This paper introduces two techniques that make the standard Quantum Approximate Optimization Algorithm (QAOA) more suitable for constrained optimization problems. The first technique describes how to use the outcome of a prior greedy classical algorithm to define an initial quantum state and mixing operation to adjust the quantum optimization algorithm to explore the possible answers around this initial greedy solution. The second technique is used to nudge the quantum exploration to avoid the local minima around the greedy solutions. To analyze the benefits of these two techniques we run the quantum algorithm on known hard instances of the Knapsack Problem using unit depth quantum circuits. The results show that the adjusted quantum optimization heuristics typically perform better than various classical heuristics.
This paper presents a method of optical magnetometry with parts-per-billion resolution that is able to detect biomagnetic signals generated from the human brain and heart in Earth’s ambient environment. The magnetically silent sensors measure the total magnetic field by detecting the free-precession frequency in a highly spin-polarized alkali-metal vapor. A first-order gradiometer is formed from two magnetometers that are separated by a 3-cm baseline. The gradiometer operates from a laptop consuming 5 W over a USB port, enabled by state-of-the-art microfabricated alkali-vapor cells, advanced thermal insulation, custom electronics, and compact lasers within the sensor head. The gradiometer has a sensitivity of 16 fT/cm/Hz1/2 outdoors, which we use to detect neuronal electrical currents and magnetic cardiography signals. Recording of neuronal magnetic fields is one of a few available methods for noninvasive functional brain imaging that usually requires extensive magnetic shielding and other infrastructure. This work demonstrates the possibility of a dense array of portable biomagnetic sensors that are deployable in a variety of natural environments.