Speed limits for quantum gates in multiqubit systems
Open accessAbstract
We use analytical and numerical calculations to obtain speed limits for various unitary quantum operations in multiqubit systems under typical experimental conditions. The operations that we consider include single-, two-, and three-qubit gates, as well as quantum-state transfer in a chain of qubits. We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates. We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system's geometry, taking only slightly longer than a two-qubit controlled-not (cnot) gate for a triangle geometry. The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.
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- Findingown data
In a triangle geometry, the Toffoli gate takes only a little more time than a CNOT gate.
“taking only slightly longer than a two-qubit controlled-NOT (CNOT) gate for a triangle geometry.”
- Also stated in: § Chain · plain
“for the triangle geometry, we find Toffoli gate times that are smaller than twice the minimum time required for a CNOT gate with the same coupling strength.”
Quote in the paperSubstantial claim - Also stated in: § Chain · plain
- Findingown data
The time needed for the three-qubit Toffoli gate depends strongly on the interaction type and the geometry of the system.
“We also find that the three-qubit Toffoli gate time varies greatly depending on the type of interactions and the system's geometry”
Quote in the paperSubstantial claim - Findingown data
For the iSWAP gate with Ising interactions, the fixed-parameter numerical estimate is about 25% larger than the tunable estimate.
“The speed limit that we find numerically for the fixed-case is about 25% higher than that for the tunable-case.”
Quote in the paperNot a substantial claim - Findingown data
In a chain geometry, the Toffoli gate requires about three times the minimum CNOT gate time.
“The Toffoli gate requires approximately three times the minimum time required for a CNOT gate in a chain geometry”
Quote in the paperSubstantial claim - Findingown data
For a triangle geometry, the Toffoli gate time found here is less than twice the CNOT gate time with the same coupling strength.
“for the triangle geometry, we find Toffoli gate times that are smaller than twice the minimum time required for a CNOT gate with the same coupling strength.”
Quote in the paperSubstantial claim
- Findingreasoning
For the iSWAP gate, Heisenberg and Ising interactions yield the same minimum gate time.
“such that Heisenberg interactions and Ising interactions give the same minimum gate times.”
Quote in the paperSubstantial claim - Findingnone given
For Ising interactions, the spin-wave energy spectrum is E_k = 2J cos k.
“The energy spectrum of these waves is given by E k = 2J cos k.”
Quote in the paperSubstantial claim - Findingown data
For the √SWAP gate with Heisenberg interactions, the numerical fidelity data are well fitted by a function that gives a minimum gate time of π/(8J).
“We can see that the results fit very well with a function that gives the gate time π/(8J ).”
Quote in the paperSubstantial claim - Findingreasoning
For Ising interactions, the maximum group velocity of a wave packet in the chain is 2J.
“which has a maximum at k = π/2, and the maximum is given by 2J .”
Quote in the paperSubstantial claim - Findingown data
For the two-qubit gates examined, the minimum gate times are essentially the same whether the single-qubit parameters are fixed or tunable.
“The main observation that we make from the results in Table I is that all of the results remained unchanged whether the parameters i were taken to be fixed or tunable, a result that is not a priori obvious.”
Quote in the paperSubstantial claim - Interpretationreasoning
Because single-qubit Hamiltonian parameters are usually much larger than the interqubit coupling, interactions between qubits can be neglected for single-qubit gates.
“Since the parameters of the single-qubit Hamiltonian are typically much larger than the interqubit coupling strength, one can ignore interqubit interactions when performing single-qubit gates.”
Quote in the paperNot a substantial claim- Rests on an assumption: Single-qubit Hamiltonian parameters are typically much larger than the interqubit coupling strength.
- Interpretationreasoning
For single-qubit operations, the speed limit is determined by the smaller of the two largest achievable qubit parameters.
“One can therefore say that the speed limit is set by the smaller of the two qubit parameters (or, more accurately, the smaller of the largest achievable values of the two parameters), which in the above example is .”
- Also stated in: § VII. CONCLUSION · plain
“Single-qubit operation speeds are limited by the smaller of the Pauli-matrix coefficients in the Hamiltonian.”
