Exact and approximate unitary 2-designs and their application to fidelity estimation

Journal Article · Wed Jul 15 00:00:00 EDT 2009 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.80.012304· OSTI ID:21313214

Dankert, Christoph ^[1]; Cleve, Richard ^[1]; Emerson, Joseph ^[2]; Livine, Etera ^[3]

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1. David R. Cheriton School of Computer Science and Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada)
2. Department of Applied Mathematics and Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada)
3. Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, N2L 2Y5 (Canada)

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{sup 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.

• OSTI ID: 21313214
• Journal Information: Physical Review. A, Vol. 80, Issue 1; Other Information: DOI: 10.1103/PhysRevA.80.012304; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
DESIGN
GROUP THEORY
INFORMATION THEORY
PROBABILITY
QUBITS
STOCHASTIC PROCESSES