Quantum control techniques are one of the most efficient tools for attaining high-fidelity quantum operations and a convenient approach for quantum sensing and quantum noise spectroscopy. In this work, we investigate dynamical decoupling while processing an entangling two-qubit gate based on an Ising-xx interaction, each qubit affected by pure dephasing classical correlated 1/f-noises. To evaluate the gate error, we used the Magnus expansion introducing generalized filter functions that describe decoupling while processing and allow us to derive an approximate analytic expression as a hierarchy of nested integrals of noise cumulants. The error is separated in contributions of Gaussian and non-Gaussian noise, with the corresponding generalized filter functions calculated up to the fourth order. By exploiting the properties of selected pulse sequences, we show that it is possible to extract the second-order statistics (spectrum and cross-spectrum) and to highlight non-Gaussian features contained in the fourth-order cumulant. We discuss the applicability of these results to state-of-the-art small networks based on solid-state platforms.
Quantum control techniques are one of the most efficient tools for attaining high-fidelity quantum operations and a convenient approach for quantum sensing and quantum noise spectroscopy. In this work, we investigate dynamical decoupling while processing an entangling two-qubit gate based on an Ising-xx interaction, each qubit affected by pure dephasing classical correlated 1/f-noises. To evaluate the gate error, we used the Magnus expansion introducing generalized filter functions that describe decoupling while processing and allow us to derive an approximate analytic expression as a hierarchy of nested integrals of noise cumulants. The error is separated in contributions of Gaussian and non-Gaussian noise, with the corresponding generalized filter functions calculated up to the fourth order. By exploiting the properties of selected pulse sequences, we show that it is possible to extract the second-order statistics (spectrum and cross-spectrum) and to highlight non-Gaussian features contained in the fourth-order cumulant. We discuss the applicability of these results to state-of-the-art small networks based on solid-state platforms.
Dynamical decoupling sequences are a convenient tool to reduce decoherence due to intrinsic fluctuations with 1 / f power spectrum hindering quantum circuits. We study the possibility to achieve an efficient universal two-qubit gate in the presence of 1 / f noise by periodic and Carr-Purcell dynamical decoupling. The high degree of selectivity achieved by these protocols also provides a valuable tool to infer noise characteristics, as the high-frequency cut off and the noise variance. Different scalings of the gate error with noise variance signal the contribution of different noise statistical properties to the gate error.
We consider a class of multi-qubit dephasing models that combine classical noise sources and linear coupling to a bosonic environment, and are controlled by arbitrary sequences of dynamical decoupling pulses. Building on a general transfer filter-function framework for open-loop control, we provide an exact representation of the controlled dynamics for arbitrary stationary non-Gaussian classical and quantum noise statistics, with analytical expressions emerging when all dephasing sources are Gaussian. This exact characterization is used to establish two main results. First, we construct multi-qubit sequences that ensure maximum high-order error suppression in both the time and frequency domain and that can be exponentially more efficient than existing ones in terms of total pulse number. Next, we show how long-time multi-qubit storage may be achieved by meeting appropriate conditions for the emergence of a fidelity plateau under sequence repetition, thereby generalizing recent results for single-qubit memory under Gaussian dephasing. In both scenarios, the key step is to endow multi-qubit sequences with a suitable displacement anti-symmetry property, which is of independent interest for applications ranging from environment-assisted entanglement generation to multi-qubit noise spectroscopy protocols.
Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of noncommuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.
We study the dissipative dynamics of a qubit that is afflicted by classical random telegraph noise and is subject to dynamical decoupling. We derive exact formulas for the qubit dynamics at arbitrary working points in the limit of infinitely strong control pulses (bang-bang control), and we investigate in great detail the efficiency of the dynamical decoupling techniques for both Gaussian and non-Gaussian (slow) noise at qubit pure dephasing and at optimal point. We demonstrate that control sequences can be successfully implemented as diagnostic tools to infer spectral properties of a few fluctuators interacting with the qubit. The analysis is extended in order to include the effect of noise in the pulses, and we give upper bounds on the noise levels that can be tolerated in the pulses while still achieving an efficient dynamical decoupling performance.
