泡利分辨的虚拟蒸馏
Pauli-resolved virtual distillation
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中文总结 AI 辅助
本文提出泡利分辨的虚拟蒸馏协议，通过成对副本抵消反交换符号，以指数加速学习平方泡利矩，并引入量子伯恩斯坦范数度量非兼容性，实现最优副本数。
中文摘要 AI 辅助
学习虚拟蒸馏量子态 $\rho^m/\text{tr}(\rho^m)$ 的完整泡利轮廓，迄今为止需要指数多个 $\rho$ 的副本。我们证明，所有 $4^n$ 个平方泡利矩 $[\text{tr}(P\rho^m)]^2$ 可以在一个 $2m$ 副本测量设置下，使用 $O(m[n+\log(1/\delta)]/\varepsilon^2)$ 个副本，以加性误差 $\varepsilon$ 和置信度 $1-\delta$ 学习。这相对于之前的协议，在系统规模 $n$ 上实现了指数加速。对于 $m=2$，我们提出了相干贝尔差分采样电路，可在当前设备上实现该测量。加速源于成对副本抵消了泡利算符的反交换符号，从而消除了泡利族的非兼容性。我们通过引入量子伯恩斯坦范数（一种可计算的非线性泛函非兼容性度量）来证明这种消除。进一步的信息论 $m$ 副本协议使用 $O(m[n+\log(1/\delta)]/\varepsilon^4)$ 个副本恢复带符号矩 $\text{tr}(P\rho^m)$。对于所述下界范围内的固定 $m$，它达到了最优副本数，因为任何使用更少副本的协议都需要指数多个副本。
英文摘要
Learning the full Pauli profile of the virtually distilled quantum state $ρ^m/\text{tr}(ρ^m)$ has so far required exponentially many copies of $ρ$. We show that all $4^n$ squared Pauli moments $[\text{tr}(Pρ^m)]^2$ can be learned to additive error $\varepsilon$ with confidence $1-δ$ from one $2m$-replica measurement setting using $O(m[n+\log(1/δ)]/\varepsilon^2)$ copies. This is an exponential speedup in the system size $n$ over previous protocols. For $m = 2$, we propose the coherent Bell difference sampling circuit that realizes this measurement on current devices. The speedup originates from paired replicas that cancel the anticommutation signs of Pauli operators, collapsing the incompatibility of the Pauli family. We certify this collapse by introducing the quantum Bernstein norm, a computable incompatibility measure for nonlinear functionals. A further information-theoretic $m$-replica protocol recovers the signed moments $\text{tr}(Pρ^m)$ using $O(m[n+\log(1/δ)]/\varepsilon^4)$ copies. For fixed $m$ in the stated lower-bound regime, it attains the optimal replica number, since any protocol with fewer replicas requires exponentially many copies.
发表机构
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China（中国科学技术大学物理科学学院和微观尺度物理国家研究中心）
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China（中国科学技术大学上海量子科学研究与创新中心和中国科学院量子信息与量子物理学前沿卓越创新中心）
- Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）
- State Key Lab of Millimeter Waves, Southeast University（东南大学毫米波国家重点实验室）
- College of Computer Science and Technology, National University of Defense Technology（国防科技大学计算机学院）
机构由 AI 辅助整理，请以论文原文为准。
