Medium-scale quantum devices that integrate about hundreds of physical qubits are likely to be developed in the near future. However, these devices will lack the resources for realizing quantum fault tolerance. Therefore, the main challenge of exploring the advantage of quantum computation is to minimize the impact of device and control imperfections without complete logical encoding. Quantum error mitigation is a solution satisfying the requirement. Here, we demonstrate an error mitigation protocol based on gate set tomography and quasi-probability decomposition. One- and two-qubit circuits are tested on a superconducting device, and computation errors are successfully suppressed. Because this protocol is universal for digital quantum computers and algorithms computing expected values, our results suggest that error mitigation can be an essential component of near-future quantum computation.

In electro discharge machining (EDM) for 3D micro structures, the electrode wear is serious and it needs to be compensated in process. To obtain a better balance of the machining accuracy and efficiency, a servo scanning EDM method is proposed for 3D micro structures, in which the electrode wear is compensated on real-time by controlling the discharge gap constant. It is supposed reasonably that the machining depth of each layer in servo scanning EDM is consistent if discharge gap is kept preferably. The servo scanning EDM strategies include the model design by Pro/Engineer (Pro/E), the plan and simulation of scanning path, and the machining process. The 3D micro structures are machined by scanning layer-by-layer under servo control of the electrode with monitoring discharge gap signal. The CAM, gap servo control, and real-time electrode wear compensating are integrated into the machining system. The evaluation experiments of servo scanning EDM and the typical machining experiments of 3D micro structures have been carried out. The machining results show that the electro discharge in the servo scanning EDM is more stable. Servo scanning micro EDM is propitious to improve machining accuracy and efficiency in 3D micro structures.

The discrimination between two unknown states can be performed by a universal programmable discriminator, where the copies of the two possible states are stored in two program systems respectively and the copies of data, which we want to confirm, are provided in the data system. In the present paper, we propose a group-theretic approach to the multi-copy programmable state discrimination problem. By equivalence of unknown pure states to known mixed states and with the representation theory of $U(n)$ group, we construct the Jordan basis to derive the analytical results for both the optimal unambiguous discrimination and minimum-error discrimination. The POVM operators for unambiguous discrimination and orthogonal measurement operators for minimum-error discrimination are obtained. We find that the optimal failure probability and minimum-error probability for the discrimination between the mean input mixd states are dependent on the dimension of the unknown qudit states. We applied the approach to generalize the results of He and Bergou (2007) from qubit to qudit case, and we further solve the problem of programmable dicriminators with arbitrary copies of unknown states in both program and data systems.

Kraus operators are widely used in describing the evolution of an open quantum system. In this paper, we study the properties of a Kraus operator as a linear combination of unitary matrices and demonstrate that every single Kraus operator can be realized in an interference quantum circuit. We determine the minima of both l 1 and l 0 norm of the combination coefficients, where l 1 norm means the sum of the absolute values of the coefficients and l 0 norm means the number of non-zero coefficients. We find that both of them have clear physical meanings. The l 1 minimum signifies the most constructive interference, and the l 0 minimum provides the simplest way to construct a Kraus operator in a quantum circuit. These results may be useful in understanding interference and Kraus operators as well as in designing a quantum algorithm with a quantum computer in an open environment.

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