Universal quantum computation with the exchange interaction
Open accessAbstract
Various physical implementations of quantum computers are being investigated, although the requirements that must be met to make such devices a reality in the laboratory at present involve capabilities well beyond the state of the art. Recent solid-state approaches have used quantum dots, donor-atom nuclear spins or electron spins; in these architectures, the basic two-qubit quantum gate is generated by a tunable exchange interaction between spins (a Heisenberg interaction), whereas the one-qubit gates require control over a local magnetic field. Compared to the Heisenberg operation, the one-qubit operations are significantly slower, requiring substantially greater materials and device complexity--potentially contributing to a detrimental increase in the decoherence rate. Here we introduced an explicit scheme in which the Heisenberg interaction alone suffices to implement exactly any quantum computer circuit. This capability comes at a price of a factor of three in additional qubits, and about a factor of ten in additional two-qubit operations. Even at this cost, the ability to eliminate the complexity of one-qubit operations should accelerate progress towards solid-state implementations of quantum computation.
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The array of 12 quantum dots can be operated as physical qubits in a variety of spin encodings, including single spin qubits or exchange-only qubits.
“The array of 12 quantum dots can be operated as physical qubits in a variety of spin encodings, including single spin qubits39 (in a 12-qubit array) or exchange-only qubits40 (in a four-qubit array).”
From Probing single electrons across 300-mm spin qubit wafers (2024) · cites this paper as [40]
The main text (p. 3) describes an exchange-based encoding that uses three spins per coded qubit, so a 12-spin array could in principle hold four such qubits. The paper does not establish that the citing authors’ particular 12-quantum-dot array can be operated this way; it presents a theoretical scheme rather than an operation of that array. (LLM, conf=0.85)
Experimental — accuracy not yet measuredThe classical mean hitting time between the antipodes in a one-link and two-link d-dimensional hypercube is given, for large d, by 2^d and 3^d, respectively.
“The classical mean hitting time between the antipodes in a one-link and two-link d -dimensional hypercube is given, for large d , by 2 d and 3 d , respectively.”
From Perfect State Transfer in Quantum Spin Networks (2004) · cites this paper as [12]
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Cites
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Research works printed but not linked: 1
- [10][10] J. Kempe, D. Bacon, D.A. Lidar and K.B. Whaley, 'Theory of Decoherence-Free FaultTolerant Universal Quantum Compuation,' submitted to Physical Review A, quantph/0004064. -
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- Authors
- DiVincenzo, D. P., Bacon, D., Kempe, J., Burkard, G., & Whaley, K. B.
- Affiliations
- IBM (United States) (US)
- Télécom Paris (FR)
- University of Basel (CH)
- Corresponding author
- DiVincenzo, D. P.
- Venue
- Nature
- Published
- 2000-11
- Volume
- 408
- Issue
- 6810
- Pages
- 339-342
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- OpenAlex
- W1629173918
- Cited by
- 924
- References
- 28
- Citations by year
- 2026: 27 · 2025: 36 · 2024: 19 · 2023: 20 · 2022: 24 · 2021: 38 · 2020: 30 · 2019: 30 · 2018: 39 · 2017: 37 · 2016: 39 · 2015: 38 · 2014: 33 · 2013: 32 · 2012: 46
- FWCI
- 27.51
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nature (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- universal quantum computation, exchange interaction, Heisenberg exchange interaction, spin qubits, two-qubit gates, one-qubit gates, solid-state quantum computing, decoherence
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