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Register a new userSwarm optimization for adaptive phase measurements with low visibility
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Added by
Dominic William Berry
Publication date
2013
fields
Physics
and research's language is
English
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Adaptive feedback normally provides the greatest accuracy for optical phase measurements. New advances in nitrogen vacancy centre technology have enabled magnetometry via individual spin measurements, which are similar to optical phase measurements but with low visibility. The adaptive measurements that previously worked well with high-visibility optical interferometry break down and give poor results for nitrogen vacancy centre measurements. We use advanced search techniques based on swarm optimisation to design better adaptive measurements that can provide improved measurement accuracy with low-visibility interferometry, with applications in nitrogen vacancy centre magnetometry.
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In fitting data with a spline, finding the optimal placement of knots can significantly improve the quality of the fit. However, the challenging high-dimensional and non-convex optimization problem associated with completely free knot placement has been a major roadblock in using this approach. We present a method that uses particle swarm optimization (PSO) combined with model selection to address this challenge. The problem of overfitting due to knot clustering that accompanies free knot placement is mitigated in this method by explicit regularization, resulting in a significantly improved performance on highly noisy data. The principal design choices available in the method are delineated and a statistically rigorous study of their effect on performance is carried out using simulated data and a wide variety of benchmark functions. Our results demonstrate that PSO-based free knot placement leads to a viable and flexible adaptive spline fitting approach that allows the fitting of both smooth and non-smooth functions.
We analyze the problem of quantum-limited estimation of a stochastically varying phase of a continuous beam (rather than a pulse) of the electromagnetic field. We consider both non-adaptive and adaptive measurements, and both dyne detection (using a local oscillator) and interferometric detection. We take the phase variation to be dotphi = sqrt{kappa}xi(t), where xi(t) is delta-correlated Gaussian noise. For a beam of power P, the important dimensionless parameter is N=P/hbaromegakappa, the number of photons per coherence time. For the case of dyne detection, both continuous-wave (cw) coherent beams and cw (broadband) squeezed beams are considered. For a coherent beam a simple feedback scheme gives good results, with a phase variance simeq N^{-1/2}/2. This is sqrt{2} times smaller than that achievable by nonadaptive (heterodyne) detection. For a squeezed beam a more accurate feedback scheme gives a variance scaling as N^{-2/3}, compared to N^{-1/2} for heterodyne detection. For the case of interferometry only a coherent input into one port is considered. The locally optimal feedback scheme is identified, and it is shown to give a variance scaling as N^{-1/2}. It offers a significant improvement over nonadaptive interferometry only for N of order unity.
We derive, and experimentally demonstrate, an interferometric scheme for unambiguous phase estimation with precision scaling at the Heisenberg limit that does not require adaptive measurements. That is, with no prior knowledge of the phase, we can obtain an estimate of the phase with a standard deviation that is only a small constant factor larger than the minimum physically allowed value. Our scheme resolves the phase ambiguity that exists when multiple passes through a phase shift, or NOON states, are used to obtain improved phase resolution. Like a recently introduced adaptive technique [Higgins et al 2007 Nature 450 393], our experiment uses multiple applications of the phase shift on single photons. By not requiring adaptive measurements, but rather using a predetermined measurement sequence, the present scheme is both conceptually simpler and significantly easier to implement. Additionally, we demonstrate a simplified adaptive scheme that also surpasses the standard quantum limit for single passes.
Coordinated motion control in swarm robotics aims to ensure the coherence of members in space, i.e., the robots in a swarm perform coordinated movements to maintain spatial structures. This problem can be modeled as a tracking control problem, in which individuals in the swarm follow a target position with the consideration of specific relative distance or orientations. To keep the communication cost low, the PID controller can be utilized to achieve the leader-follower tracking control task without the information of leader velocities. However, the controllers parameters need to be optimized to adapt to situations changing, such as the different swarm population, the changing of the target to be followed, and the anti-collision demands, etc. In this letter, we apply a modified Brain Storm Optimization (BSO) algorithm to an incremental PID tracking controller to get the relatively optimal parameters adaptively for leader-follower formation control for swarm robotics. Simulation results show that the proposed method could reach the optimal parameters during robot movements. The flexibility and scalability are also validated, which ensures that the proposed method can adapt to different situations and be a good candidate for coordinated motion control for swarm robotics in more realistic scenarios.
The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes the solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which two unitary operators are alternately applied to the qubits. In this paper, this procedure is modified by updating the operators themselves to include local fields, using information from the measured wavefunction at the end of one iteration step to improve the operators at later steps. It is shown by numerical simulation on MAXCUT problems that this decreases the runtime of QAOA very substantially. This improvement appears to increase with the problem size. Our method requires essentially the same number of quantum gates per optimization step as the standard QAOA. Application of this modified algorithm should bring closer the time to quantum advantage for optimization problems.
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