Motivated by studies of typical properties of quantum states in statistical mechanics, we introduce phase-random states, an ensemble of pure states with fixed amplitudes and uniformly distributed phases in a fixed basis. We first show that canonical states typically appear in subsystems of phase-random states. We then investigate the simulatability of phase-random states, which is directly related to that of time evolution in closed systems, by studying their entanglement properties. We find that starting from a separable state, time evolutions under Hamiltonians composed of only separable eigenstates generate extremely high entanglement and are difficult to simulate with matrix product states. We also show that random quantum circuits consisting of only two-qubit diagonal unitaries can generate an ensemble with the same average entanglement as phase-random states.
Quantum supremacy with spin squeezed atomic ensembles
我们提出了一种方法来实现量子霸权使用合奏的量子比特，只使用自旋压缩，基础旋转，和Fock状态的测量。每个系综被假定为只能用它的总自旋来控制。使用重复序列的随机基旋转，然后挤压，我们表明，最终测量的概率分布迅速接近波特-托马斯分布。我们表明，采样概率可以与一个P-硬问题的复杂性缩放为$(N+1)^M$，其中$N$是在一个合奏和$ M $是合奏的量子比特数。该方案可以用热原子系综或冷原子系综实现。由于在典型的原子系综中有大量的原子，这允许使用适度数量的系综或门深度来访问量子霸权机制。
Partial projected ensembles reveal slow tilt-constrained information spreading
Institute for Quantum Science and Technology, Shanghai University（上海大学量子科学与技术研究院）；School of Physics and Optoelectronics, Xiangtan University（湘潭大学物理与光电工程学院）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
Real time quantum dynamics preaveraged over imaginary time path integral: A formal basis for both Centroid Molecular Dynamics and Ring Polymer Molecular Dynamics
