Interaction Cost of Nonlocal Gates
Open accessAbstract
We introduce the interaction cost of a nonlocal gate as the minimal time of interaction required to perform the gate when assisting the process with fast local unitaries. This cost, of interest both in the areas of quantum control and quantum information, depends on the specific interaction, and allows one to compare in an operationally meaningful manner any two nonlocal gates. In the case of a two-qubit system, an analytical expression for the interaction cost of any unitary operation given any coupling Hamiltonian is obtained. One gate may be more time consuming than another for any possible interaction. This defines a partial order structure in the set of nonlocal gates, that compares their degree of nonlocality. We analytically characterize this partial order in a region of the set of two-qubit gates.
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With Ising interactions, letting the resonant Hamiltonian act for a time π/(2J) produces an iSWAP gate, apart from single-qubit rotations.
“When allowed to act for a duration t = π/(2J ), the Hamiltonian in Eq. ( 4) effects an iSWAP gate, in addition to two single-qubit rotations.”
From Speed limits for quantum gates in multiqubit systems (2012) · cites this paper as [14]
With Ising interactions and both single-qubit parameters set to zero, letting the Hamiltonian act for π/(4J) produces a CZ gate, apart from single-qubit rotations and an overall phase.
“When allowed to act for a duration t = π/(4J ), the Hamiltonian in Eq. ( 5) effects a CZ gate, in addition to two single-qubit rotations and an (unimportant) overall phase factor.”
From Speed limits for quantum gates in multiqubit systems (2012) · cites this paper as [14]
A CNOT gate can be built from a CZ gate plus two π/2 pulses on the target qubit, so its time with Ising interactions is about π/(4J).
“The CNOT gate can be obtained by combining the CZ gate with two single-qubit gates.These are π/2 pulses applied to the target qubit before and after the CZ gate.As a result, the amount of time required to obtain the CNOT gate using this approach is approximately equal to the amount of time required for the CZ gate, i.e., π/(4J ) with Ising interactions.”
From Speed limits for quantum gates in multiqubit systems (2012) · cites this paper as [14]
With Heisenberg interactions and equal single-qubit parameters, letting the system evolve for π/(8J) produces a √SWAP gate.
“In this case, one sets 1 = 2 and 1 = 2 , and after a time t = π/(8J ), one obtains the √ SWAP gate.”
From Speed limits for quantum gates in multiqubit systems (2012) · cites this paper as [14]
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Cites
Time optimal control in spin systems
Khaneja, N., Brockett, R. W., & Glaser, S. J. (2001) · Physical Review A · doi:10.1103/physreva.63.032308 · Cited by 755 · see citing works
Optimal creation of entanglement using a two-qubit gate
Kraus, B., & Cirac, J. I. (2001) · Physical Review A · doi:10.1103/physreva.63.062309 · Cited by 432 · see citing works
Self-citationEntanglement Capabilities of Nonlocal Hamiltonians
Dür, W., Vidal, G., Cirac, J. I., et al. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.137901 · Cited by 173 · see citing works
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Research works printed but not linked: 2
- [1]N. Khaneja, R. Brockett and S.J. Glaser, Phys. Rev. A 63, 032308 (2001).
- [4]W. D¨ ur, G. Vidal, J.I. Cirac, N. Linden and S. Popescu, Phys. Rev. Lett. 87, 137901 (2001).
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Time-optimal unitary operations
Carlini, A., Hosoya, A., Koike, T., & Okudaira, Y. (2007) · Physical Review A · doi:10.1103/physreva.75.042308 · Cited by 126 · see citing works
Speed limits for quantum gates in multiqubit systems
Ashhab, S., de Groot, P. C., & Nori, F. (2012) · Physical Review A · doi:10.1103/physreva.85.052327 · Cited by 89 · see citing works
- Authors
- Vidal, G., Hammerer, K., & Cirac, J. I.
- Affiliations
- Universität Innsbruck (AT)
- Max Planck Institute of Quantum Optics (DE)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2002-05-24
- Volume
- 88
- Issue
- 23
- Pages
- 237902-237902
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1982747126
- Cited by
- 89
- References
- 3
- Citations by year
- 2026: 1 · 2025: 6 · 2024: 1 · 2023: 4 · 2022: 2 · 2021: 1 · 2020: 1 · 2019: 3 · 2018: 1 · 2017: 1 · 2015: 4 · 2014: 2 · 2013: 1 · 2012: 2
- FWCI
- 11.00
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- interaction costs, two-qubit gates, local unitaries, quantum control, partially ordered sets, time-optimal control
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