dorsal/arxiv
View SchemaAre all reversible computations tidy?
| Authors | O. J. E. Maroney |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0403079 |
| URL | https://arxiv.org/abs/quant-ph/0403079 |
Abstract
It has long been known that to minimise the heat emitted by a deterministic computer during it's operation it is necessary to make the computation act in a logically reversible manner\cite{Lan61}. Such logically reversible operations require a number of auxiliary bits to be stored, maintaining a history of the computation, and which allows the initial state to be reconstructed by running the computation in reverse. These auxiliary bits are wasteful of resources and may require a dissipation of energy for them to be reused. A simple procedure due to Bennett\cite{Ben73} allows these auxiliary bits to be "tidied", without dissipating energy, on a classical computer. All reversible classical computations can be made tidy in this way. However, this procedure depends upon a classical operation ("cloning") that cannot be generalised to quantum computers\cite{WZ82}. Quantum computations must be logically reversible, and therefore produce auxiliary qbits during their operation. We show that there are classes of quantum computation for which Bennett's procedure cannot be implemented. For some of these computations there may exist another method for which the computation may be "tidied". However, we also show there are quantum computations for which there is no possible method for tidying the auxiliary qbits. Not all reversible quantum computations can be made "tidy". This represents a fundamental additional energy burden to quantum computations. This paper extends results in \cite{Mar01}.
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"abstract": "It has long been known that to minimise the heat emitted by a deterministic\ncomputer during it\u0027s operation it is necessary to make the computation act in a\nlogically reversible manner\\cite{Lan61}. Such logically reversible operations\nrequire a number of auxiliary bits to be stored, maintaining a history of the\ncomputation, and which allows the initial state to be reconstructed by running\nthe computation in reverse. These auxiliary bits are wasteful of resources and\nmay require a dissipation of energy for them to be reused. A simple procedure\ndue to Bennett\\cite{Ben73} allows these auxiliary bits to be \"tidied\", without\ndissipating energy, on a classical computer. All reversible classical\ncomputations can be made tidy in this way. However, this procedure depends upon\na classical operation (\"cloning\") that cannot be generalised to quantum\ncomputers\\cite{WZ82}. Quantum computations must be logically reversible, and\ntherefore produce auxiliary qbits during their operation. We show that there\nare classes of quantum computation for which Bennett\u0027s procedure cannot be\nimplemented. For some of these computations there may exist another method for\nwhich the computation may be \"tidied\". However, we also show there are quantum\ncomputations for which there is no possible method for tidying the auxiliary\nqbits. Not all reversible quantum computations can be made \"tidy\". This\nrepresents a fundamental additional energy burden to quantum computations. This\npaper extends results in \\cite{Mar01}.",
"arxiv_id": "quant-ph/0403079",
"authors": [
"O. J. E. Maroney"
],
"categories": [
"quant-ph"
],
"title": "Are all reversible computations tidy?",
"url": "https://arxiv.org/abs/quant-ph/0403079"
},
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