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Register a new userAdaptive Circuit Learning for Quantum Metrology
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Quantum metrology is an important application of emerging quantum technologies. We explore whether a hybrid system of quantum sensors and quantum circuits can surpass the classical limit of sensing. In particular, we use a circuit learning approach to search for encoder and decoder circuits that scalably improve sensitivity under given application and noise characteristics. Our approach uses a variational algorithm that can learn a quantum sensing circuit based on platform-specific control capacity, noise, and signal distribution. The quantum circuit is composed of an encoder which prepares the optimal sensing state and a decoder which gives an output distribution containing information of the signal. We optimize the full circuit to maximize the Signal-to-Noise Ratio (SNR). Furthermore, this learning algorithm can be run on real hardware scalably by using the parameter-shift rule which enables gradient evaluation on noisy quantum circuits, avoiding the exponential cost of quantum system simulation. We demonstrate a 1.69x SNR improvement over the classical limit on a 5-qubit IBM quantum computer. More notably, our algorithm overcomes the plateauing (or even decreasing) performance of existing entanglement-based protocols with increased system sizes.
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We consider a general model of unitary parameter estimation in presence of Markovian noise, where the parameter to be estimated is associated with the Hamiltonian part of the dynamics. In absence of noise, unitary parameter can be estimated with precision scaling as $1/T$, where $T$ is the total probing time. We provide a simple algebraic condition involving solely the operators appearing in the quantum Master equation, implying at most $1/sqrt{T}$ scaling of precision under the most general adaptive quantum estimation strategies. We also discuss the requirements a quantum error-correction like protocol must satisfy in order to regain the $1/T$ precision scaling in case the above mentioned algebraic condition is not satisfied. Furthermore, we apply the developed methods to understand fundamental precision limits in atomic interferometry with many-body effects taken into account, shedding new light on the performance of non-linear metrological models.
Experimentally achieving the precision that standard quantum metrology schemes promise is always challenging. Recently, additional controls were applied to design feasible quantum metrology schemes. However, these approaches generally does not consider ease of implementation, raising technological barriers impeding its realization. In this paper, we circumvent this problem by applying closed-loop learning control to propose a practical controlled sequential scheme for quantum metrology. Purity loss of the probe state, which relates to quantum Fisher information, is measured efficiently as the fitness to guide the learning loop. We confirm its feasibility and certain superiorities over standard quantum metrology schemes by numerical analysis and proof-of-principle experiments in a nuclear magnetic resonance (NMR) system.
Quantum metrology offers a quadratic advantage over classical approaches to parameter estimation problems by utilizing entanglement and nonclassicality. However, the hurdle of actually implementing the necessary quantum probe states and measurements, which vary drastically for different metrological scenarios, is usually not taken into account. We show that for a wide range of tasks in metrology, 2D cluster states (a particular family of states useful for measurement-based quantum computation) can serve as flexible resources that allow one to efficiently prepare any required state for sensing, and perform appropriate (entangled) measurements using only single qubit operations. Crucially, the overhead in the number of qubits is less than quadratic, thus preserving the quantum scaling advantage. This is ensured by using a compression to a logarithmically sized space that contains all relevant information for sensing. We specifically demonstrate how our method can be used to obtain optimal scaling for phase and frequency estimation in local estimation problems, as well as for the Bayesian equivalents with Gaussian priors of varying widths. Furthermore, we show that in the paradigmatic case of local phase estimation 1D cluster states are sufficient for optimal state preparation and measurement.
Sensing and imaging are among the most important applications of quantum information science. To investigate their fundamental limits and the possibility of quantum enhancements, researchers have for decades relied on the quantum Cramer-Rao lower error bounds pioneered by Helstrom. Recent work, however, has called into question the tightness of those bounds for highly nonclassical states in the non-asymptotic regime, and better methods are now needed to assess the attainable quantum limits in reality. Here we propose a new class of quantum bounds called quantum Weiss-Weinstein bounds, which include Cramer-Rao-type inequalities as special cases but can also be significantly tighter to the attainable error. We demonstrate the superiority of our bounds through the derivation of a Heisenberg limit and phase-estimation examples.
The quantum circuit layout problem is to map a quantum circuit to a quantum computing device, such that the constraints of the device are satisfied. The optimality of a layout method is expressed, in our case, by the depth of the resulting circuits. We introduce QXX, a novel search-based layout method, which includes a configurable Gaussian function used to: emph{i)} estimate the depth of the generated circuits; emph{ii)} determine the circuit region that influences most the depth. We optimize the parameters of the QXX model using an improved version of random search (weighted random search). To speed up the parameter optimization, we train and deploy QXX-MLP, an MLP neural network which can predict the depth of the circuit layouts generated by QXX. We experimentally compare the two approaches (QXX and QXX-MLP) with the baseline: exponential time exhaustive search optimization. According to our results: 1) QXX is on par with state-of-the-art layout methods, 2) the Gaussian function is a fast and accurate optimality estimator. We present empiric evidence for the feasibility of learning the layout method using approximation.
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