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

International Conference on Micro- and Nano-Electronics (ICMNE)

On the fidelity of quantum gates under T1 and T2 relaxation

Andrey Yu. Chernyavskiy

Published Mar 15, 2019• 1 citation
Publisher

Abstract

The present work analyses the effect of T1 and T2 relaxation on the fidelity of quantum gates in terms of Choi-Jamiolkowski isomorphism. Numerical computations is used to show that the value of fidelity is nearly independent of the gate Hamiltonian. This fact leads to the universal estimate of fidelity, and the accuracy of this estimate is studied, especially for the case of one qubit.

DOI
10.1117/12.2522383

Related papers

Quantum gate fidelity in terms of Choi matrices

Nathaniel Johnston, David W. Kribs

We provide new results for computing and comparing the quantum gate fidelity of quantum channels via their Choi matrices. We extend recent work that showed that there exist non-dual pairs of quantum channels with equal gate fidelity by providing an explicit characterization of all such channels. We use our characterization to show that when the dimension is 2 (or 3, under slightly stronger hypotheses), the gate fidelity of two channels is equal if and only if their difference equals the difference of some unital map and its dual—a fact that has been shown to be false when the dimension is 4 or larger. We also present a formula for the minimum gate fidelity of a channel in terms of a well-studied norm on a compression of its Choi matrix. As a consequence, several new ways of bounding and approximating the minimum gate fidelity follow, including a simple semidefinite program to compute it for qubit channels.

arXiv:1102.0948•Journal of Physics A Mathematical and Theoretical•Nov 18, 2011•21 citations

Optimal Clock Speed of Single-Qubit Operations

Nilanjana Chanda, Rangeet Bhattacharyya

Efficient implementation of quantum algorithms requires single- or multi-qubit gates with high fidelity. We use a recently reported thermal fluctuation-regulated quantum master equation to estimate the fidelity of single-qubit gates on open quantum systems. We show that the fidelity is a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves non-monotonically with the drive-amplitude. The calculated fidelity is found to have a maximum corresponding to an optimum value of the drive-amplitude. Therefore, the highest fidelity of the single-qubit operations on open quantum systems would require an optimal clock speed. The arguments are also extended to multi-qubit systems.

•Aug 1, 2019•0 citations

1D Cluster State Generation On Superconducting Hardware

Sharma, Rahul Dev

Measurement-based Quantum Computation(MBQC) utilize entanglement as resource for performing quantum computation. Generating cluster state using entanglement as resource is a key bottleneck for the adoption of MBQC. To generate cluster state with charge-qubit arrrays, we provide analytical derivations and numerical validations for 4-qubit cluster state. We compare our fidelities under ideal (noise-free) Hamiltonian evolution and due to effect of decoherence. We show incorporating energy relaxation ($T_1$) yields $>$90\% fidelity while pure dephasing $T_2$ show $70\%$ decays at fourth harmonics. We further show under noise $T_2$ decays to 50\% within 15 time units, versus $>$70\% under relaxation time units ($T_1$)--only. This decay quantify degradation effect of $T_2$ on preparing cluster--state preparation is more than $T_1$. We highlight the critical need for targeted error-mitigation strategies in near-term MBQC implementations.

arXiv:2508.21798•Aug 29, 2025•0 citations

Fast and Sure-ious Quantum Process Tomography

A. Afham, Sayantan Sen, Marco Tomamichel

Quantum process tomography (QPT) protocols are often designed by lifting quantum state tomography (QST) protocols through the Choi-Jamiolkowski isomorphism, at the cost of an extra step enforcing the trace-preserving (TP) constraint. Existing approaches fall into two classes. The folklore partial normalization, which sandwiches the density estimate between inverse square roots of its input marginal, has a closed form but is used as a heuristic, its only analyses being asymptotic and losing a factor polynomial in the dimension. Projection-based methods are principled but have no closed forms and scale poorly with dimension. We resolve this dichotomy by showing that the partial normalization is the exact projection onto the Choi states of quantum channels in fidelity (equivalently in Bures or purified distance). Consequently, any QST algorithm with guarantees in fidelity lifts to a QPT algorithm that inherits its sample complexity, through a single closed-form congruence that preserves the Choi rank and is computed in Kraus form without any eigendecomposition of Choi dimension. We lift two single-copy protocols and prove that the non-adaptive one (Fidelity Projected Least Squares) recovers the Choi rank and reaches infidelity $\varepsilon$ from a number of channel uses proportional to $1/\varepsilon$. Numerically, for channels of low Choi rank, it improves on the state-of-the-art projected least squares in accuracy, and by orders of magnitude in the time and memory of the TP-regularization step and of the returned estimate.