Dynamical decoupling and shaped control are standard tools for mitigating dephasing noise in solid-state qubits. Most analyses either assume commuting pure dephasing with longitudinal control, where filter-function theory applies exactly, or move to fully numerical non-commuting dynamics with limited interpretability. Here I introduce Q-Loop, a scalar modulation protocol designed to suppress low-frequency 1/f γ dephasing more efficiently than standard Carr–Purcell (CP) sequences, and I connect its performance across both regimes. First, in the commuting pure-dephasing limit I compute the filter functions F(ω, τ ) and decoherence functionals χ(τ ) for free evolution, CP, and Q-Loop under 1/f γ noise with γ ∈ {0.5, 0.9, 1.2}. For γ = 0.9 I find that Q-Loop reduces the integrated noise susceptibility to χQ-Loop/χCP ≈ 0.36, with even stronger suppression for steeper spectra (χQ-Loop/χCP ≈ 0.14 at γ = 1.2). Monte Carlo simulations of classical noise trajectories verify that the resulting coherence W(τ ) = ⟨e −iϕ⟩ matches the analytic prediction e −χ(τ) . Second, I move beyond the commuting approximation and study an n-qubit GHZ state evolving under a time-dependent Hamiltonian with transverse control and longitudinal dephasing noise, H(t) = β 2 y(t) Xn i=1 Xi + 1 2 Xn i=1 Bi(t)Zi, where Bi(t) are mixed local+collective classical 1/f 0.9 fields and y(t) is either Q-Loop or CP. Using QuTiP to simulate unitary dynamics conditioned on classical noise, I determine the minimum control amplitude β ∗ (n) required to maintain fidelity F ≥ 0.9 with the GHZ state at a fixed interrogation time. For n = 2, 3, 4 qubits I obtain β ∗ Q-Loop ≃ (2.03, 2.28, 2.53) and β ∗ CP ≃ (15.53, 15.53, 16.00), corresponding to an average efficiency gain ⟨β ∗ CP/β∗ Q-Loop⟩ ≈ 6.9. Thus the spectral advantage of Q-Loop in reducing χ(τ ) is reflected in a substantial reduction of transverse control power required to stabilize entanglement under realistic non-commuting dynamics. I also discuss the limitations of the present analysis—classical noise, finite system size, and the restricted range n = 2–4—and outline how the framework can be extended to larger systems and more microscopic noise models.
Realistic multiqubit noise processes often result in error mechanisms that are not captured by the probabilistic Markovian error models commonly employed in circuit-level analyses of quantum fault tolerance. By working within an open-quantum system Hamiltonian formulation, we revisit the validity of the notion of a constant gate error in the presence of noise that is both and , and the impact of which is mitigated through perfect instantaneous dynamical decoupling subject to finite timing constraints. We study a minimal exactly solvable single-qubit model under Gaussian quantum dephasing noise, showing that the fidelity of a dynamically protected idling gate can depend strongly on its location in the circuit and the history of applied control, even when the system-side error propagation is fully removed through perfect reset operations. For digital periodic control, we prove that, under mild conditions on the low-frequency behavior of the nonclassical noise spectrum, at a value that is strictly smaller than the one attainable in the absence of control history; the presence of high-frequency noise peaks is also found as especially harmful, due to the possible onset of . We explicitly relate these features to the evolution of the bath statistics during the computation, which has not been fully accounted for in existing treatments. We find that only if decoupling can keep the qubit highly pure over a time scale larger than the correlation time of the noise, the bath approximately converges to its original statistics and a stable-in-time control performance is recovered. Our work highlights the significance of the full bath evolution between circuit locations and suggests that additional trade-offs and design constraints may arise in layered quantum fault-tolerant architectures from the need to appropriately reequilibrate the quantum bath statistics, particularly when Markovian noise is present alongside temporally correlated noise.