A computer is imagined in which all the parts are simple two-state objects obeying quantum mechanical laws. A time-independent Hamiltonian for such a system is written and analyzed. The computation is done in logically reversible steps. It is used to study possible limitations on computers due to fundamental physical laws. The ideal machine can run ballistically, coasting through the calculation in a short time TB. If there are imperfections due to irregularities in construction or finite temperatures the forward moving calculation is often reversed or scattered. External work must be done to drag the computer forward. The free energy lost in doing a calculation is kT In2 per logical step divided by turn factors. One is the mean free number of steps per scattering, measuring how perfectly the machine is built. The other is the mean time (divided by TB) that the calculation actually takes, which measures how gently you urge it forward.

© 1984 Optical Society of America

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