quant-pharXiv:2609.39941•Oct 1, 2026•0 citations

Fidelity-dissipation relations in quantum gates

Tan Van Vu, Tomotaka Kuwahara, Keiji Saito

Accurate quantum computing relies on the precision of quantum gates. However, quantum gates in practice are generally affected by dissipative environments, which can significantly reduce their fidelity. In this paper, we elucidate the fundamental relations between the average fidelity of generic quantum gates and the dissipation that occurs during the computing processes. Considering scenarios in which a quantum gate is subject to Markovian environments, we rigorously derive fidelity-dissipation relations that hold for arbitrary operational times. Intriguingly, when the quantum gate undergoes thermal relaxation, the result can be used as a valuable tool for estimating dissipation through experimentally measurable fidelity, without requiring detailed knowledge of the dissipative structure. For the case of arbitrary environments, we uncover a trade-off relation between the average fidelity and energy dissipation, implying that these quantities cannot be large simultaneously. Our results unveil the computational limitations imposed by thermodynamics, shedding light on the profound connection between thermodynamics and quantum computing. Published by the American Physical Society 2024

arXiv:2311.15762•Physical Review Research•Aug 28, 2024•7 citations

Variational Quantum Algorithm for Solving the Liouvillian Gap

Xu-Dan Xie, Zheng‐Yuan Xue, Dan-Bo Zhang

Abstract In open quantum systems, the Liouvillian gap characterizes the relaxation time toward the steady state. However, accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the non-Hermitian nature of the Liouvillian superoperator. In this work, we propose a variational quantum algorithm for efficiently estimating the Liouvillian gap. By utilizing the Choi–Jamiołkowski isomorphism, we reformulate the problem as finding the first excitation energy of an effective non-Hermitian Hamiltonian. Our method employs variance minimization with an orthogonality constraint to locate the first excited state and adopts a two-stage optimization scheme to enhance convergence. Moreover, to address scenarios with degenerate steady states, we introduce an iterative energy-offset scanning technique. Numerical simulations on the dissipative XXZ model confirm the accuracy and robustness of our algorithm across a range of system sizes and dissipation strengths. These results demonstrate the promise of variational quantum algorithms for simulating open quantum many-body systems on near-term quantum hardware.

