Simple pulses for universal quantum computation with a HeisenbergABABchain
Open accessAbstract
Recently, Levy has shown that quantum computation may be performed using an $\mathrm{ABAB}\dots{}$ chain of spin-1/2 systems with nearest-neighbor Heisenberg interactions. Levy notes that all necessary elementary computational ``gates'' may be achieved purely by manipulating the spin-spin interaction: he proposes using ``spin-resonance'' techniques involving modulating the interaction strength at high frequency. Here, we establish an alternative: it is possible to perform the elementary gates via simple, nonoscillatory switching of the interaction strength. This approach removes a time ``bottle neck'' in Levy's scheme, so that all elementary operations may now be performed within a time scale of order $\ensuremath{\Elzxh}{/(E}_{A}\ensuremath{-}{E}_{B}).$
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The time evolution of the network in the S_G subspace can be expressed as a continuous-time quantum walk on G.
“Due to this, one may express the time evolution of the network in the S G subspace as a continuous-time quantum walk on G (first considered by Farhi and Gutmann in 1998 [10]).”
From Perfect State Transfer in Quantum Spin Networks (2004) · cites this paper as [10]
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Universal quantum computation with the exchange interaction
DiVincenzo, D. P., Bacon, D., Kempe, J., Burkard, G., & Whaley, K. B. (2000) · Nature · doi:10.1038/35042541 · Cited by 924 · see citing works
Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures
Vrijen, R. B., Yablonovitch, E., Wang, K., Jiang, H. W., Balandin, A. A., Roychowdhury, V., Mor, T., & Divincenzo, D. P. (2000) · Physical Review A · doi:10.1103/physreva.62.012306 · Cited by 836 · see citing works
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Perfect State Transfer in Quantum Spin Networks
Christandl, M., Datta, N., Ekert, A., & Landahl, A. J. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.187902 · Cited by 1,179 · see citing works
Prospects for Spin-Based Quantum Computing in Quantum Dots
Kloeffel, C., & Loss, D. (2013) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-030212-184248 · Cited by 404 · see citing works
Semiconductor qubits in practice
Chatterjee, A., Stevenson, P., Franceschi, S. D., Morello, A., de Leon, N. P., & Kuemmeth, F. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00283-9 · Cited by 387 · see citing works
Quantum Computing with an Always-On Heisenberg Interaction
Benjamin, S. C., & Bose, S. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.247901 · Cited by 190 · see citing works
Self-citationJones, J. A. (2010) · Progress in Nuclear Magnetic Resonance Spectroscopy · doi:10.1016/j.pnmrs.2010.11.001 · Cited by 185 · see citing works
Globally Controlled Quantum Wires for Perfect Qubit Transport, Mirroring, and Computing
Fitzsimons, J. F., & Twamley, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.090502 · Cited by 119 · see citing works
Reducing Constraints on Quantum Computer Design by Encoded Selective Recoupling
Lidar, D. A., & Wu, L.-A. (2001) · Physical Review Letters · doi:10.1103/physrevlett.88.017905 · Cited by 110 · see citing works
Singlet-triplet splitting in double quantum dots due to spin-orbit and hyperfine interactions
Stepanenko, D., Rudner, M. S., Halperin, B. I., & Loss, D. (2012) · Physical Review B · doi:10.1103/physrevb.85.075416 · Cited by 97 · see citing works
Universal Quantum Computation through Control of Spin-Orbit Coupling
Stepanenko, D., & Bonesteel, N. E. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.140501 · Cited by 81 · see citing works
Quantum Computing Without Local Control of Qubit-Qubit Interactions
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Quantum-dot cluster-state computing with encoded qubits
Weinstein, Y. S., Hellberg, C. S., & Levy, J. (2005) · Physical Review A · doi:10.1103/physreva.72.020304 · Cited by 59 · see citing works
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Warner, J. H., Watt, A. A. R., Ge, L., Porfyrakis, K., Akachi, T., Okimoto, H., Ito, Y., Ardavan, A., Montanari, B., Jefferson, J. H., et al. (2008) · Nano Letters · doi:10.1021/nl0726104 · Cited by 55 · see citing works
Quantum cellular automaton for universal quantum computation
Raussendorf, R. (2005) · Physical Review A · doi:10.1103/physreva.72.022301 · Cited by 54 · see citing works
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Benjamin, S. C., & Bose, S. (2004) · Physical Review A · doi:10.1103/physreva.70.032314 · Cited by 54 · see citing works
Self-citationExchange-based CNOT gates for singlet-triplet qubits with spin-orbit interaction
Klinovaja, J., Stepanenko, D., Halperin, B. I., & Loss, D. (2012) · Physical Review B · doi:10.1103/physrevb.86.085423 · Cited by 53 · see citing works
Implementation of chiral quantum optics with Rydberg and trapped-ion setups
