Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2305.05019 · Physical Review Research

Competition of decoherence and quantum speed limits for quantum-gate fidelity in the Jaynes-Cummings model

Sagar Silva Pratapsi, Lorenzo Buffoni, Stefano Gherardini

Published Jun 20, 2024• 2 citations
arXivHTMLPDF

Abstract

Quantum computers are operated by external driving fields, such as lasers, microwaves, or transmission lines, that execute logical operations on multiqubit registers, leaving the system in a pure state. However, the drive and the logical system might become correlated in such a way that, after tracing out the degrees of freedom of the driving field, the output state will not be pure. Previous works have pointed out that the resulting error scales inversely with the energy of the drive, thus imposing a limit on the energy efficiency of quantum computing. In this study, focusing on the Jaynes-Cummings model, we show how the same scaling can be seen as a consequence of two competing phenomena: the entanglement-induced error, which grows with time, and a minimal time for computation imposed by quantum speed limits. This evidence is made possible by quantifying, at any time, the computation error via the spectral radius associated with the density operator of the logical qubit. Moreover, we also prove that, in order to attain a given target state at a chosen fidelity, it is energetically more efficient to perform a single driven evolution of the logical qubits rather than to split the computation in subroutines, each operated by a dedicated pulse. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023296

Related papers

Optimal Quantum Driving for Single-Qubit Gates

Joni Ikonen

Quantum computers store and manipulate information in individual quantized energy levels. These devices, not yet realized in their full potential, have the ability to perform certain computational tasks more efficiently than any classical computer. One possible way to implement a quantum computer is to use superconducting circuits controlled by single-mode electromagnetic fields. These circuits constitute the physical quantum bits, or qubits, that are used to store quantum information. A complete, fault-tolerant quantum computer potentially consists of at least millions of physical qubits which are grouped to form fault-tolerant logical qubits. Controlling each physical qubit individually requires a great amount of energy, and hence a future challenge is to reduce the energy consumption in qubit control while maintaining the high precision. In this thesis, we derive a fundamental upper bound for the gate fidelity of a single-qubit not gate implemented with a single resonant driving pulse. It is shown that the upper bound approaches unity inversely proportionally to the increasing mean photon number of the pulse. Furthermore, we find that the upper bound is achieved with an optimal superposition of squeezed states. The typically employed coherent state produces twice as high gate error as the corresponding optimal state. In addition, we present and numerically study a correction protocol that allows using the same drive state for multiple qubit operations. This sustained state is refreshed by sequentially coupling ancillary qubits to it, effectively resetting it and removing entanglement with the previously operated qubits. Thus our protocol allows using the same drive state to implement not gates for different qubits indefinitely, and hence provides a possible route to energy-efficient large-scale quantum computing.

Työväentutkimus Vuosikirja•Jan 1, 2016•0 citations

Impact of decoherence on the fidelity of quantum gates leaving the computational subspace

Tahereh Abad, Yoni Schattner, Anton Frisk Kockum +1 more

The fidelity of quantum operations is often limited by incoherent errors, which typically can be modeled by fundamental Markovian noise processes such as amplitude damping and dephasing. In Phys. Rev. Lett. 129, 150504 (2022), we presented an analytical result for the average gate fidelity of a general multiqubit operation in terms of the dissipative rates and the corresponding Lindblad jump operators, provided that the operation remains in the computational subspace throughout the time evolution. Here we generalize this expression for the average gate fidelity to include the cases where the system state temporarily leaves the computational subspace during the gate. Such gate mechanisms are integral to several quantum-computing platforms, and our formula is applicable to all of them; as examples, we employ it for the two-qubit controlled-Z gate in both superconducting qubits and neutral atoms. We also obtain the average gate fidelity for simultaneous operations applied in multiqubit systems. These results are useful for understanding the error budgets of quantum gates while scaling up quantum computers.

