Circuit-based quantum random access memory for sparse quantum state preparation

Abstract

In order to use a quantum device to assess a classical dataset D, we need to representthe set D in a quantum state. Applying a quantum algorithm, that is a quantum state preparation algorithm, to convert classical data into quantum data would be the common method. Loading classical data into a quantum device is required in many current applications. Efficiently preparing a quantum state to be used as the initial state of a quantum algorithm is an essential step in developing efficient quantum algorithms, since many algorithms need to reload the initial state several times during their execution. The cost to initialize a quantum state can compromise the algorithm efficiency if the process of quantum states preparation is not efficient. The topic of quantum states preparation in quantum computing has been the focus of much attention. In this scope, preparing sparse quantum states is a more specific problem that remains open since many quantum algorithms also require sparse initialization. This dissertation presents the results of an investigation on sparse quantum states preparation with the development of three algorithms, with highlight to the preparation of sparse quantum states, the main contributionof this dissertation. From a classical input dataset with M patterns formed by pairs composed of a complex number and a binary pattern with n bits, this algorithm can prepare a quantum state with n qubits and continuous amplitudes. The cost of its steps is O(nM), classical cost of o(MlogM+nM)and requires a lower CNOT number than the main quantum state preparation algorithms currently known. The preparation of a quantumstate with 2𝑠 non-zero amplitudes reveals the need of fewer CNOT gates in n>>1 relation to the main known state preparation algorithms, with even more favorable results with s higher and less 1S in the binary string.