Quote in the paperSubstantial claim- Rests on an assumption: Single-qubit Hamiltonian parameters are typically much larger than the interqubit coupling strength.
- Also stated in: § VII. CONCLUSION · plain
- Interpretationreasoning
The limiting speed for transferring a quantum state along a qubit chain is the maximum spin-wave speed in that chain.
“The speed limit for quantum-state transfer across a qubit chain is set by the maximum spin-wave speed in the chain.”
- Also stated in: § VI. QUANTUM-STATE TRANSFER IN A CHAIN OF QUBITS · plain
“The speed limit is then determined by the maximum group velocity of a wave packet traveling through the chain.”
Quote in the paperSubstantial claim - Also stated in: § VI. QUANTUM-STATE TRANSFER IN A CHAIN OF QUBITS · plain
- Premisecitation
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.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [14] source
Not checked in the free run.
- Premisecitation
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.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [14] source
Not checked in the free run.
- Interpretationcitation
For two-qubit gates, straightforward implementation techniques are usually time-optimal.
“We find in particular that simple methods for implementing two-qubit gates generally provide the fastest possible implementations of these gates.”
- Also stated in: § IV. TWO-QUBIT GATES · plain
“The basic techniques, which can also be shown to be time optimal [6], are summarized as follows [14].”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [6] source
Not checked in the free run.
- Also stated in: § IV. TWO-QUBIT GATES · plain
- Interpretationreasoning
The interqubit coupling strength is the factor that limits the speed of two-qubit gates.
“The coupling strength must, however, be the limiting factor for performing two-qubit gates.”
Quote in the paperSubstantial claim - Interpretationreasoning
For the iSWAP gate with Ising interactions, the speed limit is π/(2J) for both fixed and tunable single-qubit parameters.
“Since the fixed-speed limit cannot be higher than the tunable-speed limit, one can conclude that the speed limit is π/(2J ) in both cases.”
Quote in the paperSubstantial claim - Interpretationnone given
The minimum transfer time N/(2J) is faster by a factor of π than applying iSWAP operations sequentially along the chain.
“It is worth noting that T min is faster by a factor of π than the sequential application of iSWAP operations across the chain.”
Quote in the paperSubstantial claim - Interpretationown data
For triangle geometry, the Toffoli gate time factor 1.9 is about 15% better than the 2.2 factor from Ref. [3].
“In particular, one can compare the factor 1.9 in Table II with the corresponding factor of 2.2 in Ref. [3]: an improvement of about 15%.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [3] source
Not checked in the free run.
- Interpretationreasoning
The 25% discrepancy between fixed and tunable iSWAP estimates is due to numerical inaccuracies.
“However, this difference is again caused by numerical inaccuracies.”
Quote in the paperNot a substantial claim - Interpretationreasoning
For Heisenberg interactions with one excitation, the dynamics reduce to those of Ising interactions with twice the coupling strength.
“Taking J , = 0, and assuming only one excitation in the system, the problem reduces to that with Ising interactions but with twice the coupling strength”
Quote in the paperSubstantial claim- The authors state this as an assumption: For the Heisenberg state-transfer analysis, the system contains only one excitation.
- Interpretationnone given
For Heisenberg interactions, the wave propagation speed does not depend on the external fields.
“For the case of Heisenberg interactions, the speed of wave propagation is independent of the external fields.”
Quote in the paperNot a substantial claim - Premisecitation
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.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [14] source
Not checked in the free run.
- Premisecitation
Six CNOT gates are the minimum number needed to construct a Toffoli gate.
“Recently it has been shown that this number (i.e., six) is the minimum number of CNOT gates required in order to construct the Toffoli gate [18].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [18] source
Not checked in the free run.
- Interpretationreasoning
Heisenberg interactions do not always produce faster two-qubit gates than Ising interactions.
“it is not the case that Heisenberg interactions will always result in faster two-qubit gates.”
Quote in the paperSubstantial claim - Interpretationown data
The Toffoli gate times reported here are faster than previous literature results for the maximum speed of Toffoli gates.
“We should point out here that the results presented here give faster gates than any results for the maximum speed of Toffoli gates in the literature [2,3].”
Quote in the paperSubstantial claim0 of 2 sources checked - Interpretationnone given
Two-qubit gate speeds are limited by the interqubit coupling strength.
