We discuss the applicability of large quantum annealers for the purpose of processing Remote Sensing images. We show an application of currently existing quantum annealers for the purpose of post-processing segmentation of a hyperspectral image. We show that in principle there might exist useful applications of large scale quantum annealers for the purpose of Remote Sensing data processing.

Supervised machine learning techniques are widely used for hyper-spectral images segmentation. A typical simple scheme of classification of such images probabilistically assigns a label to each individual pixel omitting information about pixel surroundings. In order to achieve better classification results for real world images one has to agree the local label obtained from the classifier with the classes of pixel neighborhood. A popular way to do it is through a probabilistic graphical model, where label distributions for individual pixels are mapped into a graph of neighborhood relations. One way to realize this approach is to use Ising models, where class probability is mapped to spin energy and class-class interaction is mapped to the spins coupling. By finding low energy states of such an Ising model we can perform post-processing of segmented images. In this work we present how this postprocessing can be implemented using a quantum annealer.

This article describes a practical Earth Observation use case that would benefit from quantum computing. We analyze three quantum neural network algorithms. We implemented one of the algorithms on the EuroSAT dataset. We compare the algorithms with respect to complexity and degree of quantization. We believe that the algorithms we propose would be useful for the remote sensing community when quantum computing technologies become widely available.1

Probabilistic quantum error correction is an error-correcting procedure which uses postselection to determine if the encoded information was successfully restored. In this work, we analyze the probabilistic version of the error-correcting procedure for general noise. We generalize the Knill-Laflamme conditions for probabilistically correctable errors. We show that for some noise channels, the initial information has to be encoded into a mixed state to maximize the probability of successful error correction. Finally, the probabilistic error-correcting procedure offers an advantage over the deterministic procedure. Reducing the probability of successful error correction allows for correcting errors generated by a broader class of noise channels. Significantly, if the errors are caused by a unitary interaction with an auxiliary qubit system, we can probabilistically restore a qubit state by using only one additional physical qubit.

In this work, we present an in-depth study of average-case quantum distances introduced in Maciejewski et al. (2022). The average-case distances approximate, up to the relative error, the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in which quantum objects of interest (states, measurements, or channels) are intertwined with random quantum circuits. Contrary to conventional distances, such as trace distance or diamond norm, they quantifyaverage-casestatistical distinguishability via random quantum circuits. We prove that once a family of random circuits forms an$\delta $-approximate 4-design, with$\delta =o(d^{-8})$, then the average-case distances can be approximated by simple explicit functions that can be expressed via simple degree two polynomials in objects of interest. For systems of moderate dimension, they can be easily explicitly computed – no optimization is needed as opposed to diamond norm distance between channels or operational distance between measurements. We prove that those functions, which we call quantum average-case distances, have a plethora of desirable properties, such as subadditivity w.r.t. tensor products, joint convexity, and (restricted) data-processing inequalities. Notably, all distances utilize the Hilbert-Schmidt (HS) norm, which provides this norm with a new operational interpretation. We also provide upper bounds on the maximal ratio between worst-case and average-case distances, and for each of them, we provide an example that saturates the bound. Specifically, we show that for each dimension$d$this ratio is at most$d^{\frac {1}{2}}, d, d^{\frac {3}{2}}$for states, measurements, and channels, respectively. To support the practical usefulness of our findings, we study multiple examples in which average-case quantum distances can be calculated analytically.

We introduce and analyse the problem of encoding classical information into different resources of a quantum state. More precisely, we consider a general class of communication scenarios characterised by encoding operations that commute with a unique resource destroying map and leave free states invariant. Our motivating example is given by encoding information into coherences of a quantum system with respect to a fixed basis (with unitaries diagonal in that basis as encodings and the decoherence channel as a resource destroying map), but the generality of the framework allows us to explore applications ranging from super-dense coding to thermodynamics. For any state, we find that the number of messages that can be encoded into it using such operations in a one-shot scenario is upper bounded in terms of the information spectrum relative entropy between the given state and its version with erased resources. Furthermore, if the resource destroying map is the twirling channel over some unitary group, we find matching one-shot lower bounds as well. In the asymptotic setting where we encode into many copies of the resource state, our bounds yield an operational interpretation of resource monotones such as the relative entropy of coherence and its corresponding relative entropy variance.