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The abstract notion of a Universal Turing machine cannot exist as a physical subsystem without the introduction of noise from an external energy source. Like all other physical systems, physical Turing machines must convert energy sourced from an external environment into useful work, thus subjecting them to the laws of thermodynamics. Consequently, asymptotic mathematical theorems including those derived by Godel and Turing do not bear any consequence on physical world because they can never be truly realised in physical systems. Rather these theorems highlight the seemingly unbridgeable chasm between Platonic forms (mathematics) and objects (physics).
As a milestone for general-purpose computing machines, we demonstrate that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. Moreover, on noisy devices without error correction, we show that si
We propose a realistic hybrid classical-quantum linear solver to solve systems of linear equations of a specific type, and demonstrate its feasibility using Qiskit on IBM Q systems. This algorithm makes use of quantum random walk that runs in $mathca
Recent years have enjoyed an overwhelming interest in quantum thermodynamics, a field of research aimed at understanding thermodynamic tasks performed in the quantum regime. Further progress, however, seems to be obstructed by the lack of experimenta
The seminal work by Sadi Carnot in the early nineteenth century provided the blueprint of a reversible heat engine and the celebrated second law of thermodynamics eventually followed. Almost two centuries later, the quest to formulate a quantum theor
The study of quantum cryptography and quantum entanglement has traditionally been based on two-level quantum systems (qubits) and more recently on three-level systems (qutrits). We investigate several classes of state-dependent quantum cloners for fo