Miquel César, Paz Juan Pablo, Saraceno Marcos, Knill Emanuel, Laflamme Raymond, Negrevergne Camille
Departamento de Física, FCEN, UBA, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina.
Nature. 2002 Jul 4;418(6893):59-62. doi: 10.1038/nature00801.
It is important to be able to determine the state of a quantum system and to measure properties of its evolution. State determination can be achieved using tomography, in which the system is subjected to a series of experiments, whereas spectroscopy can be used to probe the energy spectrum associated with the system's evolution. Here we show that, for a quantum system whose state or evolution can be modelled on a quantum computer, tomography and spectroscopy can be interpreted as dual forms of quantum computation. Specifically, we find that the phase estimation algorithm (which underlies a quantum computer's ability to perform efficient simulations and to factorize large numbers) can be adapted for tomography or spectroscopy. This is analogous to the situation encountered in scattering experiments, in which it is possible to obtain information about both the state of the scatterer and its interactions. We provide an experimental demonstration of the tomographic application by performing a measurement of the Wigner function (a phase space distribution) of a quantum system. For this purpose, we use three qubits formed from spin-1/2 nuclei in a quantum computation involving liquid-state nuclear magnetic resonance.
能够确定量子系统的状态并测量其演化特性非常重要。状态确定可以通过断层扫描来实现，在断层扫描中，系统要进行一系列实验，而光谱学可用于探测与系统演化相关的能谱。在此我们表明，对于一个其状态或演化可以在量子计算机上建模的量子系统，断层扫描和光谱学可以被解释为量子计算的对偶形式。具体而言，我们发现相位估计算法（它是量子计算机执行高效模拟和分解大数能力的基础）可以适用于断层扫描或光谱学。这类似于在散射实验中遇到的情况，在散射实验中可以获得关于散射体状态及其相互作用的信息。我们通过对一个量子系统的维格纳函数（一种相空间分布）进行测量，给出了断层扫描应用的实验演示。为此，我们在涉及液态核磁共振的量子计算中，使用由自旋 - 1/2 原子核形成的三个量子比特。