“As expected, two-qubit gate speeds are limited by the interqubit coupling strength.”
Quote in the paperSubstantial claim - Interpretationreasoning
For Ising interactions, the condition J is optimal for maximizing the propagation speed.
“We therefore conclude that the condition J is optimal for maximizing the propagation speed.”
Quote in the paperSubstantial claim
- May combine two claims. 4
- Classified as probably not a substantial claim. 2
May combine two claims.
Interpretationnone givenReaching the maximum wave speed is not enough for high-fidelity state transfer; the state must also be transferred without distortion.
“Even though the maximum wave speed sets an upper limit to the speed of quantum-state transfer, one still needs to make sure that the quantum state is transferred without distortion.”
Quote in the paperSubstantial claimMay combine two claims.
Study design and conductown dataThe numerical Toffoli gate times may be substantially larger than the true minimum because the results depend on guess pulses and do not yield smooth fitting functions.
“we would like to point out that the results of the calculations also showed stronger dependence on the guess pulses than in the case of two-qubit gates (the data also did not result in smooth fitting functions as shown in Fig. 2).We therefore cannot exclude the possibility that some of the expressions in Table II are substantially larger than the true minimum gate time.”
Quote in the paperSubstantial claimMay combine two claims.
PremisereasoningA 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.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [14] source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationAn optimal-control calculation found a Toffoli gate time of about 2.2 times the CNOT gate time for qubits in a triangle geometry.
“An optimal-control-theory-related calculation based on certain forms of pulses has found a gate time of about 2.2 times the CNOT gate time for qubits coupled in a triangle geometry [3].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [3] source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
InterpretationcitationThe Heisenberg minimum transfer time expression agrees with the one given in Ref. [11].
“This expression is essentially the same as the one given in Ref. [11].”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [11] source
Not checked in the free run.
May combine two claims.
Interpretationnone givenThe speed-limit expressions derived here agree with known analytical results and with recent numerical results.
“The expressions that we find agree with analytical results known in the literature and also with recent numerical results.”
Quote in the paperNot a substantial claim
The authors state this as an assumption.
Qubits can be described using only two quantum states.
“With the assumption of two-state qubits, the single-qubit Hamiltonian can be expressed in terms of the two-dimensional Pauli matrices σα (with α = x, y, or z):”
The authors state this as an assumption.
Any arbitrary driving signal can be applied to the system.
“We shall assume that any arbitrary driving signal can be applied to the system.”
The paper relies on this without support.
Single-qubit Hamiltonian parameters are typically much larger than the interqubit coupling strength.
“The parameters of the single-qubit Hamiltonian are typically much larger than the interqubit coupling strength, i.e., J , .”
The paper relies on this without support.
Single-qubit gate durations are typically negligibly short compared with two- or multiqubit gate durations.
“Furthermore, performing single-qubit gates typically requires a negligibly short duration compared to the duration required for performing a two-or multiqubit gate”
The authors state this as an assumption.
For the Heisenberg state-transfer analysis, the system contains only one excitation.
“Taking J , = 0, and assuming only one excitation in the system”
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Huang, L., Tan, Z., Zhong, H., & Zhu, B. (2022) · Physical Review A · doi:10.1103/physreva.106.022419 · Cited by 22 · see citing works
Dependence of the quantum speed limit on system size and control complexity
Lee, J., Arenz, C., RABITZ, H. A., & Russell, B. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aac6f3 · Cited by 22 · see citing works
Time-optimal control with finite bandwidth
Hirose, M., & Cappellaro, P. (2018) · Quantum Information Processing · doi:10.1007/s11128-018-1845-6 · Cited by 20 · see citing works
Yang, C., Su, Q.-P., Zhang, Y., & Nori, F. (2020) · Physical Review A · doi:10.1103/physreva.101.032329 · Cited by 21 · see citing works
Self-citationFast and robust magnon transport in a spin chain
Kiely, A., & Campbell, S. (2021) · New Journal of Physics · doi:10.1088/1367-2630/abea43 · Cited by 20 · see citing works
“[36] it was found that high fidelity numerically optimal protocols could not be found for velocities greater than 2∆x J/~, which also corresponds to the maximal allowed group velocity in the system [40, 41], and thus represents an attainable speed limit for transport.”
