发表机构
USRA Research Institute for Advanced Computer Science（美国大学研究协会高级计算机科学研究机构）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探究量子优化的量子松弛中经典变量压缩的资源权衡，明确马约拉纳编码的通用裕度缩放规律，指出压缩虽省量子比特但会转移成本。
AI 中文摘要
量子比特高效的量子松弛将经典决策变量压缩为数量显著更少的量子比特上的期望值，我们探究这种压缩对量子优化带来的资源权衡。对于n个量子比特上的完全二次-马约拉纳编码，成对关联子可表示m=Θ(n²)个二元变量。我们将通用裕度定义为，在所有目标符号分配下能保证的最小关联子幅值。我们证明其恰好为Δ_Maj(n)=tan(π/(4n))=Θ(1/n)，而均匀随机符号分配保留Θ(1/√n)的目标特定裕度，更强的1/n最坏情况缩放是马约拉纳特有的。此外，任意密度算子和费米高斯态生成相同的二次-马约拉纳协变体，因此非高斯态资源无法扩展这种两点松弛。超出马约拉纳范围，标准量子随机存取码界限提供通用信息论基线：对于n个量子比特上任意固定的m个指定二元可观测量族，通用裕度至多为√((2ln2·n/m))；而从N份副本中以高于1/2的恒定成功概率进行任意随机存取解码，要求nN=Ω(m)。对于需在所有目标上均匀工作的固定泡利关联编码，在平滑符号解码下维持固定非零解码幅值，需要缩放参数随可用裕度缩小而增大。因此，压缩虽能提供可观的量子比特节省，却会将成本转移至受限的期望值几何结构、更小的期望值幅值或更苛刻的信息恢复，而非消除成本。
英文摘要
Qubit-efficient quantum relaxations compress classical decision variables into expectation values on substantially fewer qubits. We ask what resource tradeoffs this compression entails for quantum optimization. For the complete quadratic-Majorana encoding of $m=Θ(n^2)$ binary variables on~$n$ qubits, we define the universal margin as the smallest correlator magnitude that can be guaranteed with prescribed signs for every target sign (bit) assignment. We show that it is exactly $Δ_{\rm Maj}(n)=\tan\!\left(\fracπ{4n}\right)=Θ(1/n)$, whereas uniformly random sign assignments retain $Θ(1/\sqrt n)$ target-specific margins. Arbitrary density operators and mixed fermionic Gaussian states generate the same quadratic-Majorana covariance body, so non-Gaussian state resources cannot enlarge this two-point relaxation. More generally, standard quantum random access code bounds provide general information-theoretic baselines. For any fixed family of $m$ designated binary observables on~$n$ qubits, the universal margin is at most $\sqrt{(2\ln2\,n/m)}$, and random access decoding from $N$ copies with constant success probability above $1/2$ requires $nN=Ω(m)$. For a fixed Pauli correlation encoding required to work uniformly over all targets, maintaining a fixed nonzero decoded magnitude under smooth sign decoding therefore requires a rescaling parameter that grows as the available margin shrinks. Thus, while providing substantial qubit savings, compression can shift cost into restricted expectation value geometry, smaller expectation value magnitudes, or more demanding information recovery rather than eliminate it.
