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digital data processors, but others remain time-consuming. In particular, the rapidly increasing volume of image data as well as increasingly challenging computational tasks have become important driving forces for further improving the efficiency of image processing and analysis.Quantum information processing (QIP), which exploits quantum-mechanical phenomena such as quantum superpositions and quantum entanglement [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], allows one to overcome the limitations of classical computation and reaches higher computational speed for certain problems like factoring large numbers [24,25] , searching an unsorted database [26], boson sampling [27][28][29][30][31][32], quantum simulation [33-40], solving linear systems of equations [41][42][43][44][45], and machine learning [46][47][48]. These unique quantum properties, such as quantum superposition and quantum parallelism, may also be used to speed up signal and data processing [49,50]. For quantum image processing, quantum image representation (QImR) plays a key role, which substantively determines the kinds of processing tasks and how well they can be performed. A number of QImRs [51-54] have been discussed.In this article, we demonstrate the basic framework of quan-arXiv:1801.01465v1 [quant-ph]

Certain n-qubit quantum systems can be faithfully simulated by quantum circuits with only O(log(n)) qubits [B. Kraus, Phys. Rev. Lett. 107, 250503 (2011)]. Here we report an experimental realization of this compressed quantum simulation on a one-dimensional Ising chain. By utilizing an nuclear magnetic resonance quantum simulator with only five qubits, the property of ground-state magnetization of an open-boundary 32-spin Ising model is experimentally simulated, prefacing the expected quantum phase transition in the thermodynamic limit. This experimental protocol can be straightforwardly extended to systems with hundreds of spins by compressing them into up to merely 10-qubit systems. Our experiment paves the way for exploring physical phenomena in large-scale quantum systems with quantum simulators under current technology.

Quantum coherence is an invaluable physical resource for various quantum technologies. As a bona fide measure in quantifying coherence, the robustness of coherence (ROC) is not only mathematically rigorous, but also physically meaningful. We experimentally demonstrate the witness-observable and operational feature of the ROC in a multiqubit nuclear magnetic resonance system. We realize witness measurements by detecting the populations of quantum systems in one trial. The approach may also apply to physical systems compatible with ensemble or nondemolition measurements. Moreover, we experimentally show that the ROC quantifies the advantage enabled by a quantum state in a phase discrimination task.

Topological orders are exotic phases of matter existing in strongly correlated quantum systems, which are beyond the usual symmetry description and cannot be distinguished by local order parameters. Here we report an experimental quantum simulation of the Wen-plaquette spin model with different topological orders in a nuclear magnetic resonance system, and observe the adiabatic transition between two Z(2) topological orders through a spin-polarized phase by measuring the nonlocal closed-string (Wilson loop) operator. Moreover, we also measure the entanglement properties of the topological orders. This work confirms the adiabatic method for preparing topologically ordered states and provides an experimental tool for further studies of complex quantum systems.