BackgroundFast quantum communication in linear networks
Jacobs, K. A., Wu, R.-B., Wang, X., Ashhab, S., Chen, Q., & RABITZ, H. A. (2016) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/114/40007 · Cited by 18 · see citing works
Self-citationGeneralised quantum speed limit for arbitrary time-continuous evolution
Thakuria, D., Srivastav, A., Mohan, B., Kumari, A., & Pati, A. K. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad15ad · Cited by 19 · see citing works
“In recent years, QSL has been extensively investigated for applications in quantum computing [1], quantum batteries [2–5], quantum control theory [6, 7], quantum metrology [8–12], quantum thermodynamics [13, 14] etc.”
BackgroundControlled quantum state transfer in XX spin chains at the Quantum Speed Limit
Coden, D. S. A., Gómez, S. S., Ferrón, A., & Osenda, O. (2020) · Physics Letters A · doi:10.1016/j.physleta.2020.127009 · Cited by 18 · see citing works
Controlling Qubit Networks in Polynomial Time
Arenz, C., & RABITZ, H. A. (2018) · Physical Review Letters · doi:10.1103/physrevlett.120.220503 · Cited by 17 · see citing works
Kuzmak, A. R., & Tkachuk, V. M. (2013) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/46/15/155305 · Cited by 15 · see citing works
Speed limits for two-qubit gates with weakly anharmonic qubits
Ashhab, S., Yoshihara, F., Fuse, T., Yamamoto, N., Lupaşcu, A., & Semba, K. (2022) · Physical Review A · doi:10.1103/physreva.105.042614 · Cited by 16 · see citing works
Self-citationShrimali, D., Panda, B., & Pati, A. K. (2024) · Physical Review A · doi:10.1103/physreva.110.022425 · Cited by 13 · see citing works
Quantum circuit synthesis via a random combinatorial search
Ashhab, S., Yoshihara, F., Tsuji, M., Sato, M., & Semba, K. (2024) · Physical Review A · doi:10.1103/physreva.109.052605 · Cited by 13 · see citing works
“Physical constraints on control signals can lead to technology-specific preferences in the elementary gate set used in the compilation step, i.e. in quantum circuit design [21].”
BackgroundSelf-citationBhatia-Davis formula in the quantum speed limit
Liu, J., Miao, Z., Fu, L., & Wang, X. (2021) · Physical Review A · doi:10.1103/physreva.104.052432 · Cited by 11 · see citing works
Quantum speed limit of a noisy continuous-variable system
Wu, W., & An, J. (2022) · Physical Review A · doi:10.1103/physreva.106.062438 · Cited by 11 · see citing works
“From the application perspective, the QSL in open quantum systems is closely related to the greatest efficiency of charging power in quantum batteries [17–19], the minimum operation time of quantum gates [20, 21], the entropy production rate of nonequilibrium quantum thermodynamics [22–27], as well as the quantum Fish…”
BackgroundLiu, Z., Hong, J., Guo, J., Li, T., Ai, Q., Alsaedi, A., Hayat, T., & Deng, F. (2018) · Annalen der Physik · doi:10.1002/andp.201800029 · Cited by 11 · see citing works
Stojanović, V. M. (2019) · Physical Review A · doi:10.1103/physreva.99.012345 · Cited by 11 · see citing works
Deterministic quantum controlled-PHASE gates based on non-Markovian environments
Zhang, R., Chen, T., & Wang, X. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa9510 · Cited by 10 · see citing works
Shi, Z., Zhang, C., Shen, L.-T., Xia, Y., Yi, X. X., & Zheng, S.-B. (2020) · Physical Review A · doi:10.1103/physreva.101.042314 · Cited by 9 · see citing works
Hamazaki, R. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.013018 · Cited by 10 · see citing works
Fundamental speed limits on entanglement dynamics of bipartite quantum systems
Pandey, V., Bhowmick, S., Mohan, B., Sohail, S., & Sen, U. (2024) · Physical Review A · doi:10.1103/physreva.110.052420 · Cited by 10 · see citing works
“QSLs have several applications in various quantum technologies such quantum computing [21, 22], quantum metrology [23, 24], optimal control theory [25, 26], quantum communication [27], quantum batteries [28–30] and quantum re-frigerator [31].”
