A divide-and-conquer algorithm for quantum state preparation

Abstract

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 exponential time advantage using 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 divide-and-conquer strategy to exchange computational time for space. We demonstrate a proof of concept on a real quantum device and present two applications for quantum machine learning. We expect that this new loading strategy allows the quantum speedup of tasks that require to load a significant volume of information to quantum devices.

Efficient Boolean Methods for Preparing Uniform Quantum States

“…Multiple algorithms have been proposed for preparing them. The algorithm presented in [8] prepares quantum states with a divide-and-conquer strategy. Although it creates quantum circuits with poly-logarithmic depth, it uses additional n freequbits and increases the number of elementary quantum gates.…”

“…Multiple algorithms [1]- [8] have been proposed for preparing arbitrary quantum states, which require an exponential number of CNOTs and runtime with respect to the number of qubits [9]. To alleviate this complexity, researchers either use free-qubits or prepare quantum states approximately-both ways add overheads.…”

Detailed Account of Complexity for Implementation of Circuit-Based Quantum Algorithms

“…As an example of state preparation, the Divide-and-Conquer scheme [34] presents an algorithm for amplitude encoding in the form of a superposition like…”

“…So, although the system is prepared in a superposition state, the results after observation of ancilla qubtis will be left the work system as a mixed density matrix, what, in the case of algorithms for solving systems of linear or differential equations, this could be a disadvantage. Nevertheless, the algorithm is useful for machine learning and statistical analysis, and other applications, such as data sorting [34]. The algorithm structure presents the idea of dividing a problem into subproblems of the same class.…”

“…The idea for creating the quantum superposition is to divide the problem like the scheme presented in Figure 1. The algorithm is based on the circuit model for quantum computing, which are presented in detail in [34], and presents space and time costs that scales as O(N) and O log 2 2 N , respectively. The circuit for implementation of the Divide-and-Conquer algorithm for state preparation presents polylogarithmic depth and has a simplified structure, with the tasks divided into problems of the same class.…”