Bell's Inequality and Entanglement in Qubits

We propose an alternative evaluation of quantum entanglement by measuring the maximum violation of the Bell's inequality without performing a partial trace operation. This proposal is demonstrated by bridging the maximum violation of the Bell's inequality and the concurrence of a pure state in an $n$-qubit system, in which one subsystem only contains one qubit and the state is a linear combination of two product states. We apply this relation to the ground states of four qubits in the Wen-Plaquette model and show that they are maximally entangled. A topological entanglement entropy of the Wen-Plaquette model could be obtained by relating the upper bound of the maximum violation of the Bell's inequality to the concurrences of a pure state with respect to different bipartitions.Comment: 10 page

Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions

The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments. Power-law interactions with strength decaying as $1/r^\alpha$ in the distance $r$ provide an experimentally realizable resource for information processing, whilst still retaining long-range connectivity. We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets. Our implementation allows the quantum Fourier transform (QFT) and Shor's algorithm to be performed on a $D$-dimensional lattice in time logarithmic in the number of qubits for interactions with $\alpha \le D$. As a corollary, we show that power-law systems with $\alpha \le D$ are difficult to simulate classically even for short times, under a standard assumption that factoring is classically intractable. Complementarily, we develop a new technique to give a general lower bound, linear in the size of the system, on the time required to implement the QFT and the fanout gate in systems that are constrained by a linear light cone. This allows us to prove an asymptotically tighter lower bound for long-range systems than is possible with previously available techniques.Comment: 6 pages, 1 figur

SIMD Everywhere Optimization from ARM NEON to RISC-V Vector Extensions

Many libraries, such as OpenCV, FFmpeg, XNNPACK, and Eigen, utilize Arm or x86 SIMD Intrinsics to optimize programs for performance. With the emergence of RISC-V Vector Extensions (RVV), there is a need to migrate these performance legacy codes for RVV. Currently, the migration of NEON code to RVV code requires manual rewriting, which is a time-consuming and error-prone process. In this work, we use the open source tool, "SIMD Everywhere" (SIMDe), to automate the migration. Our primary task is to enhance SIMDe to enable the conversion of ARM NEON Intrinsics types and functions to their corresponding RVV Intrinsics types and functions. For type conversion, we devise strategies to convert Neon Intrinsics types to RVV Intrinsics by considering the vector length agnostic (vla) architectures. With function conversions, we analyze commonly used conversion methods in SIMDe and develop customized conversions for each function based on the results of RVV code generations. In our experiments with Google XNNPACK library, our enhanced SIMDe achieves speedup ranging from 1.51x to 5.13x compared to the original SIMDe, which does not utilize customized RVV implementations for the conversions