Optimal remote restoring of quantum states in communication lines via local magnetic field
Fel’dman, E. B., Pechen, A. N., & Zenchuk, A. I. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad16cc · Cited by 7 · see citing works
Purity speed limit of open quantum systems from magic subspaces
V., A. A. D., Martikyan, V., Glaser, S. J., & Sugny, D. (2020) · Physical Review A · doi:10.1103/physreva.102.033104 · Cited by 6 · see citing works
Electrically Controlled Eight‐Spin‐Qubit Entangled‐State Generation in a Molecular Break Junction
Chattopadhyaya, M., Alam, M. M., Sarkar, D., & Chakrabarti, S. (2014) · ChemPhysChem · doi:10.1002/cphc.201400029 · Cited by 6 · see citing works
Lyapunov control on quantum systems
Wang, L. C., & Yi, X. X. (2014) · International Journal of Modern Physics B · doi:10.1142/s0217979214300205 · Cited by 6 · see citing works
Nearly optimal quantum control: an analytical approach
Sun, C., Saxena, A., & Sinitsyn, N. A. (2017) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/1361-6455/aa807d · Cited by 6 · see citing works
Pechen, A. N., Petruhanov, V. N., Morzhin, O. V., & Volkov, B. O. (2024) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-024-05143-w · Cited by 5 · see citing works
Minimal time robust control for two superconducting qubits
George, N., Allen, J. L., Kosut, R. L., & Ginossar, E. (2025) · Scientific Reports · doi:10.1038/s41598-025-32747-8 · Cited by 5 · see citing works
“However, a fundamental speed limit exists for gate operations [7, 8, 9, 10, 11, 12, 13, 14].”
Robust optimal control for a systematic error in the control amplitude of transmon qubits
Cykiert, M., & Ginossar, E. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad7540 · Cited by 5 · see citing works
“025, or for a short gate time, longer than the time needed to have a non-robust gate[52], makes the optimization prone to trapping.”
BackgroundPeng, Z., Céleri, L. C., Basit, A., & Xianlong, G. (2024) · Physical Review A · doi:10.1103/physreva.110.052433 · Cited by 5 · see citing works
Experimentally optimized implementation of the Fredkin gate with atoms in cavity QED
Song, L.-C., Xia, Y., & Song, J. (2014) · Quantum Information Processing · doi:10.1007/s11128-014-0884-x · Cited by 5 · see citing works
Properties and dynamics of generalized squeezed states
Ashhab, S., & Ayyash, M. (2025) · New Journal of Physics · doi:10.1088/1367-2630/add7fc · Cited by 4 · see citing works
“…asymptotically approaches If we consider an analogy of a particle propagating in a lattice or a spin wave propagating in a spin chain with nearest-neighbour matrix elements all (approximately) given by J in a certain region in space, the maximum group velocity of propagation is given by 2 J [38].”
Self-citationMorzhin, O. V., & Pechen, A. N. (2024) · Lobachevskii Journal of Mathematics · doi:10.1134/s1995080224600110 · Cited by 4 · see citing works
“Proposed in [27] approach for modelling generation of M -qubit quantum gates ( M ≥ 1 ) considers dissipative dynamics depending only on coherent control and uses only three initial density matrices instead of the corresponding full basis (e.g., three matrices instead of sixteen for the two-qubit…”
Observation of minimal and maximal speed limits for few and many-body states
Zhu, Z., Gao, L., Bao, Z., Xiang, L., Song, Z., Xu, S., Wang, K., Chen, J., Jin, F., Zhu, X., et al. (2025) · Nature Communications · doi:10.1038/s41467-025-56451-3 · Cited by 4 · see citing works
Quantum speed limit on the production of quantumness of observables
Shrimali, D., Bhowmick, S., & Pati, A. K. (2025) · Physical Review A · doi:10.1103/physreva.111.022445 · Cited by 4 · see citing works
“Due to their fundamental nature, QSLs have found applications in rapidly developing quantum technologies such as quantum control [26–28], quantum computation [29–31], quantum communication [32], quantum energy storage devices [25, 33], and quantum thermal machines [34, 35].”
