量子比特映射：自适应分治方法

Qurzon: A Prototype for a Divide and Conquer Based Quantum Compiler

When working with algorithms on quantum devices, quantum memory becomes a crucial bottleneck due to low qubit count in NISQ-era devices. In this context, the concept of `divide and compute', wherein a quantum circuit is broken into several subcircuits and executed separately, while stitching the results of the circuits via classical post-processing, becomes a viable option, especially in NISQ-era devices. This paper introduces \textbf{Qurzon}, a proposed novel quantum compiler that incorporates the marriage of techniques of divide and compute with the state-of-the-art algorithms of optimal qub…

关于分治算法的量子时间复杂度

On the quantum time complexity of divide and conquer

本文研究了量子分治算法在经典问题中的时间复杂度，通过建立通用条件证明了多个问题的量子加速，并展示了与查询下界的匹配性。

量子输运计算中的性能提升：一种基于 S矩阵的分治方法

Improved performance in quantum transport calculations: A divide-and-conquer method based on S-matrices

本文提出一种基于散射矩阵的精确分治递归算法，用于紧束缚结构的量子输运计算，并在多种晶格上验证其相对现有方法的显著性能优势。

Semiclassical "Divide-and-Conquer" Method for Spectroscopic Calculations of High Dimensional Molecular Systems

A new semiclassical "divide-and-conquer" method is presented with the aim of demonstrating that quantum dynamics simulations of high dimensional molecular systems are doable. The method is first tested by calculating the quantum vibrational power spectra of water, methane, and benzene - three molecules of increasing dimensionality for which benchmark quantum results are available - and then applied to C60, a system characterized by 174 vibrational degrees of freedom. Results show that the approach can accurately account for quantum anharmonicities, purely quantum features like overtones, and t…

A Divide-and-Conquer Approach to Dicke State Preparation

We present a divide-and-conquer approach to deterministically prepare Dicke states $\lvert D_k^n\rangle$ (i.e., equal-weight superpositions of all $n$-qubit states with Hamming Weight $k$) on quantum computers. In an experimental evaluation for up to $n=6$ qubits on IBM Quantum Sydney and Montreal devices, we achieve significantly higher state fidelity compared to previous results [Mukherjee and others, TQE'2020], [Cruz and others, QuTe'2019]. The fidelity gains are achieved through several techniques: Our circuits first "divide" the Hamming weight between blocks of $n/2$ qubits, and then "con…

多维量子游走、递归与量子分治法

Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer

本文提出子空间图以形式化多维量子游走，支持经典结构与量子子程序的无缝组合，并据此实现量子分治法，对有向 $st$-连通性的 Savitch 算法取得二次加速。

Large-scale Quantum Approximate Optimization via Divide-and-Conquer

Quantum Approximate Optimization Algorithm (QAOA) is a promising hybrid quantum-classical algorithm for solving combinatorial optimization problems. However, it cannot overcome qubit limitation for large-scale problems. Furthermore, the execution time of QAOA scales exponentially with the problem size. We propose a Divide-and-Conquer QAOA (DC-QAOA) to address the above challenges for graph maximum cut (MaxCut) problem. The algorithm works by recursively partitioning a larger graph into smaller ones whose MaxCut solutions are obtained with small-size NISQ computers. The overall solution is retr…

Machine Learning for Vibrational Spectroscopy via Divide-and-Conquer Semiclassical Initial Value Representation Molecular Dynamics with Application to N-Methylacetamide

A machine learning algorithm for partitioning the nuclear vibrational space into subspaces is introduced. The subdivision criterion is based on Liouville's theorem, i.e. best preservation of the unitary of the reduced dimensionality Jacobian determinant within each subspace along a probe full-dimensional classical trajectory. The algorithm is based on the idea of evolutionary selection and it is implemented through a probability graph representation of the vibrational space partitioning. We interface this customized version of genetic algorithms with our divide-and-conquer semiclassical initia…

"Divide and Conquer" Semiclassical Molecular Dynamics: A practical method for Spectroscopic calculations of High Dimensional Molecular Systems

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits to perform spectroscopic calculations of high dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Lio…

关于最小字符串旋转问题的量子分治注记

A Note on Quantum Divide and Conquer for Minimal String Rotation

本文针对字典序最小字符串旋转问题，改进分治量子算法的查询复杂度至 √n·2^{O(√log n)}，仅以逐层对数优化和容错量子最小元查找实现准多对数级提升。

量子分治

Quantum divide and conquer

提出量子分治框架，通过引入平方根递推关系降低量子查询复杂度，并应用于正则语言识别等字符串问题，获得了近乎最优的量子查询复杂度。

Solving Quadratic Unconstrained Binary Optimization with divide-and-conquer and quantum algorithms

Quadratic Unconstrained Binary Optimization (QUBO) is a broad class of optimization problems with many practical applications. To solve its hard instances in an exact way, known classical algorithms require exponential time and several approximate methods have been devised to reduce such cost. With the growing maturity of quantum computing, quantum algorithms have been proposed to speed up the solution by using either quantum annealers or universal quantum computers. Here we apply the divide-and-conquer approach to reduce the original problem to a collection of smaller problems whose solutions…

Hybrid divide-and-conquer approach for tree search algorithms

One of the challenges of quantum computers in the near- and mid- term is the limited number of qubits we can use for computations. Finding methods that achieve useful quantum improvements under size limitations is thus a key question in the field. In this vein, it was recently shown that a hybrid classical-quantum method can help provide polynomial speed-ups to classical divide-and-conquer algorithms, even when only given access to a quantum computer much smaller than the problem itself. In this work, we study the hybrid divide-and-conquer method in the context of tree search algorithms, and e…

A divide-and-conquer algorithm for quantum state preparation

Advantages in several fields of research and industry are expected with the rise of quantum computers. However, the computational cost to load classical data in quantum computers can impose restrictions on possible quantum speedups. Known algorithms to create arbitrary quantum states require quantum circuits with depth O(N) to load an N-dimensional vector. Here, we show that it is possible to load an N-dimensional vector with a quantum circuit with polylogarithmic depth and entangled information in ancillary qubits. Results show that we can efficiently load data in quantum devices using a divi…