Quantum unsupervised and supervised learning on superconducting processors (pp541-552)
          Abhijat Sarma, Rupak Chatterjee, Kaitlin Gili, and Ting Yu
Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the data, the computation time for training and using these statistical models grows quickly. Here, we propose and implement on the IBMQ a quantum analogue to K-means clustering, and compare it to a previously developed quantum support vector machine. We find the algorithm's accuracy comparable to the classical K-means algorithm for clustering and classification problems, and find that it becomes less computationally expensive to implement for large datasets as compared to its classical counterpart.

Quantum coherence, discord and correlation measures based on Tsallis relative entropy (pp553-569)
          Anna Vershynina
Several ways have been proposed in the literature to define a coherence measure based on Tsallis relative entropy. One of them is defined as a distance between a state and a set of incoherent states with Tsallis relative entropy taken as a distance measure. Unfortunately, this measure does not satisfy the required strong monotonicity, but a modification of this coherence has been proposed that does. We introduce three new Tsallis coherence measures coming from a more general definition that also satisfy the strong monotonicity, and compare all five definitions between each other. Using three coherence measures that we discuss, one can also define a discord. Two of these have been used in the literature, and another one is new. We also discuss two correlation measures based on Tsallis relative entropy. We provide explicit expressions for all three discord and two correlation measure on pure states.  Lastly, we provide tight upper and lower bounds on two discord and correlations measures on any quantum state, with the condition for equality.

About quantum computer software (pp570-580)
         Yuri I. Ozhigov
Quantum computer is the key to controlling complex processes. If its hardware, in general is successfully created on the basis of the physical baggage of the 20th century, the mathematical software is fundamentally lagging behind. Feynman's user interface in the form of quantum gate arrays, cannot be used for the control because it gives the solution of the Schrödinger equation with quadratic slowdown compared to the real process. The software must then imitate the real process using appropriate program primitives written as the programs for classical supercomputer. The decoherence will be reflected by some constant - the number of basic states that can fit into the limited of memory available to software. The real value of this constant can be found in the experimental realization of Grover search algorithm. Rough estimates of this constant are given based on the  simplest processes of quantum electrodynamics and nuclear decay.

CNOT circuit extraction for topologically-constrained quantum memories (pp581-596)
         Aleks Kissinger and Arianne Meijer-van de Griend
Many physical implementations of quantum computers impose stringent memory constraints in which 2-qubit operations can only be performed between qubits which are nearest neighbours in a lattice or graph structure. Hence, before a computation can be run on such a device, it must be mapped onto the physical architecture. That is, logical qubits must be assigned physical locations in the quantum memory, and the circuit must be replaced by an equivalent one containing only operations between nearest neighbours. In this paper, we give a new technique for quantum circuit mapping (a.k.a. routing), based on Gaussian elimination constrained to certain optimal spanning trees called Steiner trees. We give a reference implementation of the technique for CNOT circuits and show that it significantly out-performs general-purpose routines on CNOT circuits. We then comment on how the technique can be extended straightforwardly to the synthesis of CNOT+Rz circuits and as a modification to a recently-proposed circuit simplification/extraction procedure for generic circuits based on the ZX-calculus.

A quantum algorithm for simulating non-sparse Hamiltonians (pp597-615)
         Chunhao Wang and Leonard Wossnig
We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the input model where the entries of the Hamiltonian are stored in a data structure in a quantum random access memory (qRAM) which allows for the efficient preparation of states that encode the rows of the Hamiltonian. We use a linear combination of quantum walks to achieve poly-logarithmic dependence on precision. The time complexity of our algorithm, measured in terms of the circuit depth, is $O(t\sqrt{N}\norm{H}\,\polylog(N, t\norm{H}, 1/\epsilon))$, where $t$ is the evolution time, $N$ is the dimension of the system, and $\epsilon$ is the error in the final state, which we call precision. Our algorithm can be directly applied as a subroutine for unitary implementation and quantum linear systems solvers, achieving $\widetilde{O}(\sqrt{N})$ dependence for both applications.

Perspective: 

Image processing: why quantum? (pp616-626)
         Marius Nagy and Naya Nagy
Quantum Image Processing has exploded in recent years with dozens of papers trying to take advantage of quantum parallelism in order to offer a better alternative to how current computers are dealing with digital images. The vast majority of these papers define or make use of quantum representations based on very large superposition states spanning as many terms as there are pixels in the image they try to represent. While such a representation may apparently offer an advantage  in terms of space (number of qubits used) and speed of processing (due to quantum parallelism), it also harbors a fundamental flaw: only one pixel can be recovered from the quantum representation of the entire image, and even that one is obtained non-deterministically through a measurement operation applied on the superposition state. We investigate in detail this measurement bottleneck problem by looking at the number of copies of the quantum representation that are necessary in order to recover various fractions of the original image. The results clearly show that any potential advantage a quantum representation might bring with respect to a classical one is paid for dearly with the huge amount of resources (space and time) required by a quantum approach to image processing.