Randomized measurement protocols for lattice gauge theories

Randomized measurement protocols, including classical shadows, entanglement tomography, and randomized benchmarking are powerful techniques to estimate observables, perform state tomography, or extract the entanglement properties of quantum states. While unraveling the intricate structure of quantum states is generally difficult and resource-intensive, quantum systems in nature are often tightly constrained by symmetries. This can be leveraged by the symmetry-conscious randomized measurement schemes we propose, yielding clear advantages over symmetry-blind randomization such as reducing measurement costs, enabling symmetry-based error mitigation in experiments, allowing differentiated measurement of (lattice) gauge theory entanglement structure, and, potentially, the verification of topologically ordered states in existing and near-term experiments.Comment: 18 pages, 15 figure

Feasibility of a trapped atom interferometer with accelerating optical traps

In order to increase the measured phase of an atom interferometer and improve its sensitivity, researchers attempt to increase the enclosed space-time area using two methods: creating larger separations between the interferometer arms and having longer evolution times. However, increasing the evolution time reduces the bandwidth that can be sampled, whereas decreasing the evolution time worsens the sensitivity. In this paper, we attempt to address this by proposing a setup for high-bandwidth applications, with improved overall sensitivity. This is realized by accelerating and holding the atoms using optical dipole traps. We find that accelerations of up to $10^{3}$-$10^{5}$ m/s$^2$ can be achieved using acousto-optic deflectors (AODs) to move the traps. By comparing the sensitivity of our approach to acceleration as a baseline to traditional atom interferometry, we find a substantial improvement to the state of the art. In the limit of appropriate beam and optics stabilization, sensitivities approaching 10$^{-14}$ (m/s$^2$)/$\sqrt{\rm Hz}$ may be achievable at 1 Hz, while detection at 1 kHz with a sensitivity an order of magnitude better than traditional free-fall atom interferometers is possible with today's systems.Comment: 25 pages. 9 figures. New subsection on achievable sensitivities added. Some corrections of factors of 2 and \pi. Numerics update

Shadow process tomography of quantum channels

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scale exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. We make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.Comment: 12 pages, 5 figures; Added citation to similar work; Errors corrected. Previous statements of main result first missed and then miscalculated an exponential cost in system size; Version accepted for publicatio

Decoherence from Long-Range Forces in Atom Interferometry

Atom interferometers provide a powerful means of realizing quantum coherent systems with increasingly macroscopic extent in space and time. These systems provide an opportunity for a variety of novel tests of fundamental physics, including ultralight dark matter searches and tests of modifications of gravity, using long drop times, microgravity. However, as experiments operate with longer periods of free fall and become sensitive to smaller background effects, key questions start to emerge about the fundamental limits to future atom interferometery experiments. We study the effects on atomic coherence from hard-to-screen backgrounds due to baths of ambient particles with long-range forces, such as gravitating baths and charged cosmic rays. Our approach - working in the Heisenberg picture for the atomic motion - makes proper inclusion of the experimental apparatus feasible and clearly shows how to handle long-range forces and preferred frame ambiguities. We find that these potential backgrounds are likely negligible for the next generation of interferometers, as aggressive estimates for the gravitational decoherence from a background bath of dark matter particles gives a decoherence timescale on the order of years.Comment: 32 pages, 3 figure