Sep 17, 1984 - Landauer, Ann. N.Y. Acad. Sci. (to be published). '0P. Benioff, Int. J. Theor. Phys. 21, 177 (1982). t tD. Mundici, Nuovo Cimento 61B,297 (1981).
VOLUME
53, NUMBER 12
PHYSICAL REVIEW LETTERS
Comment on "Dissipation in Computation" A paper on dissipation in computation has appeared' which attempts to show'that earlier work on physical limits of and energy dissipation in computation is ~rong. To avoid redundancy, the comments here will be limited to aspects of quantum mechanical models of the computation process and whether or not measurements at each computation step are necessary. Porod et al. ' (here abbreviated by PGFP) make the point that measurements at each computation step are an essential part of the computation process. For a Turing machine, readings or measurements of the reading head and the scanned tape cell are needed in order to force the machine along the desired logical path. But what is to prevent coninteraction so that struction of a reading-head-tape the overall system model, evolving freely without carries out the Turing machine measurements, steps? So far no one has shown that such models are not physically constructible. In Benioff's quantum mechanical models of Turing machines, 7 the Hamiltonians are constructed so that the interactions between the different components make the overall system Schrodinger-state evolution correspond at times n 6, with n = 1, 2, . . . , to successive steps of the Turing machine. 5 is a time interval which depends on the interaction strength in the Hamiltonian. Contrary to PGFP's assertion, measurements arc not needed at each step because the necessary correlations are alThe evolution is ready built into the Hamiltonian. free and not forced in any way. The models are reversible since the Hamiltonian is Hermitian. The required for such models are only measurements those which determine if the computation has halted and if so what the answer is. In the models considered here such measurements perturb the system state and introduce energy dissipation. However, the perturbation and dissipation can be reduced arbitrarily by making the duration of the measurement sufficiently short. More important is the point that such measurements have nothing to do with the computation process. They are under control of the operator and can be done as often or as rarely as is desired. Such models in which no energy dissipation or state degradation occurs, except possibly when such terminal measurements are made, are referred to as
17 SEPTEMBER 1984
models which dissipate no energy. The reason is that no state degradation occurs while the computation is in progress. In other types of quantum mechanical models' which have been constructed, the Schrodinger state of the system degrades slightly at each computation step as the system evolves even in complete isolation from the environment. In these models, restoration of the system state would require the dissipation of energy. the conAs has already been emphasized, mechanical models struction of the quantum described above is an idealized construction only. It is an open question whether such models can also be physically constructed in the laboratory. However, the idealized existence of such models demonstrates that one cannot use purely quantum mechanical arguments (such as those based on the uncertainty principle, for example" ) to deny the existence of models which dissipate no energy. This work was supported by the Applied Mathematical Sciences Research subprogram (KC04-02) of the Office of Energy Research of the U. S. Department of Energy under Contract No. W-31-
'
109-EN6-38. Paul Benioff Argonne National Laboratory Argonne, Illinois 60439
Received 8 March 1984 PACS numbers: 89.80. +h, 06.50.—x, 89.70. +c
W. Porod, R. Grondin, D. Ferry, and G. Porod, Phys. Rev. Lett. 52, 232 (1984). 2R. Landauer, IBM J. Res. Dev. 5, 183 (1961). R. W. Keyes and R. Landauer, IBM J. Res. Dev. 14, 152 (1970). 4R. Landauer, Int. J. Theor. Phys. 21, 283 (1982). 5C. H. Bennett, IBM J. Res. Dev. 17, 525 (1973), and Int. J. Theor. Phys. 21, 905 (1982). 6E. Fredkin and T. Toffoli, Int. J. Theor. Phys. 21, 219
(1982). ~P. Benioff, Phys. Rev. Lett. 48, 1581 (1982), and J. Stat. Phys. 29, 515 (1982). sK. Likharev, Int. J. Theor. Phys. 21, 311 (1982). sR. Landauer, Ann. N. Y. Acad. Sci. (to be published). '0P. Benioff, Int. J. Theor. Phys. 21, 177 (1982). t tD. Mundici, Nuovo Cimento 61B, 297 (1981).
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