) the temperature of the system must be reduced.
These factors, in addition to decoherence and sensitivity to errors, must be
considered in the implementation of quantum computers.Comment: 7 pages; the final published versio
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