量子信息方法用于超对称杨-米尔斯场的玻色化
Quantum Information Approach to Bosonization of Supersymmetric Yang-Mills Fields
AI总结：
本文提出利用量子信息方法，通过玻色化构建超对称杨-米尔斯场的表示，并探索其在混合量子计算机上的应用。
摘要：
我们考虑在Wess-Zumino量子力学背景下对超对称性进行玻色化。我们的研究动机是玻色子费米子空间的灵活性，因为它可以实现任何经典概率分布，使其成为处理量子过程的多功能框架。我们通过构建一个具有一个玻色子和两个费米子自由度的最小玻色化系统开始。我们迭代这一过程，构建出类似展开Adinkras的超对称系统塔。然后我们识别出所构建系统的osp(2|2)对称性。为了构建不可约表示，我们跨领域诱导表示，这是首次尝试，因为之前的文献仅限于在玻色子领域内诱导。首先，我们从使用Clifford代数的费米子表示开始，然后诱导到gl(2|2)并限制到osp(2|2)。在第二种方法中，我们从玻色子领域诱导表示。在两种情况下，我们的表示都是基于量子比特操作符，提供了一种使用基于量子信息的方法解决超对称问题的方式。根据诱导方向的不同，这些表示适合在混合量子比特和费米子或玻色子量子计算机上实现。
英文摘要：
We consider bosonization of supersymmetry in the context of Wess-Zumino quantum mechanics. Our motivation for this investigation is the flexibility the bosonic fock space affords as any classical probability distribution can be realized on it making it a versatile framework to work with for quantum processes. We proceed by constructing a minimal bosonization of a system with one bosonic and two fermionic degrees of freedom. We iterate this process to construct a tower of SUSY systems that is akin to unfolded Adinkras. We then identify an osp(2|2) symmetry of the system constructed. To build an irreducible representation of the system we induce representations across the sectors, a first to our knowledge, as the previous work have focused on induction only within the bosonic sector. First, we start with a fermionic representation using Clifford algebras and then induce a representation to gl(2|2) and restrict it to osp(2|2). In the second method, we induce a representation from that of the bosonic sector. In both cases, our representations are in terms of qubit operators that provide a way to solve SUSY problems using quantum information based approaches. Depending upon the direction of induction the representations are suitable for implementation on a hybrid qubit and fermionic or bosonic quantum computers.
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