Jeongwoo Jae of Samsung SDS and colleagues have demonstrated a 450-fold improvement in the success probability of a 14-qubit quantum Fourier transform using a new measurement-based Dynamical Decoupling (MDD) protocol on IBM’s Eagle processor. The researchers introduced MDD, which determines control gates from partial measurements of noisy subsystems, with a key feature being measurement overhead that scales linearly with the number of subsystems.

This scalable approach also improved the accuracy of ground-state energy estimation for N² in a 56-qubit sample-based quantum diagonalization compared with standard techniques, establishing MDD as an effective method for suppressing decoherence in large-scale quantum algorithms.

Measurement-Based Dynamical Decoupling (MDD) Protocol Overview

The protocol reconstructs the single-qubit reduced density matrix of each idle qubit from Pauli-basis measurements, a key distinction from conventional dynamical decoupling methods. This reconstruction then informs the application of a local unitary, aligning the qubit’s state as closely as possible with its ground state to minimize decoherence effects. The process uses partial measurements to determine optimal control sequences, offering a scalable approach for fidelity preservation in quantum systems.

This method differs from previous techniques by actively adapting to the specific noise characteristics of each subsystem, rather than relying on pre-defined decoupling sequences. Jeongwoo Jae of R&D center, Samsung SDS, and colleagues detailed the mathematical model underpinning their approach, defining the dynamics of local decoherence using amplitude damping and dephasing channels. Their work specifies Kraus operators for these channels, with parameters accounting for both energy relaxation and dephasing rates.

The team’s model incorporates variables such as $γ_{p}$ , representing the ratio of dephasing to relaxation times, and defines its relationship to the coherence time $T_{p}$ as $γ_{p}$ =. This theoretical framework underpins the MDD protocol’s ability to dynamically adjust control gates based on observed noise. Supplemental material details the decoherence model used, providing a deeper understanding of the noise processes targeted by MDD. The protocol’s scalability is a central benefit because the measurement overhead increases linearly with the number of subsystems, an important factor for implementation on larger quantum processors.

The ability of measurement-based dynamical decoupling (MDD) to optimize gate sequences surpasses existing methods by using partial measurements to reconstruct a qubit’s reduced density matrix, a technique previously unexplored in this context. Unlike graph-embedding schemes that face quadratic scaling with qubit connectivity, MDD’s computational cost remains manageable even with fully connected architectures, addressing a key limitation of prior learning-based strategies.

MDD’s efficacy stems from its ability to achieve the maximum entanglement fidelity attainable by any dynamical decoupling scheme using bang-bang operations, at least to first order in evolution time. The study concludes, establishing a new benchmark for decoherence suppression in quantum computing.

The measurement-based Dynamical Decoupling (MDD) protocol achieves maximal entanglement fidelity under specific noise conditions, a theoretical limit previously unattainable, according to work verified on IBM’s Eagle processor. This scaling contrasts with other approaches, like graph-embedding schemes, which face quadratic increases in computational cost as qubit connectivity grows.

IBM Eagle Processor Validation of MDD Performance

The protocol’s performance was assessed using relaxation and dephasing times of 250μs and 170μs, respectively, mirroring typical parameters of the IBM Eagle hardware. These results highlight MDD’s potential to significantly accelerate quantum computations on existing platforms. This suggests MDD can unlock performance comparable to current best results even from less advanced hardware. The study also compared MDD’s performance directly against the XX and UDD protocols for N=4, confirming its superiority in maintaining entanglement fidelity.

Lines representing entanglement fidelity were generated by averaging values across random quantum states, with shaded regions indicating the maximum and minimum fidelity observed. “MDD enhances the convergence of classical postprocessing, thereby improving the overall efficiency of the SQD workflow,” the researchers state, emphasizing the protocol’s broader applicability to quantum algorithms.

Fold QFT Success Rate Improvement with MDD

This substantial gain demonstrates MDD’s ability to mitigate decoherence in increasingly complex quantum computations, a persistent challenge in the field. The fidelity of the quantum state, a measure of how closely it resembles the ideal state, gradually decreases over time due to noise, but MDD demonstrably slows this decay.

MDD Outperforms XX-Pulse DD in N2 Quantum Diagonalization

This advancement stems from a measurement-based Dynamical Decoupling (MDD) protocol, which derives control signals from partial measurements of quantum subsystems, offering a scalable alternative to existing methods. This calculation outperformed the same diagonalization using standard XX-pulse Dynamical Decoupling, indicating a broader applicability for complex quantum simulations. The team’s work demonstrates that using information from these subsystems enables robust preservation of quantum algorithm performance against decoherence. These results establish MDD as a viable strategy for mitigating decoherence and enhancing the reliability of large-scale quantum computations.

Linear Overhead of MDD with Increasing Qubit Count

This contrasts with some graph-embedding strategies designed to optimize gate sequences, where computational demands scale quadratically with connected qubits and introduce significant overhead even on fully connected architectures. While MDD requires additional measurements, the team’s work shows this does not translate to a proportional increase in computational burden. This performance gain is particularly notable given the challenges of maintaining coherence as qubit counts rise and the increasing need for efficient error mitigation strategies.

Analysis of transpiled quantum Fourier transform circuits further highlights the benefits of MDD in managing idle time, a key source of decoherence. The protocol’s design prioritizes maximizing entanglement fidelity under common noise conditions, offering a scalable approach to preserving quantum information.

Pauli-Basis Measurements Define MDD Unitary Operators

Pauli-basis measurements are central to a new approach for defining the unitary operators used in Measurement-Based Dynamical Decoupling (MDD), enabling precise control over qubit states during idle periods. This process effectively minimizes decoherence by actively counteracting the effects of noise during computation. MDD’s reliance on the $R_{y}$ gate as its primary physical operation simplifies implementation, as the rotation about the z-axis can be achieved virtually through phase adjustments of the control signal.

The parameters defining the diagonalizing unitary, $U_{d}$ , are determined by the expectations of Pauli-basis measurements represented as r = (⟨ Z⟩). Specifically, the equations r = |r|_2 and $U_{d}$ = $R_{y} (- θ_{d}) R_{z} (- φ_{d})$ dictate how these measurements translate into precise unitary transformations. When a qubit is in a pure state (η = 1), MDD aligns it with the ground state 0| = (I + Z)/2, providing optimal protection against decoherence.

MDD Aligns Qubit States with Ground State for Decoherence Suppression

By actively reorienting qubit states, a new approach minimizes the impact of decoherence by aligning them with the stable ground state, a configuration unaffected by common noise sources like amplitude damping and dephasing. The process uses a diagonalizing unitary, $U_{d}$ , which orders the eigenvalues of a qubit’s sigma matrix, effectively prioritizing alignment with the lowest energy state. This strategy uses the inherent resilience of ground states against decoherence, ensuring greater stability during quantum computations.

MDD 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. Testing involved randomly generated N-qubit pure states, with only a single qubit exposed to decoherence, revealing the robustness of the approach.

👉 More information
🗞 Measurement-informed dynamical decoupling for fidelity preservation on large-scale quantum processors
✍️ Jeongwoo Jae, Changwon Lee, Juzar Thingna, Yeong-Dae Kwon and Daniel K. Park
🧠 DOI: http://link.aps.org/doi/10.1103/jp17-mvpr

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