Stronger Quantum Speed Limit for Mixed Quantum States
Bagchi, S., Thakuria, D., & Pati, A. K. (2023) · Entropy · doi:10.3390/e25071046 · Cited by 3 · see citing works
Quantum chip design optimization and automation in superconducting coupler architecture
Li, F.-Y., & Jin, L.-J. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/ace8b6 · Cited by 4 · see citing works
Harouni, M. B. (2020) · Chinese Physics B · doi:10.1088/1674-1056/abab75 · Cited by 4 · see citing works
Quantum dynamical speedup for correlated initial states
Gholizadeh, A., Hadipour, M., Haseli, S., Haddadi, S., & Dolatkhah, H. (2023) · Communications in Theoretical Physics · doi:10.1088/1572-9494/acdce8 · Cited by 3 · see citing works
“The QSL time can be used to obtain the shortest time needed to charge the quantum battery [ 4 ] and it is also used to fi nd the minimum time required to implement quantum gates in quantum computing [ 5 ] .”
Huang, L., Deng, M., Sun, C., & Li, F. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.014303 · Cited by 3 · see citing works
“The efficiency of quantum state transfer schemes is predominantly dictated by two main factors: the transfer speed and the fidelity 15–19 .”
BackgroundImplementation of a two-qubit state by an auxiliary qubit on the three-spin system
Kuzmak, A. R. (2019) · Physica Scripta · doi:10.1088/1402-4896/ab4b40 · Cited by 2 · see citing works
One-step implementation of a robust Fredkin gate based on path engineering
Zhang, C., Liu, W., & Lin, X. (2020) · Quantum Information Processing · doi:10.1007/s11128-020-02767-6 · Cited by 2 · see citing works
Optimally Controlled Non-Adiabatic Quantum State Transmission in the Presence of Quantum Noise
Liang, X.-H., Wu, L.-A., & Wang, Z.-M. (2023) · Photonics · doi:10.3390/photonics10030274 · Cited by 2 · see citing works
Research on network security subsystem based on digital signal
Wang, Z., & Ruan, Q. (2019) · Journal of Intelligent & Fuzzy Systems · doi:10.3233/jifs-179384 · Cited by 2 · see citing works
“VLAN[12]isavirtuallocalareanetwork(VLAN), which is a virtual workgroup technology that logically divides network devices into multiple network segments.”
Layout Synthesis for Quantum Circuits Considering Toffoli Gate Decomposition
Chen, P.-W., Huang, S.-T., & Fang, S. (2025) · ACM Transactions on Design Automation of Electronic Systems · doi:10.1145/3744646 · Cited by 1 · see citing works
“…shows that a 2-controlled Toffoli gate as a single operator requires a shorter execution time in a triangle geometry compared with a chain geometry [2]; however, due to the constraints of the target quantum hardware, a 6-CNOT Toffoli decomposition may not necessarily outperform an 8-CNOT…”
Geometric gates in atomic arrays without Rydberg blockade
Ming, Y., Fu, Z.-X., & Du, Y.-X. (2025) · Physical Review A · doi:10.1103/tmr4-gtnl · Cited by 1 · see citing works
Reinforcement learning for robust calibration of multiqudit quantum gates
Jaouadi, A., & Ashhab, S. (2026) · Physical Review A · doi:10.1103/717q-ypkg · Cited by 1 · see citing works
“GRAPE efficiently computes gradients of the fidelity with respect to the con-trol waveform and has produced fast, high-fidelity two-qubit gates [22, 24, 25], leakage-suppressed single-qubit and two-qubit gates [26, 27] and few-qudit gates [13, 28].”
Self-citationGünther, S., & Petersson, N. A. (2023) · AVS Quantum Science · doi:10.1116/5.0173373 · Cited by 1 · see citing works
“Indeed it has been demonstrated on specific examples that such limits align with the shortest durations for which numerical optimal control techniques converge, when control pulse amplitudes are unlimited [11, 3, 2].”
