量子增强的连续变量量子态学习

高效地表征连续变量量子态对于量子通信、量子传感、量子模拟和量子计算非常重要。然而,传统的量子态重构和最近提出的经典影子重构需要对希尔伯特空间或相空间进行截断,导致所需样本复杂度随着模数的增加呈指数增长。本文提出了一种量子增强学习策略,用于克服此前的缺点。我们利用该策略来估计状态特征函数的点值,这对于量子态重构和推断量子保真度、非经典性和量子非高斯性等物理性质非常有用。我们证明,对于任何具有反射对称性的连续变量量子态$\rho$,例如零均值的高斯态、Fock态、Gottesman-Kitaev-Preskill态、Schrödinger猫态和二项式码态,在实际量子器件上,我们只需恒定数量的$\rho$副本即可精确地估计其特征函数在任意相空间点的平方。这可以通过在两个$\rho$副本上进行平衡分束器然后进行同步检测来实现。基于这个结果,我们还展示了,在给定非局域量子测量的情况下,对于任何具有反射对称性的$k$模连续变量态$\rho$,我们只需要$O(\log M)$个$\rho$副本即可在任意$M$个相空间点上准确估计其特征函数值。此外,副本数量与$k$无关。这可以与传统方法进行比较,该方法需要$\Omega(M)$个副本才能在$M$个任意相空间点上估计特征函数值。
Efficient characterization of continuous-variable quantum states is important
for quantum communication, quantum sensing, quantum simulation and quantum
computing. However, conventional quantum state tomography and recently proposed
classical shadow tomography require truncation of the Hilbert space or phase
space and the resulting sample complexity scales exponentially with the number
of modes. In this paper, we propose a quantum-enhanced learning strategy for
continuous-variable states overcoming the previous shortcomings. We use this to
estimate the point values of a state characteristic function, which is useful
for quantum state tomography and inferring physical properties like quantum
fidelity, nonclassicality and quantum non-Gaussianity. We show that for any
continuous-variable quantum states $\rho$ with reflection symmetry – for
example Gaussian states with zero mean values, Fock states,
Gottesman-Kitaev-Preskill states, Schr\”odinger cat states and binomial code
states – on practical quantum devices we only need a constant number of copies
of state $\rho$ to accurately estimate the square of its characteristic
function at arbitrary phase-space points. This is achieved by performinig a
balanced beam splitter on two copies of $\rho$ followed by homodyne
measurements. Based on this result, we show that, given nonlocal quantum
measurements, for any $k$-mode continuous-variable states $\rho$ having
reflection symmetry, we only require $O(\log M)$ copies of $\rho$ to accurately
estimate its characteristic function values at any $M$ phase-space points.
Furthermore, the number of copies is independent of $k$. This can be compared
with restricted conventional approach, where $\Omega(M)$ copies are required to
estimate the characteristic function values at $M$ arbitrary phase-space
points.
论文链接:http://arxiv.org/pdf/2303.05097v1


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