Quantum process tomography of the quantum Fourier transform
Open accessAbstract
The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The quantum operation studied was the quantum Fourier transform, which is important in several quantum algorithms and poses a rigorous test for the precision of our recently developed strongly modulating control fields. The results were analyzed in an attempt to decompose the implementation errors into coherent (overall systematic), incoherent (microscopically deterministic), and decoherent (microscopically random) components. This analysis yielded a superoperator consisting of a unitary part that was strongly correlated with the theoretically expected unitary superoperator of the quantum Fourier transform, an overall attenuation consistent with decoherence, and a residual portion that was not completely positive—although complete positivity is required for any quantum operation. By comparison with the results of computer simulations, the lack of complete positivity was shown to be largely a consequence of the incoherent errors which occurred over the full quantum process tomography procedure. These simulations further showed that coherent, incoherent, and decoherent errors can often be identified by their distinctive effects on the spectrum of the overall superoperator. The gate fidelity of the experimentally determined superoperator was 0.64, while the correlation coefficient between experimentally determined superoperator and the simulated superoperator was 0.79; most of the discrepancies with the simulations could be explained by the cummulative effect of small errors in the single qubit gates.
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Experimental results suggest that even a structured transformation such as the quantum Fourier transform is sufficiently complex to approximately average the cumulative noise to an effective depolarizing channel.
“Indeed the experimental results of Ref. [2] suggest that even a structured transformation such as the quantum Fourier transform is sufficiently complex to approximately average the cumulative noise to an effective depolarizing channel”
From Scalable noise estimation with random unitary operators (2005) · cites this paper as [2]
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- Authors
- Weinstein, Y. S., Havel, T. F., Emerson, J., Boulant, N., Saraceno, M., Lloyd, S., & Cory, D. G.
- Affiliations
- Massachusetts Institute of Technology (US)
- Comisión Nacional de Energía Atómica (AR)
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 2004-10-01
- Volume
- 121
- Issue
- 13
- Pages
- 6117-6133
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W1986937067
- Cited by
- 178
- References
- 34
- Citations by year
- 2026: 4 · 2025: 10 · 2024: 3 · 2023: 3 · 2022: 3 · 2021: 12 · 2020: 4 · 2019: 8 · 2018: 7 · 2017: 4 · 2016: 6 · 2015: 13 · 2014: 13 · 2013: 11 · 2012: 10
- FWCI
- 9.81
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- The Journal of Chemical Physics (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum process tomography, quantum Fourier transform, three-qubit systems, decoherence, complete positivity, gate fidelity, quantum gate errors
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