Sci Rep. 2012;2:391. doi: 10.1038/srep00391. Epub 2012 May 2.
We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.
我们证明了 TDDFT 的定理可以扩展到一类通用量子计算的量子位哈密顿量。应用于通用哈密顿量的 TDDFT 定理意味着，单量子比特期望值可以用作量子计算和信息论中的基本变量，而不是波函数。从实际的角度来看，这使得有可能直接根据单量子比特量（即密度泛函）来近似量子计算中感兴趣的可观测量。此外，我们还证明 TDDFT 为使用具有不同（可能更容易实现的）双量子比特相互作用的其他通用哈密顿量来模拟通用哈密顿量提供了一个精确的方法。这为量子计算中的 TDDFT 奠定了基础，并为开发用于量子算法的密度泛函开辟了可能性。
