Bulk quantum computation with nuclear magnetic resonance: theory and experiment
Abstract
We show that quantum computation is possible with mixed states instead of pure states as inputs. This is performed by embedding within the mixed state a subspace that transforms like a pure state and that can be identified by labelling it based on logical (spin), temporal, or spatial degrees of freedom. This permits quantum computation to be realized with bulk ensembles far from the ground state. Experimental results are presented for quantum gates and circuits implemented with liquid nuclear magnetic resonance techniques and verified by quantum state tomography.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For N spins, the signal from the initial state 00...0 is proportional to n_{00...0} ∝ N Z^{-N}, where the single spin partition function Z ≈ 2 at high temperatures.
“for N spins the signal from the initial state 00 . . . 0 is proportional to n 00 ... 0 ∝ NZ -N where the single spin partition function Z ≈ 2 at high temperatures.”
From Experimental realization of a quantum algorithm (1998) · cites this paper as [25]
NMR quantum computers larger than about 10 qubits will require creative new approaches, since the signal strength decays exponentially with the number of qubits in the machine, using current schemes.
“However, NMR quantum computers larger than about 10 qubits will require creative new approaches, since the signal strength decays exponentially with the number of qubits in the machine, using current schemes 24,25 : for N spins the signal from the initial state 00 . . . 0 is proportional to n 00 ... 0 ∝ NZ -N where the single spin partition function Z ≈ 2 at high temperatures.”
From Experimental realization of a quantum algorithm (1998) · cites this paper as [25]
Cites
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
Einstein, A., Podolsky, B., & Rosen, N. (1935) · Physical Review · doi:10.1103/physrev.47.777 · Cited by 16,654 · see citing works
Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
Shor, P. W. (1997) · SIAM Journal on Computing · doi:10.1137/s0097539795293172 · Cited by 8,472 · see citing works
Elementary gates for quantum computation
Barenco, A., Bennett, C. H., Cleve, R., DiVincenzo, D. P., Margolus, N., Shor, P., Sleator, T., Smolin, J. A., & Weinfurter, H. (1995) · Physical Review A · doi:10.1103/physreva.52.3457 · Cited by 4,311 · see citing works
Principles of Nuclear Magnetic Resonance in One and Two Dimensions
Ernst, R. R., Bodenhausen, G., Wokaun, A. J., & Redfield, A. G. (1989) · Physics Today · doi:10.1063/1.2811094 · Cited by 4,202 · see citing works
Quantum Computations with Cold Trapped Ions
Cirac, J. I., & Zoller, P. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4091 · Cited by 3,733 · see citing works
Feynman, R. P. (1986) · Foundations of Physics · doi:10.1007/bf01886518 · Cited by 1,770 · see citing works
DiVincenzo, D. P. (1995) · Science · doi:10.1126/science.270.5234.255 · Cited by 1,651 · see citing works
Bulk Spin-Resonance Quantum Computation
Gershenfeld, N. A., & Chuang, I. L. (1997) · Science · doi:10.1126/science.275.5298.350 · Cited by 1,528 · see citing works
Self-citationMeasurement of Conditional Phase Shifts for Quantum Logic
Turchette, Q. A., Hood, C. J., Lange, W., Mabuchi, H., & Kimble, H. J. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.4710 · Cited by 1,409 · see citing works
Two-bit gates are universal for quantum computation
DiVincenzo, D. P. (1995) · Physical Review A · doi:10.1103/physreva.51.1015 · Cited by 1,069 · see citing works
Ensemble quantum computing by NMR spectroscopy
Cory, D. G., Fahmy, A. F., & Havel, T. F. (1997) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.94.5.1634 · Cited by 964 · see citing works
Sending entanglement through noisy quantum channels
Schumacher, B. W. (1996) · Physical Review A · doi:10.1103/physreva.54.2614 · Cited by 824 · see citing works
General state changes in quantum theory
Kraus, K. (1971) · Annals of Physics · doi:10.1016/0003-4916(71)90108-4 · Cited by 749 · see citing works
Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate
Poyatos, J. F., Cirac, J. I., & Zoller, P. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.390 · Cited by 694 · see citing works
A Potentially Realizable Quantum Computer
Lloyd, S. (1993) · Science · doi:10.1126/science.261.5128.1569 · Cited by 649 · see citing works
Maintaining coherence in quantum computers
Unruh, W. G. (1995) · Physical Review A · doi:10.1103/physreva.51.992 · Cited by 594 · see citing works
The development of the number field sieve
Lenstra, A. K., Lenstra, H. W., Lenstra, A. K., Lenstra, H. W., Manasse, M. S., & Pollard, J. M. (1993) · Lecture notes in mathematics · doi:10.1007/bfb0091534 · Cited by 575 · see citing works
Realizable Universal Quantum Logic Gates
Sleator, T., & Weinfurter, H. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4087 · Cited by 515 · see citing works
Chuang, I. L., & Yamamoto, Y. (1995) · Physical Review A · doi:10.1103/physreva.52.3489 · Cited by 437 · see citing works
