dorsal/arxiv
View SchemaQuantum Circuits with Mixed States
| Authors | Dorit Aharonov, Alexei Kitaev, Noam Nisan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9806029 |
| URL | https://arxiv.org/abs/quant-ph/9806029 |
Abstract
We define the model of quantum circuits with density matrices, where non-unitary gates are allowed. Measurements in the middle of the computation, noise and decoherence are implemented in a natural way in this model, which is shown to be equivalent in computational power to standard quantum circuits. The main result in this paper is a solution for the subroutine problem: The general function that a quantum circuit outputs is a probabilistic function, but using pure state language, such a function can not be used as a black box in other computations. We give a natural definition of using general subroutines, and analyze their computational power. We suggest convenient metrics for quantum computing with mixed states. For density matrices we analyze the so called ``trace metric'', and using this metric, we define and discuss the ``diamond metric'' on superoperators. These metrics enable a formal discussion of errors in the computation. Using a ``causality'' lemma for density matrices, we also prove a simple lower bound for probabilistic functions.
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"abstract": "We define the model of quantum circuits with density matrices, where\nnon-unitary gates are allowed. Measurements in the middle of the computation,\nnoise and decoherence are implemented in a natural way in this model, which is\nshown to be equivalent in computational power to standard quantum circuits.\n The main result in this paper is a solution for the subroutine problem: The\ngeneral function that a quantum circuit outputs is a probabilistic function,\nbut using pure state language, such a function can not be used as a black box\nin other computations. We give a natural definition of using general\nsubroutines, and analyze their computational power.\n We suggest convenient metrics for quantum computing with mixed states. For\ndensity matrices we analyze the so called ``trace metric\u0027\u0027, and using this\nmetric, we define and discuss the ``diamond metric\u0027\u0027 on superoperators. These\nmetrics enable a formal discussion of errors in the computation.\n Using a ``causality\u0027\u0027 lemma for density matrices, we also prove a simple\nlower bound for probabilistic functions.",
"arxiv_id": "quant-ph/9806029",
"authors": [
"Dorit Aharonov",
"Alexei Kitaev",
"Noam Nisan"
],
"categories": [
"quant-ph"
],
"title": "Quantum Circuits with Mixed States",
"url": "https://arxiv.org/abs/quant-ph/9806029"
},
"schema_id": "dorsal/arxiv",
"source": {
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"variant": "snapshot-2026-03-01",
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