Measuring All Compatible Operators in One Series of Single-Qubit Measurements Using Unitary Transformations,Journal of Chemical Theory and Computation

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Measuring All Compatible Operators in One Series of Single-Qubit Measurements Using Unitary Transformations
Journal of Chemical Theory and Computation ( IF 5.7 ) Pub Date : 2020-03-09 , DOI: 10.1021/acs.jctc.0c00008
Tzu-Ching Yen ₁ , Vladyslav Verteletskyi _{1,

2,

3} , Artur F. Izmaylov _{1,

2}

Affiliation

The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or compatible operators simultaneously. Unfortunately, the current hardware permits measuring only a much more limited subset of operators that share a common tensor product eigen-basis. We introduce unitary transformations that transform any fully commuting group of operators to a group that can be measured on current hardware. These unitary operations can be encoded as a sequence of Clifford gates and let us not only measure much larger groups of terms but also to obtain these groups efficiently on a classical computer. The problem of finding the minimum number of fully commuting groups of terms covering the whole Hamiltonian is found to be equivalent to the minimum clique cover problem for a graph representing Hamiltonian terms as vertices and commutativity between them as edges. Tested on a set of molecular electronic Hamiltonians with up to 50 thousand terms, the introduced technique allows for the reduction of the number of separately measurable operator groups down to few hundreds, thus achieving up to 2 orders of magnitude reduction. Based on the test set results, the obtained gain scales at least linearly with the number of qubits.

中文翻译：

使用Unit变换在一系列单量子位测量中测量所有兼容算子

量子计算机上电子结构问题的变分量子本征求解器方法涉及对哈密顿期望值的测量。形式上，量子力学允许人们同时测量所有相互交换或兼容的算子。不幸的是，当前的硬件仅允许测量共享共同的张量积本征基的运算符的有限得多的子集。我们引入单一转换，将任何完全交换的运算符组转换为可以在当前硬件上测量的一组。这些unit运算可以编码为Clifford门的序列，让我们不仅可以测量更大的项组，而且可以在经典计算机上有效地获取这些组。找到覆盖整个哈密顿量的全换向项组的最小数量的问题，与将汉密尔顿项表示为顶点并将它们之间的可交换性表示为边的图的最小集团覆盖问题等效。通过对一组分子电子哈密顿量（最多5万个项）进行测试，引入的技术可将可单独测量的算子组的数量减少至数百个，从而最多可减少2个数量级。根据测试集结果，获得的增益至少与量子位的数量成线性比例关系。引入的技术在一组分子电子哈密顿量中进行了多达5万项的测试，引入的技术可将可单独测量的算子组的数量减少至数百个，从而最多可减少2个数量级。根据测试集结果，获得的增益至少与量子位的数量成线性比例关系。通过对一组分子电子哈密顿量（最多5万个项）进行测试，引入的技术可将可单独测量的算子组的数量减少至数百个，从而最多可减少2个数量级。根据测试集的结果，获得的增益至少与量子位的数量成线性比例关系。

更新日期：2020-04-24

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