arXiv:2302.13885•Quantum•Apr 3, 2025•18 citations

A Square-Root Barrier to Quantum Gate Speed under Linear Coupling

Pablo Restrepo Gaviria, Mischa P. Woods

Faster quantum gates can suppress the decoherence accumulated during a computation, but in superconducting processors stronger microwave pulses can also increase leakage, off-resonant excitation, stray-field errors, and crosstalk. This creates a central energy--speed--error tradeoff: can quantum state engineering make a gate parametrically faster without paying proportionally more drive energy? We address this question by treating the driving pulse as a quantum bosonic field rather than a classical waveform. For a finite-dimensional system coupled linearly to that field, we prove that fixed-fidelity gate transition rates grow at most as the square root of the pulse energy, under stated uniformity conditions on the coupling and accepted dynamics. The bound permits arbitrary pulse states, including squeezed and non-Gaussian states, as well as drive--system entanglement and back action; coherent Gaussian pulses attain its energy exponent. Thus squeezing or other state engineering alone cannot replace the square-root energy law of a conventional linear drive by the linear scaling allowed by general quantum speed limits. Achieving that improvement requires changing the interaction class, in addition to using a suitable nonclassical pulse, thereby identifying interaction nonlinearity as an essential resource for relaxing the practical gate-speed error tradeoff.

quant-pharXiv:2609.19280•Sep 18, 2026•0 citations

Decoherence in two-frequency-driven qubits

Väisänen, Petrus

Quantum computing has recently been a topic of great interest because quantum computers can possibly be used to solve problems that classical computers are unable to. However, the greatest holdback at the moment is that the fidelity of quantum gate operations is not high enough, which leads to inaccurate computations. A key aspect of quantum computing is single-qubit gates, which are executed utilizing external microwave photon sources, called qubit drives. Here, we theoretically investigate a quantum gate operation where a transmon qubit is controlled by two different driving frequencies at the same time. The two-frequency drive is a three-photon process, where the qubit gets excited when it absorbs two photons of one frequency and emits one photon of the other frequency. This allows placing on-chip filters on the drive ports that filter out noise at the qubit's transition frequency. We calculate the fidelity of the gate operation in the two-frequency-driven transmon starting with the Hamiltonian of the system. We assume the drive lines to be noisy, utilizing a classical model of noise, which inflicts small perturbations to the Hamiltonian. Hence, we utilize time-dependent perturbation theory in the calculations. The scaling of infidelity is found to be the same as in the case with resonant and subharmonic drives, being inversely proportional to the average photon numbers of the drives, assuming that the photon numbers are equal. The scaling of Rabi frequency is observed to be the same as with the subharmonic drive and better than with the resonant drive. Therefore, we obtain results for the two-frequency drive that are as good as the results in the subharmonic drive. An interesting observation is that decoherence seems to be partially caused by multi-photon processes at different frequencies.

•Dec 2, 2025•0 citations

Assessing fidelity-limiting factors and achieving single-qubit gate fidelity beyond 99.999% in driven silicon spin qubits

Kenta Takeda, Akito Noiri, Takashi Nakajima +4 more

In semiconductor single-spin qubits, high-fidelity quantum gates have been demonstrated; however, achieving consistent performance remains challenging due to variations in driven qubit coherence, which is less explored than free-evolution coherence such as $T_2^*$. Here, we report single-qubit gate fidelities above 99.999%, achieved by dramatically extending the driven-spin coherence time and suppressing off-resonant driving effects that are detrimental to accurate fidelity benchmarking. We demonstrate that removing proximal reservoirs significantly enhances the spin-locking coherence time ($T_{1ρ}$), a critical metric for qubits under microwave driving. Furthermore, we reveal that in typical spin qubit setups using parity readout and rectangular pulses, off-resonant excitation of neighboring qubits causes substantial benchmarking artifacts. By optimizing device conditions to mitigate microwave-induced degradation and implementing spectrally tailored pulse shaping, we achieve a $π/2$ gate fidelity of 99.99920(2)%, with remaining errors primarily limited by incoherent noise. These results showcase the mechanisms that bound fidelity benchmarking in state-of-the-art silicon spin qubits and provide practical guidelines for achieving and verifying high fidelities in these systems.

