A search algorithm for quantum state engineering and metrology

Abstract

In this paper we present a search algorithm that finds useful optical quantum states which can be created with current technology. We apply the algorithm to the field of quantum metrology with the goal of finding states that can measure a phase shift to a high precision. Our algorithm efficiently produces a number of novel solutions: we find experimentally ready schemes to produce states that show significant improvements over the state-of-the-art, and can measure with a precision that beats the shot noise limit by over a factor of 4. Furthermore, these states demonstrate a robustness to moderate/high photon losses, and we present a conceptually simple measurement scheme that saturates the Cramér-Rao bound.

Local versus global strategies in multiparameter estimation

“…For example, local strategies have greater flexibility in the distribution of resources and are more robust to local estimation failure. Furthermore, single-mode states with a large number variance can be made in experiments [14][15][16][17], and realistic schemes have been proposed to produce separable states that improve over the shot-noise limit by more than a factor of 4 [18]. By comparison, multimode-entangled states with large photon numbers are notoriously difficult to make: the largest two-mode optical NOON state that has been made experimentally contains only five photons [27].…”

“…A further discussion of this is given in Appendix C. However, the precision scaling with photon number is often not of direct relevance in an experiment, and a more relevant measure is the absolute precision that can be obtained given an allowed total photon number through the interferometer [4,29,30]. As already noted, there are a range of practical states which improve on the absolute precision of NOON states [14,18], and these are candidates for the multiparameter paradigm using the local estimation strategy considered herein.…”

“…In this more general setting we demonstrate that the same precision enhancements exhibited by the global strategies can be obtained with mode-separable states and local measurements alone. Local strategies offer a number of advantages over their global counterparts, including robustness to local estimation failure, more flexibility in the distribution of resources, and more realistic methods of state preparation [14][15][16][17][18], measurement, and control.…”

Flexible resources for quantum metrology

“…Meanwhile, the overhead needed for preparation and measurement of the optimal state does not depend on the noise, leaving room for an arbitrarily large advantage of our scheme over classical strategies for any fixed N. In addition, techniques that deal with errors and maintain a metrological advantage are known (see, e.g., [62][63][64]) and may be applicable here. We leave such extensions for future work, along with the explicit determination of optimal [68,69] and 'pretty good' states [70] for specific metrological tasks in our framework, where recent algorithmic approaches [71] may prove to be useful.…”

A hybrid machine learning algorithm for designing quantum experiments

“…The latter is of independent interest, as it quickly learned to accurately classify quantum states given their photon-number distributions.As artificial intelligence (AI) and machine learning develop, their range of applicability continues to grow. They are now being utilised in the fast-growing field of quantum machine learning [1-3], with one particular application demonstrating that AI is an effective tool for designing quantum physics experiments [4][5][6][7][8]. In this vein, here we introduce a hybrid algorithm that designs and optimises quantum optics experiments for producing a range of useful quantum states, including Schrödinger cat states [9][10][11] and cubic phase states [12].The core of our algorithm, named AdaQuantum [13] and introduced in [14] and [4], uses a genetic algorithm to search for optimal arrangements of quantum optics experimental equipment.…”