arXiv:2505.16268•Chinese Physics Letters•Jul 1, 2025•2 citations
The present work analyses the effect of T1 and T2 relaxation on the fidelity of quantum gates in terms of Choi-Jamiolkowski isomorphism. Numerical computations is used to show that the value of fidelity is nearly independent of the gate Hamiltonian. This fact leads to the universal estimate of fidelity, and the accuracy of this estimate is studied, especially for the case of one qubit.
We provide new results for computing and comparing the quantum gate fidelity of quantum channels via their Choi matrices. We extend recent work that showed that there exist non-dual pairs of quantum channels with equal gate fidelity by providing an explicit characterization of all such channels. We use our characterization to show that when the dimension is 2 (or 3, under slightly stronger hypotheses), the gate fidelity of two channels is equal if and only if their difference equals the difference of some unital map and its dual—a fact that has been shown to be false when the dimension is 4 or larger. We also present a formula for the minimum gate fidelity of a channel in terms of a well-studied norm on a compression of its Choi matrix. As a consequence, several new ways of bounding and approximating the minimum gate fidelity follow, including a simple semidefinite program to compute it for qubit channels.
Efficient implementation of quantum algorithms requires single- or multi-qubit gates with high fidelity. We use a recently reported thermal fluctuation-regulated quantum master equation to estimate the fidelity of single-qubit gates on open quantum systems. We show that the fidelity is a function of the drive-induced dissipative terms as well as the relaxation terms arising from the qubit-environment coupling; as a result, it behaves non-monotonically with the drive-amplitude. The calculated fidelity is found to have a maximum corresponding to an optimum value of the drive-amplitude. Therefore, the highest fidelity of the single-qubit operations on open quantum systems would require an optimal clock speed. The arguments are also extended to multi-qubit systems.
Measurement-based Quantum Computation(MBQC) utilize entanglement as resource for performing quantum computation. Generating cluster state using entanglement as resource is a key bottleneck for the adoption of MBQC. To generate cluster state with charge-qubit arrrays, we provide analytical derivations and numerical validations for 4-qubit cluster state. We compare our fidelities under ideal (noise-free) Hamiltonian evolution and due to effect of decoherence. We show incorporating energy relaxation (T1T_1T1​) yields $>$90\% fidelity while pure dephasing T2T_2T2​ show 70%70\%70% decays at fourth harmonics. We further show under noise T2T_2T2​ decays to 50\% within 15 time units, versus $>70%underrelaxationtimeunits(70\% under relaxation time units (70%underrelaxationtimeunits(T_1$)--only. This decay quantify degradation effect of T2T_2T2​ on preparing cluster--state preparation is more than T1T_1T1​. We highlight the critical need for targeted error-mitigation strategies in near-term MBQC implementations.
Quantum process tomography (QPT) protocols are often designed by lifting quantum state tomography (QST) protocols through the Choi-Jamiolkowski isomorphism, at the cost of an extra step enforcing the trace-preserving (TP) constraint. Existing approaches fall into two classes. The folklore partial normalization, which sandwiches the density estimate between inverse square roots of its input marginal, has a closed form but is used as a heuristic, its only analyses being asymptotic and losing a factor polynomial in the dimension. Projection-based methods are principled but have no closed forms and scale poorly with dimension. We resolve this dichotomy by showing that the partial normalization is the exact projection onto the Choi states of quantum channels in fidelity (equivalently in Bures or purified distance). Consequently, any QST algorithm with guarantees in fidelity lifts to a QPT algorithm that inherits its sample complexity, through a single closed-form congruence that preserves the Choi rank and is computed in Kraus form without any eigendecomposition of Choi dimension. We lift two single-copy protocols and prove that the non-adaptive one (Fidelity Projected Least Squares) recovers the Choi rank and reaches infidelity ε\varepsilonε from a number of channel uses proportional to 1/ε1/\varepsilon1/ε. Numerically, for channels of low Choi rank, it improves on the state-of-the-art projected least squares in accuracy, and by orders of magnitude in the time and memory of the TP-regularization step and of the returned estimate.
Accurate quantum computing relies on the precision of quantum gates. However, quantum gates in practice are generally affected by dissipative environments, which can significantly reduce their fidelity. In this paper, we elucidate the fundamental relations between the average fidelity of generic quantum gates and the dissipation that occurs during the computing processes. Considering scenarios in which a quantum gate is subject to Markovian environments, we rigorously derive fidelity-dissipation relations that hold for arbitrary operational times. Intriguingly, when the quantum gate undergoes thermal relaxation, the result can be used as a valuable tool for estimating dissipation through experimentally measurable fidelity, without requiring detailed knowledge of the dissipative structure. For the case of arbitrary environments, we uncover a trade-off relation between the average fidelity and energy dissipation, implying that these quantities cannot be large simultaneously. Our results unveil the computational limitations imposed by thermodynamics, shedding light on the profound connection between thermodynamics and quantum computing. Published by the American Physical Society 2024
Abstract In open quantum systems, the Liouvillian gap characterizes the relaxation time toward the steady state. However, accurately computing this quantity is notoriously difficult due to the exponential growth of the Hilbert space and the non-Hermitian nature of the Liouvillian superoperator. In this work, we propose a variational quantum algorithm for efficiently estimating the Liouvillian gap. By utilizing the Choi–Jamiołkowski isomorphism, we reformulate the problem as finding the first excitation energy of an effective non-Hermitian Hamiltonian. Our method employs variance minimization with an orthogonality constraint to locate the first excited state and adopts a two-stage optimization scheme to enhance convergence. Moreover, to address scenarios with degenerate steady states, we introduce an iterative energy-offset scanning technique. Numerical simulations on the dissipative XXZ model confirm the accuracy and robustness of our algorithm across a range of system sizes and dissipation strengths. These results demonstrate the promise of variational quantum algorithms for simulating open quantum many-body systems on near-term quantum hardware.