Principles and symmetries of complexity in quantum field theory

Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the complexity in continuous systems. Due to fundamental symmetries of quantum field theories, the Finsler metric is more constrained and consequently, the complexity of SU($n$) operators is uniquely determined as a length of a geodesic in the Finsler geometry. Our Finsler metric is bi-invariant contrary to the right-invariance of discrete qubit systems. We clarify why the bi-invariance is relevant in quantum field theoretic systems. After comparing our results with discrete qubit systems we show most results in $k$-local right-invariant metric can also appear in our framework. Based on the bi-invariance of our formalism, we propose a new interpretation for the Schr\"{o}dinger's equation in isolated systems - the quantum state evolves by the process of minimizing "computational cost."Comment: Published version; added a short introduction on Finsler geometr

Experimental demonstration of a non-destructive controlled-NOT quantum gate for two independent photon-qubits

Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum information processing. However, the photons, one of the best candidates for qubits, suffer from the lack of strong nonlinear coupling required for quantum logic operations. Here we show how this drawback can be overcome by reporting a proof-of-principle experimental demonstration of a non-destructive controlled-NOT (CNOT) gate for two independent photons using only linear optical elements in conjunction with single-photon sources and conditional dynamics. Moreover, we have exploited the CNOT gate to discriminate all the four Bell-states in a teleportation experiment.Comment: 4 pages, 4 figures, submitte

Resistance imparted by vitamin C, vitamin e and vitamin B12 to the acute hepatic glycogen change in rats caused by noise.

The effects of vitamin C, vitamin E and vitamin B12 on the noise-induced acute change in hepatic glycogen content in rats were investigated. The exposure of rats to 95 dB and 110 dB of noise acutely reduced their hepatic glycogens. Vitamin C (ascorbic acid) and vitamin E (alpha -tocopherol) attenuated the noise-inducedacute reduction in the hepatic glycogen contents. This result suggests that antioxidants could reduce the change via reactive oxygen species. Vitamin B12 (cobalamin) delayed the noiseinduced change, a finding that suggests that vitamin B12 could postpone the acute change via compensating for vitamin B12 deficiency