Abstract Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is estimated in the presence of statistical errors using entangled quantum states. We present a novel approach for finding (near) optimal states for metrology in the presence of noise, using variational techniques as a tool for efficiently searching the high-dimensional space of quantum states, which would be classically intractable. We comprehensively explore systems consisting of up to 9 qubits and find new highly entangled states that are not symmetric under permutations and non-trivially outperform previously known states up to a constant factor 2. We consider a range of environmental noise models; while passive quantum states cannot achieve a fundamentally superior scaling (as established by prior asymptotic results) we do observe a significant absolute quantum advantage. We finally outline a possible experimental setup for variational quantum metrology which can be implemented in near-term hardware.
Abstract Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is estimated in the presence of statistical errors using entangled quantum states. We present a novel approach for finding (near) optimal states for metrology in the presence of noise, using variational techniques as a tool for efficiently searching the high-dimensional space of quantum states, which would be classically intractable. We comprehensively explore systems consisting of up to 9 qubits and find new highly entangled states that are not symmetric under permutations and non-trivially outperform previously known states up to a constant factor 2. We consider a range of environmental noise models; while passive quantum states cannot achieve a fundamentally superior scaling (as established by prior asymptotic results) we do observe a significant absolute quantum advantage. We finally outline a possible experimental setup for variational quantum metrology which can be implemented in near-term hardware.
The advent of quantum entanglement has revolutionized metrology, enabling the development of ultra-precise measurement techniques that surpass the limitations of classical systems. However, the delicate nature of entangled states makes them vulnerable to various noise sources, significantly impeding their metrological utility. To address this challenge, we delve into the intricate relationship between noise and the metrological usefulness of highly entangled multiqubit systems. By studying the impact of various factors, we aim to unravel the fundamental limits of quantum metrology and devise strategies to enhance the resilience of quantum systems against noise. Our investigation reveals that increasing the number of qubits in an entangled state can significantly enhance its noise robustness, particularly for certain entangled states. Furthermore, we uncover the surprising advantage of utilizing different local operators, surpassing the robustness offered by the conventional identical-operator approach. Additionally, by employing a technique that utilizes multiple copies of the quantum state, we identified many states with latent metrological usefulness and demonstrated their hidden noise robustness. While these strategies significantly enhance the robustness of many studied states, it is crucial to note that generalizations may not apply universally. Therefore, validating these findings for each specific state is essential before practical implementation. Our findings proved that by rigorously assessing noise susceptibility and adopting appropriate strategies, we can achieve substantial gains in precision and noise robustness. This paves the way for the development of more robust and reliable quantum metrological techniques, offering valuable insights across a wide range of applications, from fundamental physics to cutting-edge technologies like quantum computing, sensing, and communication.
By leveraging quantum effects, such as superposition and entanglement, quantum metrology promises higher precision than classical strategies. It is, however, a challenging task to achieve the higher precision on practical systems. This is mainly due to difficulties in engineering nonclassical states and performing nontrivial measurements on the system, especially when the number of particles is large. Here we propose a variational scheme with the Loschmidt echo for quantum metrology. By utilizing hardware-efficient ansatzes in the design of variational quantum circuits, the quantum Fisher information (QFI) of the probe state can be extracted from the experimentally measured Loschmidt echo in a scalable manner. This QFI is then used to guide the online optimization of the preparation of the probe state. We experimentally implement the scheme on an ensemble of 10-spin quantum processors and achieve a 12.4-dB enhancement of the measurement precision over the uncorrelated states, which is close to the theoretical limit. The scheme can also be employed on various other noisy intermediate-scale quantum devices, which provides a promising protocol to demonstrate quantum advantages.
Quantum metrology exploits quantum mechanical effects to increase the precision of measurements of physical quantities. A wide variety of applications are currently being developed for scientific and technological purposes, however, most research relies on the use of highly entangled resource states that are challenging to generate and control in a given physical system. Here, we study the use of weighted graph states as more accessible resources for quantum metrology, which yield a favorable precision beyond the classical limit, approaching the Heisenberg limit. We find a notable robustness to variation in weights and less challenging weight requirements compared to standard graph states, which require a maximal weight at all edges. Both of these aspects reduce the practical demands in a physical setup, with the latter implying significantly less entanglement is required to gain a quantum advantage in metrology. We study the quantum Fisher information and optimized estimator variance of two identified sub classes of weighted graph states for an arbitrary number of N qubits, providing analytical forms and investigating their scaling. Our work opens up opportunities for using weakly entangled states in quantum-enhanced metrology.
By utilizing quantum mechanical effects, such as superposition and entanglement, quantum metrology promises higher precision than the classical strategies. It is, however, practically challenging to realize the quantum advantages. This is mainly due to the difficulties in engineering non-classical probe state and performing nontrivial measurement in practise, particularly with a large number of particles. Here we propose a scalable scheme with a symmetrical variational quantum circuit which, same as the Loschmidt echo, consists of a forward and a backward evolution. We show that in this scheme the quantum Fisher information, which quantifies the precision limit, can be efficiently obtained from a measurement signal of the Loschmidt echo. We experimentally implement the scheme on an ensemble of 10-spin quantum processor and successfully achieves a precision near the theoretical limit which outperforms the standard quantum limit with 12.4 dB. The scheme can be efficiently implemented on various noisy intermediate-scale quantum devices which provides a promising routine to demonstrate quantum advantages.
In an idealistic setting, quantum metrology protocols allow to sense physical parameters with mean squared error that scales as 1/N2 with the number of particles involved---substantially surpassing the 1/N-scaling characteristic to classical statistics. A natural question arises, whether such an impressive enhancement persists when one takes into account the decoherence effects that are unavoidable in any real-life implementation. In this thesis, we resolve a major part of this issue by describing general techniques that allow to quantify the attainable precision in metrological schemes in the presence of uncorrelated noise. We show that the abstract geometrical structure of a quantum channel describing the noisy evolution of a single particle dictates then critical bounds on the ultimate quantum enhancement. Our results prove that an infinitesimal amount of noise is enough to restrict the precision to scale classically in the asymptotic N limit, and thus constrain the maximal improvement to a constant factor. Although for low numbers of particles the decoherence may be ignored, for large N the presence of noise heavily alters the form of both optimal states and measurements attaining the ultimate resolution. However, the established bounds are then typically achievable with use of techniques natural to current experiments. In this work, we thoroughly introduce the necessary concepts and mathematical tools lying behind metrological tasks, including both frequentist and Bayesian estimation theory frameworks. We provide examples of applications of the methods presented to typical qubit noise models, yet we also discuss in detail the phase estimation tasks in Mach-Zehnder interferometry both in the classical and quantum setting---with particular emphasis given to photonic losses while analysing the impact of decoherence.
Quantum metrology is a promising practical use case for quantum technologies, where physical quantities can be measured with unprecedented precision. In lieu of quantum error correction procedures, near term quantum devices are expected to be noisy, and we have to make do with noisy probe states. We prove that, for a set of carefully chosen symmetric probe states that lie within certain quantum error correction codes, quantum metrology exhibits an advantage over classical metrology even after the probe states are corrupted by a constant number of erasure and dephasing errors. These probe states prove useful for robust metrology not only in the NISQ regime, but also in the asymptotic setting where they achieve Heisenberg scaling. This brings us closer towards making robust quantum metrology a technological reality.