Effective pure states for bulk quantum computation
Open accessAbstract
In bulk quantum computation one can manipulate a large number of indistinguishable quantum computers by parallel unitary operations and measure expectation values of certain observables with limited sensitivity. The initial state of each computer in the ensemble is known but not pure. Methods for obtaining effective pure input states by a series of manipulations have been described by Gershenfeld and Chuang (logical labeling) [Science 275, 350 (1997)] and Cory et al. (spatial averaging) [Proc. Natl. Acad. Sci. USA 94, 1634 (1997)] for the case of quantum computation with nuclear magnetic resonance. We give a different technique called temporal averaging. This method is based on classical randomization, requires no ancilla quantum bits, and can be implemented in nuclear magnetic resonance without using gradient fields. We introduce several temporal averaging algorithms suitable for both high-temperature and low-temperature bulk quantum computing and analyze the signal-to-noise behavior of each. Most of these algorithms require only a constant multiple of the number of experiments needed by the other methods for creating effective pure states.
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The longitudinal and transverse relaxation time constants T1 and T2 were measured using standard inversion-recovery and Carr-Purcell-Meiboom-Gill pulse sequences, giving T1 ≈ 19 and 25 seconds, and T2 ≈ 7 and 0.3 seconds, respectively, for proton and carbon.
“The longitudinal and transverse relaxation time constants T 1 and T 2 were measured using standard inversion-recovery and Carr-Purcell-MeiboomGill pulse sequences 23 , giving T 1 ≈ 19 and 25 seconds, and T 2 ≈ 7 and 0 . 3 seconds, respectively, for proton and carbon; these were much longer than required for our experiment, which finished in about 7 milliseconds.”
From Experimental realization of a quantum algorithm (1998) · cites this paper as [23]
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Research works printed but not linked: 2
- [3]D. G. Cory, A. F. Fahmy, and T. F. Havel, in Proceedings of the 4th Workshop on Physics and Computation (New England Complex Systems Institute, Boston, Massachusetts, 1996), pp. 87-91.
- [4]D. G. Cory, A. F. Fahmy, and T. F. Havel, Proceedings of the National Academy of Sciences of the United States of America 94 , 1634 (1997).
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Experimental realization of a quantum algorithm
Chuang, I. L., Vandersypen, L. M. K., Zhou, X., Leung, D. W., & Lloyd, S. (1998) · Nature · doi:10.1038/30181 · Cited by 604 · see citing works
Self-citationExperimental Quantum Error Correction
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Self-citationNuclear magnetic resonance spectroscopy: An experimentally accessible paradigm for quantum computing
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Bulk quantum computation with nuclear magnetic resonance: theory and experiment
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Self-citationAn algorithmic benchmark for quantum information processing
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Self-citationClassical model for bulk-ensemble NMR quantum computation
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- Authors
- Knill, E., Chuang, I., & Laflamme, R.
- Affiliations
- Los Alamos National Laboratory (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1998-05-01
- Volume
- 57
- Issue
- 5
- Pages
- 3348-3363
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2262539039
- Cited by
- 245
- References
- 14
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 3 · 2023: 4 · 2022: 5 · 2021: 5 · 2020: 4 · 2019: 7 · 2018: 5 · 2017: 6 · 2016: 6 · 2015: 5 · 2014: 3 · 2013: 7 · 2012: 3
- FWCI
- 28.65
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- University of North Texas Digital Library (University of North Texas) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (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
- time averaging, nuclear magnetic resonance, spatial averaging
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