dorsal/arxiv
View SchemaExact and Approximate Unitary 2-Designs: Constructions and Applications
| Authors | Christoph Dankert, Richard Cleve, Joseph Emerson, Etera Livine |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606161 |
| URL | https://arxiv.org/abs/quant-ph/0606161 |
| DOI | 10.1103/PhysRevA.80.012304 |
| Journal | Physical Review A 80, 012304 (2009) |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We develop the concept of a unitary t-design as a means of expressing operationally useful subsets of the stochastic properties of the uniform (Haar) measure on the unitary group U(2^n) on n qubits. In particular, sets of unitaries forming 2-designs have wide applicability to quantum information protocols. We devise an O(n)-size in-place circuit construction for an approximate unitary 2-design. We then show that this can be used to construct an efficient protocol for experimentally characterizing the fidelity of a quantum process on n qubits with quantum circuits of size O(n) without requiring any ancilla qubits, thereby improving upon previous approaches.
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"abstract": "We develop the concept of a unitary t-design as a means of expressing\noperationally useful subsets of the stochastic properties of the uniform (Haar)\nmeasure on the unitary group U(2^n) on n qubits. In particular, sets of\nunitaries forming 2-designs have wide applicability to quantum information\nprotocols. We devise an O(n)-size in-place circuit construction for an\napproximate unitary 2-design. We then show that this can be used to construct\nan efficient protocol for experimentally characterizing the fidelity of a\nquantum process on n qubits with quantum circuits of size O(n) without\nrequiring any ancilla qubits, thereby improving upon previous approaches.",
"arxiv_id": "quant-ph/0606161",
"authors": [
"Christoph Dankert",
"Richard Cleve",
"Joseph Emerson",
"Etera Livine"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.80.012304",
"journal_ref": "Physical Review A 80, 012304 (2009)",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Exact and Approximate Unitary 2-Designs: Constructions and Applications",
"url": "https://arxiv.org/abs/quant-ph/0606161"
},
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