发表机构
Colorado School of Mines（科罗拉多矿业学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出卷积型吸收边界，突破波动方程显式量子电路的封闭域限制，通过李雅普诺夫对称化器解决薛定谔化的后选择成本问题，大幅降低模拟成本。
AI 中文摘要
通过哈密顿模拟构建的波动方程显式量子电路局限于封闭域，其中出射波会从计算区域的边缘反射并返回。我们利用卷积型吸收边界突破了这一限制——该边界是通过指数核记忆变量实现的复频移完全匹配层，并通过薛定谔化使由此产生的非幺正动力学可在量子硬件上实现。我们取得了三项结果：第一，得到了用于吸收演化的显式门级电路，该电路通过将贝尔基项演化电路扩展到投影值算子串并进行二阶 Trotter 化得到；这些电路在17至21个量子比特上全程运行，与精确参考结果的误差在0.1%至1%之间。第二，存在一个结构障碍：吸收生成器的记忆形式带有不可约的不定厄米部分，其最大特征值随吸收强度的平方根除以网格间距而增长，且在对记忆场进行任何对角重标度后仍存在。薛定谔化的已知恢复阈值使得后选择成本随模拟时间呈指数增长。第三，提出了一种补救措施：通过经典预计算的李雅普诺夫对称化器，可使变换后的生成器成为耗散型，将该与时间相关的惩罚替换为与时间无关的条件因子，在多达4000个未知量的网格上测得该因子为数百，且在网格细化时趋于饱和。该转变发生得较早：超过转变点后，对称化后的恢复在后选择成本上便宜4至26个数量级，且在测试的最长时间范围内，它是唯一可行的恢复方法。
英文摘要
Explicit quantum circuits for the wave equation, built by Hamiltonian simulation, are restricted to closed domains, in which outgoing waves reflect off the edge of the computational region and return. We lift that restriction with absorbing boundaries of the convolution type - a complex-frequency-shifted perfectly matched layer realised through exponential-kernel memory variables - and make the resulting non-unitary dynamics quantum-implementable by Schrodingerisation. We obtain three results. First, explicit gate-level circuits for the absorbing evolution, obtained by extending a Bell- basis term-evolution circuit to projector-valued operator strings and Trotterising to second order; these run end to end on seventeen to twenty-one qubits and agree with exact references to within a tenth of a percent to a percent. Second, a structural obstruction: the memory form of the absorbing generator carries an irreducibly indefinite Hermitian part, whose largest eigenvalue grows as the square root of the absorption strength divided by the grid spacing and survives any diagonal rescaling of the memory fields. The known recovery threshold for Schrodingerisation then makes the post-selection cost grow exponentially in the simulated time. Third, a remedy: a Lyapunov symmetrizer, precomputed classically, renders the transformed generator dissipative and replaces that time-dependent penalty with a time-independent conditioning factor of several hundred, measured on grids of up to four thousand unknowns and saturating under mesh refinement. The crossover is early: past it the symmetrized recovery is cheaper by four to twenty-six orders of magnitude in post-selection cost, and at the longest horizons tested it is the only recovery that works.
