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Measurement-based Dynamical Decoupling for Fidelity Preservation on Large-scale Quantum Processors

Jeongwoo Jae, Changwon Lee, Juzar Thingna, Yeong-Dae Kwon, Daniel K. Park

TL;DR

This work tackles decoherence in large-scale quantum processors by introducing measurement-based dynamical decoupling (MDD), which derives local gate sequences from partial measurements of idle qubits to optimally preserve quantum information. MDD diagonalizes each idle-qubit reduced state with a local unitary $U_d$, achieving maximal entanglement fidelity to first order in time and proven optimal among bang-bang DD strategies. The authors validate MDD experimentally on IBM Eagle and demonstrate substantial gains: up to a 450-fold improvement in QFT success probability for 14 qubits and faster, more accurate ground-state energy estimates for $N_2$ in 35- and 56-qubit SQD experiments, outperforming standard DD methods. These results establish MDD as a scalable, hardware-friendly approach to suppress decoherence in large-scale quantum algorithms, leveraging subsystem information to enhance fidelity preservation. The work also provides a rigorous theoretical framework for MDD’s optimality and discusses extensions to correlated decoherence and two-qubit MDD under crosstalk.

Abstract

Dynamical decoupling (DD) is a key technique for suppressing decoherence and preserving the performance of quantum algorithms. We introduce a measurement-based DD (MDD) protocol that determines control unitary gates from partial measurements of noisy subsystems, with measurement overhead scaling linearly with the number of subsystems. We prove that, under local energy relaxation and dephasing noise, MDD achieves the maximum entanglement fidelity attainable by any DD scheme based on bang-bang operations to first order in evolution time. On the IBM Eagle processor, MDD achieved up to a $450$-fold improvement in the success probability of a $14$-qubit quantum Fourier transform, and improved the accuracy of ground-state energy estimation for $N_2$ in the $56$-qubit sample-based quantum diagonalization compared with the standard XX-pulse DD. These results establish MDD as a scalable and effective approach for suppressing decoherence in large-scale quantum algorithms.

Measurement-based Dynamical Decoupling for Fidelity Preservation on Large-scale Quantum Processors

TL;DR

This work tackles decoherence in large-scale quantum processors by introducing measurement-based dynamical decoupling (MDD), which derives local gate sequences from partial measurements of idle qubits to optimally preserve quantum information. MDD diagonalizes each idle-qubit reduced state with a local unitary , achieving maximal entanglement fidelity to first order in time and proven optimal among bang-bang DD strategies. The authors validate MDD experimentally on IBM Eagle and demonstrate substantial gains: up to a 450-fold improvement in QFT success probability for 14 qubits and faster, more accurate ground-state energy estimates for in 35- and 56-qubit SQD experiments, outperforming standard DD methods. These results establish MDD as a scalable, hardware-friendly approach to suppress decoherence in large-scale quantum algorithms, leveraging subsystem information to enhance fidelity preservation. The work also provides a rigorous theoretical framework for MDD’s optimality and discusses extensions to correlated decoherence and two-qubit MDD under crosstalk.

Abstract

Dynamical decoupling (DD) is a key technique for suppressing decoherence and preserving the performance of quantum algorithms. We introduce a measurement-based DD (MDD) protocol that determines control unitary gates from partial measurements of noisy subsystems, with measurement overhead scaling linearly with the number of subsystems. We prove that, under local energy relaxation and dephasing noise, MDD achieves the maximum entanglement fidelity attainable by any DD scheme based on bang-bang operations to first order in evolution time. On the IBM Eagle processor, MDD achieved up to a -fold improvement in the success probability of a -qubit quantum Fourier transform, and improved the accuracy of ground-state energy estimation for in the -qubit sample-based quantum diagonalization compared with the standard XX-pulse DD. These results establish MDD as a scalable and effective approach for suppressing decoherence in large-scale quantum algorithms.

Paper Structure

This paper contains 16 sections, 2 theorems, 42 equations, 12 figures, 3 tables.

Table of Contents

  1. Decoherence model
  2. Proofs of the Lemma and Theorem
  3. The optimality of the diagonalizing unitary operator
  4. Gate error and Bounds of fidelity for mixed states
  5. First-order representation of the typical DD and the entanglement fidelity
  6. Proof of Theorem
  7. Generalization to multiple noisy subsystems
  8. Numerical comparison
  9. The minimum decay rate of the entanglement fidelity
  10. Uncorrelated decoherence
  11. Correlated decoherence
  12. Experimental details
  13. Quantum Fourier Transform
  14. Sample-based Quantum Diagonalization
  15. Idle time analysis
  16. ...and 1 more sections

Key Result

Theorem 1

Let $\Lambda^t_{\mathrm{BB}}$ and $\Lambda^t_{\mathrm{MDD}}$ denote the quantum channels corresponding to a standard DD sequence based on $m$ bang–bang operations $\{g_\alpha\}_{\alpha=1}^m$ and MDD, respectively. Then, for any initial pure state $|\psi\rangle_S$ and sufficiently short evolution tim

Figures (12)

  • Figure 1: Workflow of MDD. (a) Identify idle qubits of a quantum circuit after transpilation. (b) Perform Pauli-basis measurements on each idle qubit. (c) Classically compute the corresponding diagonalizing unitary $U_d$. (d) Apply the MDD sequence $(U_d,U_d^\dagger)$ to the idle qubit. Steps (b)--(d) are iterated sequentially throughout the quantum circuit over all idle intervals.
  • Figure 2: Entanglement fidelity of four-qubit states ($N=4$) under different DD schemes: MDD (red), $XX$ (green), UDD$8$ (blue), and without DD (black). Each curve indicates the average over the same $20$ randomly chosen states. The red (MDD) and blue (UDD) shaded regions represent the maximum and minimum values of fidelity across these states. The relaxation and dephasing times are set to $T_1 = 250\mu s$ and $T_2=170\mu s$, respectively, matching typical values of the IBM Eagle processor.
  • Figure 3: Success probability of QFT circuits up to $14$ qubits. Without DD (black dashed line), the success probability rapidly decreases as the number of qubits increases, implying the accumulation of errors. MDD (red solid line) preserves the QFT performance significantly better than the standard $XX$ scheme (blue dot-dashed line). Each point represents the mean success probability over five independent experiments, and error bars indicate the standard deviations.
  • Figure 4: Comparison of estimated ground-state energy errors for $\mathrm{N}_2$ obtained using the SQD workflow with three DD schemes: without DD (black dashed line), $XX$ (blue dotdashed line), and MDD (red solid line). Panels (a) and (b) show the mean energy errors versus the number of self-consistent configuration recovery iterations for $35$- and $56$-qubit experiments, respectively. Error bars represent the standard deviation over five independent runs.
  • Figure S1: Numerical comparison among various DD schemes: MDD, $XX$, $XY4$, and MDD$+$$XX$. For a randomly sampled hundred states, we assume that one of single-qubit subsystems experience the decoherence given by the relaxation and dephasing channel. We consider $T_1 = 250\mu s$, $T_2=170\mu s$, and the total idle time $t=1000\mu s$. The relaxation and dephasing times are set to the values similar to those of IBM Eagle processor ibm_yonsei.
  • ...and 7 more figures

Theorems & Definitions (2)

  • Theorem : First-order optimality of MDD
  • Lemma