轴向规范下量子色动力学的量子模拟
Quantum Simulation of QCD in Axial Gauge
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中文总结 AI 辅助
该研究提出轴向规范下的格点SU(3)非阿贝尔规范理论量子模拟方法，证明所需量子资源随相关参数多项式缩放，构建了基于Trotter化等的量子算法。
中文摘要 AI 辅助
我们研究在轴向规范下，利用格点哈密顿量对3+1维中与基本费米子动态耦合的SU(3)非阿贝尔规范理论进行量子模拟，该方法可避免高斯定律约束。规范场的时间分量可通过独立场自由度和格点正则化格林函数解析求解。轴向规范条件在时间演化过程中可轻易保持，即使在Trotter化后仍成立。规范场自由度以局域场基表示，可通过局域量子傅里叶变换高效转换为正则共轭动量基。我们证明，在体积为V、裸耦合为g的格点上，以精度ε描述能量E以内所有态所需的量子比特数有界为16n_A V + 12n_f V，其中n_A≈log₂(64 E' V^(4/3)/(π²ε) + 32√2 g n_f E'^(1/2) V^(7/6)/(√3 π³ ε^(1/2)))，E'为每个独立规范场位点的平移能量，n_f为费米子味数。随后我们分析了基于Trotter化、量子傅里叶变换和约旦-维格纳变换的时间演化量子算法，该算法可在任意规范场截断和数字化下显式构造量子电路。我们发现，对于固定n_f≤6，每步Trotter的CNOT门和单量子比特旋转门数量均按O(n_A⁴ V^(4/3)) + O(V^(5/3))缩放。我们得出结论，模拟格点量子色动力学实时动力学所需的量子资源随体积、能量、时间、精度和裸哈密顿量参数呈多项式缩放。
英文摘要
We study quantum simulation of SU(3) non-Abelian gauge theory dynamically coupled with fundamental fermions in $3+1$ dimensions by employing the lattice Hamiltonian in axial gauge that avoids Gauss's law constraints. The temporal component of the gauge field is analytically solved in terms of independent field degrees of freedom and a lattice regulated Green's function. The axial gauge condition is trivially maintained in time evolution, even under Trotterization. The gauge field degrees of freedom are expressed in the local field basis and can be efficiently transformed into the canonical conjugate momentum basis by local quantum Fourier transforms. We prove the number of qubits needed for describing all states up to an energy $E$ with an accuracy $ε$ on a lattice of volume $V$ at bare coupling $g$ is bounded as $16n_A V + 12n_f V$, where $n_A \approx \log_2 (\frac{64 E' V^{4/3}}{π^2ε} + \frac{32\sqrt{2}g n_f E'^{1/2} V^{7/6}}{\sqrt{3}π^3ε^{1/2}} ) $ is the number of qubits needed for each independent gauge field per site with a shifted energy $E'$, and $n_f$ denotes the number of fermion flavors. We then analyze a quantum algorithm for time evolution that is based on Trotterization, quantum Fourier transform, and Jordan-Wigner transformation, for which quantum circuits can be explicitly constructed under arbitrary gauge field truncation and digitization. We find the numbers of CNOT and single-qubit rotation gates both scale as $O(n_A^4 V^{4/3}) + O(V^{5/3})$ per Trotter step for fixed $n_f\leq 6$. We conclude that quantum resources needed for simulating real-time dynamics of lattice QCD scale polynomially with volume, energy, time, accuracy, and bare Hamiltonian parameters.
