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arXiv:1512.07476 · New Journal of Physics

Dynamical decoupling leads to improved scaling in noisy quantum metrology

Pavel Sekatski, Michalis Skotiniotis, Wolfgang Dür

Published Jul 19, 2016• 87 citations
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Abstract

We consider the usage of dynamical decoupling in quantum metrology, where the joint evolution of system plus environment is described by a Hamiltonian. We show that by ultra-fast unitary control operations acting locally only on system qubits, noise can be eliminated while the desired evolution is only reduced by at most a constant factor, leading to Heisenberg scaling. We identify all kinds of noise where such an approach is applicable. Only noise that is generated by the Hamiltonian to be estimated itself cannot be altered. However, even for such parallel noise, one can achieve an improved scaling as compared to the standard quantum limit for any local noise by means of symmetrization. Our results are also applicable in other schemes based on dynamical decoupling, e.g. the generation of high-fidelity entangling gates.

DOI
10.1088/1367-2630/18/7/073034

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We consider the usage of dynamical decoupling in quantum metrology, where the joint evolution of system plus environment is described by a Hamiltonian. We show that by ultra-fast unitary control operations acting locally only on system qubits, noise can be eliminated while the desired evolution is only reduced by at most a constant factor, leading to Heisenberg scaling. We identify all kinds of noise where such an approach is applicable. Only noise that is generated by the Hamiltonian to be estimated itself cannot be altered. However, even for such parallel noise, one can achieve an improved scaling as compared to the standard quantum limit for any local noise by means of symmetrization. Our results are also applicable in other schemes based on dynamical decoupling, e.g. the generation of high-fidelity entangling gates.
We establish general limits on how precise a parameter, e.g. frequency or the strength of a magnetic field, can be estimated with the aid of full and fast quantum control. We consider uncorrelated noisy evolutions of N qubits and show that fast control allows to fully restore the Heisenberg scaling (~1/N^2) for all rank-one Pauli noise except dephasing. For all other types of noise the asymptotic quantum enhancement is unavoidably limited to a constant-factor improvement over the standard quantum limit (~1/N) even when allowing for the full power of fast control. The latter holds both in the single-shot and infinitely-many repetitions scenarios. However, even in this case allowing for fast quantum control helps to increase the improvement factor. Furthermore, for frequency estimation with finite resource we show how a parallel scheme utilizing any fixed number of entangled qubits but no fast quantum control can be outperformed by a simple, easily implementable, sequential scheme which only requires entanglement between one sensing and one auxiliary qubit.
Quantum Zeno dynamics (QZD) and dynamical decoupling (DD) are useful tools that enable the effective suppression of noise in quantum systems. We consider the problem of when (i) noise can be suppressed and (ii) Heisenberg limit (HL) can be achieved in quantum metrology, and prove necessary and sufficient conditions for when QZD and DD are useful for achieving these two goals. We further show this condition can hold even when the Hamiltonian-not-in-Lindblad-span (HNLS) condition fails, allowing QZD/DD to recover Heisenberg scaling beyond what is certified by the usual HNLS-based quantum error correction (QEC) criterion. Finally, we demonstrate that the combination of both techniques can allow individually imperfect QZD and DD strategies to saturate HL.
Non-classical resources enable measurements to achieve a precision that exceeds the limits predicted by the central limit theorem. However, environmental noise arising from system-environment interactions severely limits the performance of such resources through decoherence. While significant progress has been made in mitigating Markovian noise, the extent to which non-Markovian noise can be mitigated remains poorly understood. We demonstrate that Heisenberg Scaling, the ultimate quantum limit on measurement precision, can be recovered in quantum metrology under non-Markovian noise by leveraging carefully designed Dynamical Decoupling Techniques. Importantly, our approach does not rely on assumptions of Markovian dynamics. By imposing appropriate conditions on the control Hamiltonian, we show that HS can be achieved irrespective of whether the noise is Markovian or non-Markovian. We also prove necessary and sufficient conditions for the existence of such control Hamiltonians. As an illustrative example, we apply our framework to the damped Jaynes-Cummings model, successfully mitigating memory effects and maintaining measurement precision in complex, non-Markovian environments. These findings highlight the power of quantum control to overcome decoherence challenges and enhance metrological performance in realistic, noisy quantum systems.
Quantum metrology promises precision beyond classical limits but environmental noise, unless properly controlled, reduces the quantum advantage to at most a constant improvement. A key challenge is therefore to design quantum control strategies that suppress noise while preserving sensitivity to the targeted signal. Here, we suggest to use dressed states generated by a constant Hamiltonian to achieve this goal and show that success of this strategy depends on the spectral properties of the environment. For low-temperature noise, we show that Heisenberg scaling can be achieved if and only if the signal generator lies outside the linear span of the system-environment coupling operators. This implies that the proper dressed states may enable Heisenberg scaling even in cases where the well-known Hamiltonian-not-in-Lindblad-span criterion, evaluated without dressing, would forbid it. We illustrate dressed state metrology for the example of NV-center thermometry under magnetic-field fluctuations, with the framework readily applicable to other platforms.
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Abstract Quantum Zeno dynamics (QZD) and dynamical decoupling (DD) are useful tools that enable the effective suppression of noise in quantum systems. We consider the problem of when (i) noise can be suppressed and (ii) Heisenberg limit (HL) can be achieved in quantum metrology, and prove necessary and sufficient conditions for when QZD and DD are useful for achieving these two goals. We further show this condition can hold even when the Hamiltonian-not-in-Lindblad-span (HNLS) condition fails, allowing QZD/DD to recover Heisenberg scaling beyond what is certified by the usual HNLS-based quantum error correction (QEC) criterion. Finally, we demonstrate that the combination of both techniques can allow individually imperfect QZD and DD strategies to saturate HL.