cond-mat.mes-hallCross-listedarXiv:2608.11072•Aug 12, 2026

Energy-efficient quantum computing

Joni Ikonen, Juha Salmilehto, Mikko Möttönen

Abstract In the near future, one of the major challenges in the realization of large-scale quantum computers operating at low temperatures is the management of harmful heat loads owing to thermal conduction of cabling and dissipation at cryogenic components. This naturally raises the question that what are the fundamental limitations of energy consumption in scalable quantum computing. In this work, we derive the greatest lower bound for the gate error induced by a single application of a bosonic drive mode of given energy. Previously, such an error type has been considered to be inversely proportional to the total driving power, but we show that this limitation can be circumvented by introducing a qubit driving scheme which reuses and corrects drive pulses. Specifically, our method serves to reduce the average energy consumption per gate operation without increasing the average gate error. Thus our work shows that precise, scalable control of quantum systems can, in principle, be implemented without the introduction of excessive heat or decoherence.

arXiv:1609.02732•npj Quantum Information•Apr 10, 2017•52 citations
Quantum computers are operated by external driving fields, such as lasers, microwaves, or transmission lines, that execute logical operations on multiqubit registers, leaving the system in a pure state. However, the drive and the logical system might become correlated in such a way that, after tracing out the degrees of freedom of the driving field, the output state will not be pure. Previous works have pointed out that the resulting error scales inversely with the energy of the drive, thus imposing a limit on the energy efficiency of quantum computing. In this study, focusing on the Jaynes-Cummings model, we show how the same scaling can be seen as a consequence of two competing phenomena: the entanglement-induced error, which grows with time, and a minimal time for computation imposed by quantum speed limits. This evidence is made possible by quantifying, at any time, the computation error via the spectral radius associated with the density operator of the logical qubit. Moreover, we also prove that, in order to attain a given target state at a chosen fidelity, it is energetically more efficient to perform a single driven evolution of the logical qubits rather than to split the computation in subroutines, each operated by a dedicated pulse. Published by the American Physical Society 2024
Quantum computers store and manipulate information in individual quantized energy levels. These devices, not yet realized in their full potential, have the ability to perform certain computational tasks more efficiently than any classical computer. One possible way to implement a quantum computer is to use superconducting circuits controlled by single-mode electromagnetic fields. These circuits constitute the physical quantum bits, or qubits, that are used to store quantum information. A complete, fault-tolerant quantum computer potentially consists of at least millions of physical qubits which are grouped to form fault-tolerant logical qubits. Controlling each physical qubit individually requires a great amount of energy, and hence a future challenge is to reduce the energy consumption in qubit control while maintaining the high precision. In this thesis, we derive a fundamental upper bound for the gate fidelity of a single-qubit not gate implemented with a single resonant driving pulse. It is shown that the upper bound approaches unity inversely proportionally to the increasing mean photon number of the pulse. Furthermore, we find that the upper bound is achieved with an optimal superposition of squeezed states. The typically employed coherent state produces twice as high gate error as the corresponding optimal state. In addition, we present and numerically study a correction protocol that allows using the same drive state for multiple qubit operations. This sustained state is refreshed by sequentially coupling ancillary qubits to it, effectively resetting it and removing entanglement with the previously operated qubits. Thus our protocol allows using the same drive state to implement not gates for different qubits indefinitely, and hence provides a possible route to energy-efficient large-scale quantum computing.
The fidelity of quantum operations is often limited by incoherent errors, which typically can be modeled by fundamental Markovian noise processes such as amplitude damping and dephasing. In Phys. Rev. Lett. 129, 150504 (2022), we presented an analytical result for the average gate fidelity of a general multiqubit operation in terms of the dissipative rates and the corresponding Lindblad jump operators, provided that the operation remains in the computational subspace throughout the time evolution. Here we generalize this expression for the average gate fidelity to include the cases where the system state temporarily leaves the computational subspace during the gate. Such gate mechanisms are integral to several quantum-computing platforms, and our formula is applicable to all of them; as examples, we employ it for the two-qubit controlled-Z gate in both superconducting qubits and neutral atoms. We also obtain the average gate fidelity for simultaneous operations applied in multiqubit systems. These results are useful for understanding the error budgets of quantum gates while scaling up quantum computers.
