Trotter24: A precision-guaranteed adaptive stepsize Trotterization for Hamiltonian simulations

Choosing an optimal time step $\delta t$ is crucial for an efficient Hamiltonian simulation based on Trotterization but difficult due to the complex structure of the Trotter error. Here we develop a method measuring the Trotter error by combining the second- and fourth-order Trotterizations rather than consulting with mathematical error bounds. Implementing this method, we construct an algorithm, which we name Trotter24, for adaptively using almost the largest stepsize $\delta t$, which keeps quantum circuits shallowest, within an error tolerance $\epsilon$ preset for our purpose. Trotter24 applies to generic Hamiltonians, including time-dependent ones, and can be generalized to any orders of Trotterization. Benchmarking it in a quantum spin chain, we find the adaptively chosen $\delta t$ to be about ten times larger than that inferred from known upper bounds of Trotter errors. Trotter24 allows us to keep the quantum circuit thus shallower within the error tolerance in exchange for paying the cost of measurements.Comment: 11 pages, 6 figure

Elastic Instabilities within Antiferromagnetically Ordered Phase in the Orbitally-Frustrated Spinel GeCo2_2O4_4

Ultrasound velocity measurements of the orbitally-frustrated GeCo$_2$O$_4$ reveal unusual elastic instabilities due to the phonon-spin coupling within the antiferromagnetic phase. Shear moduli exhibit anomalies arising from the coupling to short-range ferromagnetic excitations. Diplike anomalies in the magnetic-field dependence of elastic moduli reveal magnetic-field-induced orbital order-order transitions. These results strongly suggest the presence of geometrical orbital frustration which causes novel orbital phenomena within the antiferromagnetic phase.Comment: 5 pages, 3 figure

Cooperative Step Climbing Using Connected Wheeled Robots and Evaluation of Remote Operability

The present study evaluates the remote operability of step climbing using two connected robots that are teleoperated by individual operators. In general, a teleoperated robot is manipulated by an operator who is viewing moving images from a camera, which is one of the greatest advantages of such a system. However, robot teleoperation is not easy when a teleoperated robot is affected by the force from another robot or object. We constructed a step climbing system using two connected teleoperated robots. A theoretical analysis and the results of simulations clarified the correlations among the robot velocity, the manipulation time of the robots, and the height of the front wheels when climbing a step. The experimental results demonstrate the step climbing ability of the teleoperated robot system