We present an effective evolution equation for a coarse-grained distribution function of a long-rangeinteracting system preserving the symplectic structure of the noncollisional Boltzmann, or Vlasov, equation. First, we derive a general form of such an equation based on symmetry considerations only. Then we explicitly derive the equation for one-dimensional systems, finding that it has the form predicted on general grounds. Finally, we use this equation to predict the dependence of the damping times on the coarse-graining scale and numerically check it for some one-dimensional models, including the Hamiltonian mean-field model, a scalar field with quartic interaction, a 1-d self-gravitating system, and a self-gravitating ring.
We report on a quantum thermodynamic method to purify a qubit on a quantum processing unit (QPU) equipped with (nearly) identical qubits. Our starting point is a three qubit design that emulates the well-known two qubit swap engine. Similar to standard fridges, the method would allow us to cool down a qubit at the expense of heating two other qubits. A minimal modification thereof leads to a more practical three qubit design that allows for enhanced refrigeration tasks, such as increasing the purity of one qubit at the expense of decreasing the purity of the other two. The method is based on the application of properly designed quantum circuits and can therefore be run on any gate model quantum computer. We implement it on a publicly available superconducting qubit based QPU and observe a purification capability down to 200 mK. We identify gate noise as the main obstacle toward practical application for quantum computing.
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