BackgroundQuantum Speed Limit and Nonclassicality in Open Quantum System Models Using the Wigner Function
Gaharwar, A., Tiwari, D., & Banerjee, S. (2024) · Annalen der Physik · doi:10.1002/andp.202400194 · Cited by 1 · see citing works
Coherence restoring in communication line via controlled interaction with environment
Fel’dman, E. B., Lazarev, I. D., Pechen, A. N., & Zenchuk, A. I. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05126-z · Cited by 1 · see citing works
“Speed limits for evaluation of one- two-and three-qubit operations and state transfer depending on the type of spin-interaction and geometry is studied in Ref.”
Investigating the lower bound of minimum gate times using optimal control
Zhang, X.-P., Shao, B., & Zou, J. (2018) · Modern Physics Letters B · doi:10.1142/s0217984918503220
Montangero, S. (2018) · Springer eBooks · doi:10.1007/978-3-030-01409-4_8
Quantum control and quantum speed limits of single-well systems
Song, J.-J., Li, K., & Li, S.-C. (2024) · Results in Physics · doi:10.1016/j.rinp.2024.107484
Zhang, X., Yan, Y., Zheng, L.-N., Zhang, Z., Zhong, L., Zhang, S., & Wang, H. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202400156
Restoring of quantum state transferred along XY-spin chain and entanglement evolution
Tashkeev, N. A., & Zenchuk, A. I. (2025) · International Journal of Quantum Information · doi:10.1142/s021974992550011x
Approaching the quantum speed limit in quantum gates with geometric control
Impens, F., & Guéry-Odelin, D. (2025) · Physical Review A · doi:10.1103/h747-mwwv
“While a significant body of literature has focused on QSLs for the evolution of individual states, the exploration of QSLs governing the evolution of sets of quantum states remains in its early stages [31–36].”
Implementation of multiparticle quantum speed limits on observables
Miao, R.-H., Liu, Z.-D., Ning, C.-X., Hu, Y.-C., Zhang, H., Li, C., & Guo, G. (2025) · Science Advances · doi:10.1126/sciadv.ady0497
Quantum speed limit for observables from quantum asymmetry
Budiyono, A., Moody, M. P., Prihadi, H. L., Rahmawati, R., & Deffner, S. (2026) · Physical Review A · doi:10.1103/tfnt-58sw
Jha, A. K., Konwar, L., & Mohanta, R. (2026) · Physical review. D/Physical review. D. · doi:10.1103/r6t7-wnbz
“It has broad applications across many physical systems [84–98] and has recently been applied in elementary particle systems, including neutral mesons [99] and neutrinos [100], within the ambit of an open quantum system.”
Geometric Quantum Speed Limits and Time-Cost Trade-Off in Time-Dependent Quantum ControlPreprint
Tao, H. G., & Jin, Z. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7519472
Resource‐Aware Quantum Control Under Noise: Deterministic Protocols and Deep Reinforcement Learning
Rahman, A. U., Abd‐Rabbou, M. Y., Liu, A., & Qiao, C. F. (2026) · Advanced Quantum Technologies · doi:10.1002/qute.70483
“Reducing the number of required gates, shortening the execution time, improving robustness to a specific noise channel, or tailoring a protocol to a particular hardware connectivity can determine whether the final signal remains useful or becomes dominated by noise [ 20–22 ].”
- Authors
- Ashhab, S., de Groot, P. C., & Nori, F.
- Affiliations
- University of Michigan (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2012-05-29
- Volume
- 85
- Issue
- 5
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2138618971
- Semantic Scholar
- 9b9314bd7223fa386c0c04fb2b8f63795b3983c0
- Cited by
- 89
- References
- 32
- Citations by year
- 2026: 6 · 2025: 9 · 2024: 13 · 2023: 8 · 2022: 6 · 2021: 3 · 2020: 7 · 2019: 6 · 2018: 7 · 2017: 6 · 2016: 4 · 2015: 3 · 2014: 6 · 2013: 3 · 2012: 2
- FWCI
- 4.41
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Research Repository (Delft University of Technology) (submittedVersion)
- Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- 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
- quantum speed limit, multi-qubit systems, quantum gates, two-qubit gates, CNOT gate, quantum state transfer, qubit chains, spin waves, triangle geometry
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