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Wu, L.-A., Lidar, D. A., & Friesen, M. G. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.030501 · Cited by 37 · see citing works
All-electrical quantum computation with mobile spin qubits
Popescu, A., & Ionicioiu, R. (2004) · Physical Review B · doi:10.1103/physrevb.69.245422 · Cited by 32 · see citing works
Energetic suppression of decoherence in exchange-only quantum computation
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Time independent universal computing with spin chains: quantum plinko machine
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Self-citationMulti-Qubit Gates in Arrays Coupled by 'Always On' Interactions
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Self-citationSpin-swap gate in the presence of qubit inhomogeneity in a double quantum dot
Hu, X., & Sarma, S. D. (2003) · Physical Review A · doi:10.1103/physreva.68.052310 · Cited by 13 · see citing works
Quantum computation in semiconductor quantum dots of electron-spin asymmetric anisotropic exchange
Hao, X., & Zhu, S. (2007) · Physical Review A · doi:10.1103/physreva.76.044306 · Cited by 11 · see citing works
Compatible transformations for a qudit decoherence-free/noiseless encoding
Bishop, C. A., & Byrd, M. S. (2009) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/42/5/055301 · Cited by 11 · see citing works
Time-independent quantum circuits with local interactions
Seifnashri, S., Kianvash, F., Jahangir, N., & Karimipour, V. (2016) · Physical Review A · doi:10.1103/physreva.93.062342 · Cited by 6 · see citing works
Quantum Fault Tolerance in Systems with Restricted Control
Fitzsimons, J. F., & Twamley, J. (2009) · Electronic Notes in Theoretical Computer Science · doi:10.1016/j.entcs.2009.12.012 · Cited by 6 · see citing works
Decoupling neighboring qubits in quantum computers through bang–bang pulse control
Zhang, Y., Zhou, Z.-W., & Guo, G. (2004) · Physics Letters A · doi:10.1016/j.physleta.2004.05.019 · Cited by 6 · see citing works
Quantum Information Processing by NMR using strongly coupled spinsPreprint
Mahesh, T. S., Sinha, N., Ghosh, A., Das, R., Suryaprakash, N., Levitt, M. H., Ramanathan, K. V., & Kumar, A. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0212123 · Cited by 5 · see citing works
Compatible Transformations for a Qudit Decoherence-free/Noiseless EncodingPreprint
Bishop, C. A., & Byrd, M. (2012) · Cited by 5 · see citing works
Quantum computers and decoherence: exorcising the demon from the machine
Lidar, D. A., & Wu, L.-A. (2003) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.488754 · Cited by 4 · see citing works
Robust universal Hamiltonian quantum computing using two-body interactionsPreprint
Marvian, M., & Lloyd, S. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1911.01354 · Cited by 3 · see citing works
Quantum computation using controllable exchange interactions and a global magnetic field
Ye, M.-Y., Zhang, Y.-S., & Guo, G. (2006) · Physical Review A · doi:10.1103/physreva.73.024304 · Cited by 2 · see citing works
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Aiudi, R., Despres, J., Menta, R., Abedi, A., Menichetti, G., Giovannetti, V., Polini, M., & Caravelli, F. (2025) · Physical Review A · doi:10.1103/zzzc-nqxd · Cited by 1 · see citing works
Symmetry and control in spin-based quantum computing
Stepanenko, D. (2005) · Cited by 1 · see citing works
Building globally controlled quantum processors with Z Z interactions
Menta, R., Cioni, F., Aiudi, R., Caravelli, F., Polini, M., & Giovannetti, V. (2025) · Physical Review A · doi:10.1103/lz5d-lnz2 · Cited by 1 · see citing works
Implementation of the Fredkin gate with a three-qubit mixed-spin Heisenberg model
Fan, Q.-B. (2010) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-010-3209-9 · Cited by 1 · see citing works
Quantum dissonance in chiral graphene nanoribbons
Tan, X.-D., Kang, X.-B., Zhao, L.-M., Zhang, J., & Hao, H.-S. (2019) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/ab071c · Cited by 1 · see citing works
Quantum Computing with Spin and Valley Qubits in Quantum Dots
Rohling, N. (2015) · KOPS (University of Konstanz)
- Authors
- Benjamin, S. C.
- Affiliations
- University of Oxford (GB)
- Corresponding author
- Benjamin, Simon C.
- ORCID
- Benjamin, Simon C.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2001-10-18
- Volume
- 64
- Issue
- 5
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1987335061
- Cited by
- 49
- References
- 2
- Citations by year
- 2025: 2 · 2021: 1 · 2020: 1 · 2019: 2 · 2016: 3 · 2015: 1 · 2014: 1 · 2013: 1 · 2012: 3
- FWCI
- 7.45
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (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 and electron transport phenomena
- Keywords
- universal quantum computation, spin-1/2 systems, nearest-neighbor interactions, spin resonance
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