dorsal/arxiv
View SchemaA Theory of Physical Quantum Computation: The Quantum Computer Condition
| Authors | Gerald Gilbert, Michael Hamrick, F. Javier Thayer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507141 |
| URL | https://arxiv.org/abs/quant-ph/0507141 |
Abstract
In this paper we present a new unified theoretical framework that describes the full dynamics of quantum computation. Our formulation allows any questions pertaining to the physical behavior of a quantum computer to be framed, and in principle, answered. We refer to the central organizing principle developed in this paper, on which our theoretical structure is based, as the *Quantum Computer Condition* (QCC), a rigorous mathematical statement that connects the irreversible dynamics of the quantum computing machine, with the reversible operations that comprise the quantum computation intended to be carried out by the quantum computing machine. Armed with the QCC, we derive a powerful result that we call the *Encoding No-Go Theorem*. This theorem gives a precise mathematical statement of the conditions under which fault-tolerant quantum computation becomes impossible in the presence of dissipation and/or decoherence. In connection with this theorem, we explicitly calculate a universal critical damping value for fault-tolerant quantum computation. In addition we show that the recently-discovered approach to quantum error correction known as "operator quantum error-correction" (OQEC) is a special case of our more general formulation. Our approach furnishes what we will refer to as "operator quantum fault-tolerance" (OQFT). In particular, we show how the QCC allows one to derive error thresholds for fault tolerance in a completely general context. We prove the existence of solutions to a class of time-dependent generalizations of the Lindblad equation. Using the QCC, we also show that the seemingly different circuit, graph- (including cluster-) state, and adiabatic paradigms for quantum computing are in fact all manifestations of a single, universal paradigm for all physical quantum computation.
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"abstract": "In this paper we present a new unified theoretical framework that describes\nthe full dynamics of quantum computation. Our formulation allows any questions\npertaining to the physical behavior of a quantum computer to be framed, and in\nprinciple, answered. We refer to the central organizing principle developed in\nthis paper, on which our theoretical structure is based, as the *Quantum\nComputer Condition* (QCC), a rigorous mathematical statement that connects the\nirreversible dynamics of the quantum computing machine, with the reversible\noperations that comprise the quantum computation intended to be carried out by\nthe quantum computing machine. Armed with the QCC, we derive a powerful result\nthat we call the *Encoding No-Go Theorem*. This theorem gives a precise\nmathematical statement of the conditions under which fault-tolerant quantum\ncomputation becomes impossible in the presence of dissipation and/or\ndecoherence. In connection with this theorem, we explicitly calculate a\nuniversal critical damping value for fault-tolerant quantum computation. In\naddition we show that the recently-discovered approach to quantum error\ncorrection known as \"operator quantum error-correction\" (OQEC) is a special\ncase of our more general formulation. Our approach furnishes what we will refer\nto as \"operator quantum fault-tolerance\" (OQFT). In particular, we show how the\nQCC allows one to derive error thresholds for fault tolerance in a completely\ngeneral context. We prove the existence of solutions to a class of\ntime-dependent generalizations of the Lindblad equation. Using the QCC, we also\nshow that the seemingly different circuit, graph- (including cluster-) state,\nand adiabatic paradigms for quantum computing are in fact all manifestations of\na single, universal paradigm for all physical quantum computation.",
"arxiv_id": "quant-ph/0507141",
"authors": [
"Gerald Gilbert",
"Michael Hamrick",
"F. Javier Thayer"
],
"categories": [
"quant-ph"
],
"title": "A Theory of Physical Quantum Computation: The Quantum Computer Condition",
"url": "https://arxiv.org/abs/quant-ph/0507141"
},
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