Bowtie VarQTE: 一种资源高效的量子态制备原语
Bowtie VarQTE: A Resource-Efficient Quantum State Preparation Primitive
AI总结：
本文提出了一种基于经典模拟和必要量子资源的Bowtie VarQTE方法，用于高效制备物理结构化的量子态，通过减少量子资源需求并提升数值稳定性，与基于张量网络编译Trotter算法的近似量子编译（AQC）方法进行比较，展示了其在态制备管道中的应用优势。
摘要：
量子态的制备是许多量子算法的基本要求。一种原生的制备物理结构化态的方法是基于短时间动态过程的模拟，如真实时间或虚时间演化的模拟。本文提出了一种资源高效的框架，即Bowtie VarQTE，该方法在可能时利用经典模拟，在必要时使用量子资源。我们介绍了一种框架，该框架利用现有的因果光锥来最小化量子资源需求，在评估梯度和量子几何张量项时利用经典模拟方法对因果相关的子电路进行模拟。这使得能够根据McLachlan变分原理进行精确的参数更新，从而提高数值稳定性。我们与基于张量网络编译Trotter算法的近似量子编译（AQC）方法进行了比较。在最近的工作中，这种方法表现出色。然而，其关键瓶颈是需要有经典（近似）的目标态表示。我们的数值实验表明，Bowtie VarQTE可以在不需此要求的情况下实现可比的保真度。我们进一步说明了Bowtie VarQTE如何促进结合虚时间和真实时间演化的状态制备管道，用于基于样本的量子算法。事实上，2D系统的结果展示了Bowtie VarQTE如何在与标准样本基Krylov对角化计算相比时减少量子资源需求。我们的结果表明，VarQTE是一种有前景的原语，用于制备物理结构化的量子态，通过利用现有的结构和相关的经典模拟可能性，减少了对量子资源的需求。
英文摘要：
The preparation of quantum states is a fundamental requirement for many quantum algorithms. A native route to preparing physically structured states is based on short-time simulation of dynamical processes, such as real or imaginary time evolution. This work presents a resource-efficient framework for the approximation thereof with \textit{bowtie \ac{VarQTE}} which uses classical simulation where possible and quantum resources where necessary. We introduce a framework that leverages existing causal light-cones to minimize quantum resource requirements in the evaluation of gradient and quantum geometric tensor terms by utilizing classical simulation methods for causally relevant subcircuits. This in turn enables exact parameter updates according to McLachlan's variational principle and, thereby, improves numerical stability. We conduct a comparison with a state preparation method that is based on a tensor-network compiled Trotter algorithm: approximate quantum compilation (AQC). In recent work, this approach has shown impressive performance. However, its key-bottleneck is the necessity to have a classical (approximate) representation of the target state. Our numerical experiments indicate that bowtie VarQTE can achieve comparable fidelities without this requirement. We further illustrate how bowtie VarQTE can facilitate a state-preparation pipeline that combines the simulation of imaginary and real time evolution for a sample-based quantum algorithm. In fact, results on 2D systems show how bowtie VarQTE can reduce the quantum requirements compared to standard, sample-based Krylov diagonalization calculations. Our results indicate that VarQTE is a promising primitive for the preparation of physically structured quantum states that reduces requirements on quantum resources by leveraging existing structures and the associated possibility of enabling classical simulations.
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