作为量子化学的量子场论的量子模拟
Quantum simulation of quantum field theories as quantum chemistry
摘要：
共形截断是求解一般强耦合量子场论的一种强有力的数值方法，它基于纯场论技术，不需要引入晶格正则化。我们讨论了使用量子设备执行这些计算的可能加速，以及近期和未来量子算法的帮助。我们表明，这种结构是非常相似的量子模拟问题出现在量子化学（这是广泛研究的量子信息科学），和重整化群理论提供了一个场论解释的共形截断模拟。以二维量子色动力学（QCD）为例，给出了理论水平、经典实验水平和IBM量子模拟器水平上的变分量子模拟和数字量子模拟的各种显式计算，包括绝热态制备、变分量子本征求解器、虚时间演化和量子Lanczos算法.我们的工作表明，量子计算不仅可以帮助我们理解格点近似下的基础物理，而且可以直接模拟粒子物理和核物理中广泛应用的量子场论方法，使量子丘奇-图灵命题更加尖锐。
英文摘要：
Conformal truncation is a powerful numerical method for solving generic strongly-coupled quantum field theories based on purely field-theoretic technics without introducing lattice regularization. We discuss possible speedups for performing those computations using quantum devices, with the help of near-term and future quantum algorithms. We show that this construction is very similar to quantum simulation problems appearing in quantum chemistry (which are widely investigated in quantum information science), and the renormalization group theory provides a field theory interpretation of conformal truncation simulation. Taking two-dimensional Quantum Chromodynamics (QCD) as an example, we give various explicit calculations of variational and digital quantum simulations in the level of theories, classical trials, or quantum simulators from IBM, including adiabatic state preparation, variational quantum eigensolver, imaginary time evolution, and quantum Lanczos algorithm. Our work shows that quantum computation could not only help us understand fundamental physics in the lattice approximation, but also simulate quantum field theory methods directly, which are widely used in particle and nuclear physics, sharpening the statement of the quantum Church-Turing Thesis.
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