Quantum Algorithm for Approximating Maximum Independent Sets

使用局部失谐在里德堡原子阵列上近似求解最大独立集

Approximating maximum independent set on Rydberg atom arrays using local detunings

本研究提出一种通过调整里德堡哈密顿量局部失谐以近似求解最大独立集的策略，显著降低了多种图的错误率，提升了量子多体基态制备保真度，并结合非阿贝尔绝热混合取得了优异效果。

A Framework for Approximating Qubit Unitaries

We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is asymptotically optimal. The algorithm achieves the same quality of approximation as previously-known algorithms for Clifford+T [arXiv:1212.6253], V-basis [arXiv:1303.1411] and Clifford+$π/12$ [arXiv:1409.3552], running on average in time polynomial in $O(\log(1/\varepsilon))$ (conditional on a number-theoretic conjecture). Ours is the first such algorithm th…

通过重复直到成功电路直接近似U(2)

Direct U(2) approximation via repeat-until-success circuits

本文提出一种直接高效近似任意单量子比特单位元的方法，无需欧拉分解和幅值近似问题，仅需一个辅助量子比特。该技术还可用于多量子比特门集如Clifford和CS、Clifford和CCZ，以及使用Real Clifford和CCZ近似正交矩阵。

流式模型中近似最大有向割的指数级量子空间优势

Exponential Quantum Space Advantage for Approximating Maximum Directed Cut in the Streaming Model

针对最大有向割问题，提出一种使用 polylog(n) 空间的量子流式算法，实现 0.4844 近似比，首次在自然流式问题中取得指数级量子空间优势。

Approximating the Set of Separable States Using the Positive Partial Transpose Test

The positive partial transpose test is one of the main criteria for detecting entanglement, and the set of states with positive partial transpose is considered as an approximation of the set of separable states. However, we do not know to what extent this criterion, as well as the approximation, are efficient. In this paper, we show that the positive partial transpose test gives no bound on the distance of a density matrix from separable states. More precisely, we prove that, as the dimension of the space tends to infinity, the maximum trace distance of a positive partial transpose state from …

Approximating the ground state of gapped quantum spin systems

We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset, X, of V the ground state projector can be approximated by the product of two projections, one supported on X and one …