We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H=\ensuremath{\theta}{H}_{0}$, we estimate $\ensuremath{\theta}$ by zooming in on previous estimations and by implementing an adaptive Bayesian procedure. The final result of the algorithm is an updated estimation of $\ensuremath{\theta}$ whose variance has been decreased in proportion to the time of evolution under $H$. For the problem of estimating several parameters, we implement dynamical-decoupling techniques and use the results of single parameter estimation. The cases of discrete-time evolution and reference frame alignment are also studied within the adaptive approach.
We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian H=\ensuremathθH0, we estimate \ensuremathθ by zooming in on previous estimations and by implementing an adaptive Bayesian procedure. The final result of the algorithm is an updated estimation of \ensuremathθ whose variance has been decreased in proportion to the time of evolution under H. For the problem of estimating several parameters, we implement dynamical-decoupling techniques and use the results of single parameter estimation. The cases of discrete-time evolution and reference frame alignment are also studied within the adaptive approach.
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or entanglement to sample the unitary Ntot times, the variance of the estimates can scale as O(1/Ntot2), compared to the best ``classical'' strategy with O(1/Ntot). The original algorithm for quantum phase estimation cannot be implemented on near-term hardware as it requires large-scale entangled probes and fault-tolerant quantum computing. Therefore, alternative algorithms have been introduced that rely on coherence and statistical inference. These algorithms produce quantum-boosted phase estimates without inter-probe entanglement. This family of phase-estimation algorithms have, until now, never exhibited the possibility of achieving optimal scaling O(1/Ntot2). Moreover, previous works have not considered the effect of noise on these algorithms. Here, we present a coherence-based phase-estimation algorithm which can achieve the optimal quadratic scaling in the mean absolute error and the mean squared error. In the presence of noise, our algorithm produces errors that approach the theoretical lower bound. The optimality of our algorithm stems from its adaptive nature: Each step is determined, iteratively, using a Bayesian protocol that analyses the results of previous steps.
Abstract The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation protocols. Within this context, Bayesian estimation offers a complete framework for optimal quantum metrology techniques, such as adaptive protocols. However, the use of the Bayesian approach requires extensive computational resources, especially in the multiparameter estimations that represent the typical operational scenario for quantum sensors. Hence, the requirement to characterize protocols implementing Bayesian estimations can become a significant challenge. This work focuses on the crucial task of robustly benchmarking the performances of these protocols in both single and multiple-parameter scenarios. By comparing different figures of merits, evidence is provided in favor of using the median of the quadratic error in the estimations in order to mitigate spurious effects due to the numerical discretization of the parameter space, the presence of limited data, and numerical instabilities. These results, providing a robust and reliable characterization of Bayesian protocols, find natural applications to practical problems within the quantum estimation framework.
We present a model of quantum metrology inspired by the computational model known as deterministic quantum computation with one quantum bit (DQC1). Using only one pure qubit together with l fully mixed qubits we obtain measurement precision (defined as root-mean-square error for the parameter being estimated) at the standard quantum limit, which is typically obtained using the same number of uncorrelated qubits in fully pure states. In principle, the standard quantum limit can be exceeded using an additional qubit which adds only a small amount of purity. We show that the discord in the final state vanishes only in the limit of attaining infinite precision for the parameter being estimated.
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or entanglement to sample the unitary N tot times, the variance of the estimates can scale as O ( 1 / N tot 2 ) , compared to the best “classical” strategy with O ( 1 / N tot ) . The original algorithm for quantum phase estimation cannot be implemented on near-term hardware as it requires large-scale entangled probes and fault-tolerant quantum computing. Therefore, alternative algorithms have been introduced that rely on coherence and statistical inference. These algorithms produce quantum-boosted phase estimates without interprobe entanglement. This family of phase-estimation algorithms have, until now, never exhibited the possibility of achieving optimal scaling O ( 1 / N tot 2 ) . Moreover, previous works have not considered the effect of noise on these algorithms. Here, we present a coherence-based phase-estimation algorithm which can achieve the optimal quadratic scaling in the mean absolute error and the mean squared error. In the presence of noise, our algorithm produces errors that approach the theoretical lower bound. The optimality of our algorithm stems from its adaptive nature: Each step is determined, iteratively, using a Bayesian protocol that analizes the results of previous steps. Published by the American Physical Society 2024
Characterizing the time over which quantum coherence survives is critical for any implementation of quantum bits, memories, and sensors. The usual method for determining a quantum system’s decoherence rate involves a suite of experiments probing the entire expected range of this parameter, and extracting the resulting estimation in postprocessing. Here we present an adaptive multiparameter Bayesian approach, based on a simple analytical update rule, to estimate the key decoherence timescales ( T1 , T2∗ , and T2 ) and the corresponding decay exponent of a quantum system in real time, using information gained in preceding experiments. This approach reduces the time required to reach a given uncertainty by a factor up to an order of magnitude, depending on the specific experiment, compared to the standard protocol of curve fitting. A further speedup of a factor approximately 2 can be realized by performing our optimization with respect to sensitivity as opposed to variance. Published by the American Physical Society 2024
The advancement and scaling of quantum technology has made the learning and identification of quantum systems and devices in highly multidimensional parameter spaces a pressing task for a variety of applications. In many cases, the integration of real-time feedback control and adaptive choice of measurement settings places strict demands on the speed of this task. Here we present a joint model selection and parameter estimation algorithm that is fast and operable on a large number of model parameters. The algorithm is based on variational Bayesian inference, which approximates the target posterior distribution by optimizing a tractable family of distributions, making it more scalable than exact inference methods relying on sampling and that generally suffer from high variance and computational cost in high-dimensional spaces. We show how a regularizing prior can be used to select between competing models, each comprising a different number of parameters, identifying the simplest model that explains the experimental data. The regularization can further separate the degrees of freedom, e.g., quantum systems in the environment or processes, which contribute to major features in the observed dynamics, with respect to others featuring small coupling, which only contribute to a background. As an application of the introduced framework, we consider the problem of the identification of multiple individual nuclear spins with a single electron spin quantum sensor, relevant for nanoscale nuclear magnetic resonance and for the implementation of multiqubit quantum networking nodes. With the number of environmental spins unknown a priori, our Bayesian approach is able to correctly identify the model, i.e., the number of spins and their couplings. We benchmark the algorithm on both simulated and experimental data, using standard figures of merit, and demonstrate that we can estimate dozens of parameters within minutes. Our methodology is compatible with the implementation of real-time adaptive choice of experimental settings in multiparameter estimation, which has the potential to greatly decrease the estimation time in a variety of metrology, tomography, and characterization tasks by prioritizing the measurements with the highest content of information.