Self-citationQuantum Computers, Factoring, and Decoherence
Chuang, I. L., Laflamme, R., Shor, P. W., & Zurek, W. H. (1995) · Science · doi:10.1126/science.270.5242.1633 · Cited by 289 · see citing works
Self-citationEffective pure states for bulk quantum computation
Knill, E., Chuang, I., & Laflamme, R. (1998) · Physical Review A · doi:10.1103/physreva.57.3348 · Cited by 245 · see citing works
Self-citationStudy of the Aharonov-Anandan quantum phase by NMR interferometry
Suter, D., Mueller, K. T., & Pines, A. (1988) · Physical Review Letters · doi:10.1103/physrevlett.60.1218 · Cited by 241 · see citing works
Study of the Aharonov-Anandan Phase by NMR Interferometry
Suter, D., Mueller, K. T., & Pines, A. (1988) · Technische Universität Dortmund Eldorado (Technische Universität Dortmund) · doi:10.17877/de290r-3226 · Cited by 135 · see citing works
Landauer, R. (1995) · Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences · doi:10.1098/rsta.1995.0106 · Cited by 124 · see citing works
Realistic lower bounds for the factorization time of large numbers on a quantum computer
Plenio, M. B., & Knight, P. L. (1996) · Physical Review A · doi:10.1103/physreva.53.2986 · Cited by 112 · see citing works
A general number field sieve implementation
Bernstein, D. J., & Lenstra, A. K. (1993) · Lecture notes in mathematics · doi:10.1007/bfb0091541 · Cited by 95 · see citing works
Low-temperature magnetic resonance force detection
Wago, K., Züǵer, O., Kendrick, R. D., et al. (1996) · Journal of Vacuum Science & Technology B Microelectronics and Nanometer Structures Processing Measurement and Phenomena · doi:10.1116/1.588513 · Cited by 58 · see citing works
Bandyopadhyay, S. B. S., & Roychowdhury, V. (1996) · Japanese Journal of Applied Physics · doi:10.1143/jjap.35.3350 · Cited by 47 · see citing works
Indirect Phase Detection of NMR Spinor Transitions
Suter, D., Pines, A., & Mehring, M. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.242 · Cited by 24 · see citing works
Necessary and Sufficient Conditions for Quantum Computation
Lloyd, S. (1994) · Journal of Modern Optics · doi:10.1080/09500349414552341 · Cited by 19 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
NMR techniques for quantum control and computation
Vandersypen, L. M. K., & Chuang, I. L. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.76.1037 · Cited by 1,217 · see citing works
Self-citationExperimental 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-citationSeparability of Very Noisy Mixed States and Implications for NMR Quantum Computing
Braunstein, S. L., Caves, C. M., Jozsa, R., Linden, N., Popescu, S., & Schack, R. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.1054 · Cited by 566 · see citing works
Bell States of Atoms with Ultralong Lifetimes and Their Tomographic State Analysis
Roos, C. F., Lancaster, G. P. T., Riebe, M., Häffner, H., Hänsel, W., Gulde, S., Becher, C., Eschner, J., Schmidt-Kaler, F., & Blatt, R. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.220402 · Cited by 241 · see citing works
Effective pure states for bulk quantum computation
Knill, E., Chuang, I., & Laflamme, R. (1998) · Physical Review A · doi:10.1103/physreva.57.3348 · Cited by 245 · see citing works
Self-citationCalculating the thermal rate constant with exponential speedup on a quantum computer
Lidar, D. A., & Wang, H. (1999) · Physical Review E · doi:10.1103/physreve.59.2429 · Cited by 115 · see citing works
Implementation of a three-quantum-bit search algorithm
Vandersypen, L. M. K., Steffen, M., Sherwood, M. H., Yannoni, C. S., Breyta, G., & Chuang, I. L. (2000) · Applied Physics Letters · doi:10.1063/1.125846 · Cited by 131 · see citing works
Self-citationClassical model for bulk-ensemble NMR quantum computation
Schack, R., & Caves, C. M. (1999) · Physical Review A · doi:10.1103/physreva.60.4354 · Cited by 76 · see citing works
Local Realistic Model for the Dynamics of Bulk-Ensemble NMR Information Processing
Menicucci, N. C., & Caves, C. M. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.167901 · Cited by 43 · see citing works
- Authors
- Chuang, I. L., Gershenfeld, N., Kubinec, M. G., & Leung, D. W.
- Affiliations
- Los Alamos National Laboratory (US)
- MIT Media Lab (US)
- University of California, Berkeley (US)
- Stanford University (US)
- Venue
- Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- Publisher
- The Royal Society
- Published
- 1998-01-08
- Volume
- 454
- Issue
- 1969
- Pages
- 447-467
- ISSN
- 1364-5021 (ISSN-L)
- 1471-2946
- OpenAlex
- W2100715286
- Cited by
- 316
- References
- 30
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 5 · 2023: 4 · 2022: 5 · 2021: 4 · 2020: 3 · 2019: 4 · 2018: 12 · 2017: 9 · 2016: 8 · 2015: 11 · 2014: 3 · 2013: 7 · 2012: 7
- FWCI
- 33.75
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences (publishedVersion)
- 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
- nuclear magnetic resonance, mixed states, quantum gates, quantum circuits, quantum state tomography, spin ensembles, logical qubits, spatial degrees of freedom
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