Faster quantum gates can suppress the decoherence accumulated during a computation, but in superconducting processors stronger microwave pulses can also increase leakage, off-resonant excitation, stray-field errors, and crosstalk. This creates a central energy--speed--error tradeoff: can quantum state engineering make a gate parametrically faster without paying proportionally more drive energy? We address this question by treating the driving pulse as a quantum bosonic field rather than a classical waveform. For a finite-dimensional system coupled linearly to that field, we prove that fixed-fidelity gate transition rates grow at most as the square root of the pulse energy, under stated uniformity conditions on the coupling and accepted dynamics. The bound permits arbitrary pulse states, including squeezed and non-Gaussian states, as well as drive--system entanglement and back action; coherent Gaussian pulses attain its energy exponent. Thus squeezing or other state engineering alone cannot replace the square-root energy law of a conventional linear drive by the linear scaling allowed by general quantum speed limits. Achieving that improvement requires changing the interaction class, in addition to using a suitable nonclassical pulse, thereby identifying interaction nonlinearity as an essential resource for relaxing the practical gate-speed error tradeoff.
Quantum computing has recently been a topic of great interest because quantum computers can possibly be used to solve problems that classical computers are unable to. However, the greatest holdback at the moment is that the fidelity of quantum gate operations is not high enough, which leads to inaccurate computations. A key aspect of quantum computing is single-qubit gates, which are executed utilizing external microwave photon sources, called qubit drives. Here, we theoretically investigate a quantum gate operation where a transmon qubit is controlled by two different driving frequencies at the same time. The two-frequency drive is a three-photon process, where the qubit gets excited when it absorbs two photons of one frequency and emits one photon of the other frequency. This allows placing on-chip filters on the drive ports that filter out noise at the qubit's transition frequency. We calculate the fidelity of the gate operation in the two-frequency-driven transmon starting with the Hamiltonian of the system. We assume the drive lines to be noisy, utilizing a classical model of noise, which inflicts small perturbations to the Hamiltonian. Hence, we utilize time-dependent perturbation theory in the calculations. The scaling of infidelity is found to be the same as in the case with resonant and subharmonic drives, being inversely proportional to the average photon numbers of the drives, assuming that the photon numbers are equal. The scaling of Rabi frequency is observed to be the same as with the subharmonic drive and better than with the resonant drive. Therefore, we obtain results for the two-frequency drive that are as good as the results in the subharmonic drive. An interesting observation is that decoherence seems to be partially caused by multi-photon processes at different frequencies.
In semiconductor single-spin qubits, high-fidelity quantum gates have been demonstrated; however, achieving consistent performance remains challenging due to variations in driven qubit coherence, which is less explored than free-evolution coherence such as T2∗T_2^*T2∗​. Here, we report single-qubit gate fidelities above 99.999%, achieved by dramatically extending the driven-spin coherence time and suppressing off-resonant driving effects that are detrimental to accurate fidelity benchmarking. We demonstrate that removing proximal reservoirs significantly enhances the spin-locking coherence time (T1ρT_{1ρ}T1ρ​), a critical metric for qubits under microwave driving. Furthermore, we reveal that in typical spin qubit setups using parity readout and rectangular pulses, off-resonant excitation of neighboring qubits causes substantial benchmarking artifacts. By optimizing device conditions to mitigate microwave-induced degradation and implementing spectrally tailored pulse shaping, we achieve a π/2π/2π/2 gate fidelity of 99.99920(2)%, with remaining errors primarily limited by incoherent noise. These results showcase the mechanisms that bound fidelity benchmarking in state-of-the-art silicon spin qubits and provide practical guidelines for achieving and verifying high fidelities in these systems.
Abstract In the near future, one of the major challenges in the realization of large-scale quantum computers operating at low temperatures is the management of harmful heat loads owing to thermal conduction of cabling and dissipation at cryogenic components. This naturally raises the question that what are the fundamental limitations of energy consumption in scalable quantum computing. In this work, we derive the greatest lower bound for the gate error induced by a single application of a bosonic drive mode of given energy. Previously, such an error type has been considered to be inversely proportional to the total driving power, but we show that this limitation can be circumvented by introducing a qubit driving scheme which reuses and corrects drive pulses. Specifically, our method serves to reduce the average energy consumption per gate operation without increasing the average gate error. Thus our work shows that precise, scalable control of quantum systems can, in principle, be implemented without the introduction of excessive heat or decoherence.