Quantum State Preparation without Coherent Arithmetic

Physical Review Letters, vol. 136, pp. 240603

Abstract

We introduce a versatile method for preparing a quantum state whose amplitudes are given by some known function. Unlike existing approaches, our method does not require handcrafted reversible arithmetic circuits, or quantum table reads, to encode the function values. Instead, we use a template quantum eigenvalue transformation circuit to convert a low-cost block encoding of the sine function into the desired function. Our method uses only four ancilla qubits (three if the approximating polynomial has definite parity), providing order-of-magnitude qubit count reductions compared to state-of-the-art approaches, while using a similar number of gates if the function can be well represented by a polynomial or Fourier approximation. We demonstrate the algorithmic utility of our method, including preparing Gaussian and Kaiser window states.

Authors 3

1. Sam McArdle
   Affiliation as printed

   AWS Center for Quantum Computing

2. András Gilyén

   HUN-REN Alfréd Rényi Institute of Mathematics

   Affiliation as printed

   Alfréd Rényi Institute of Mathematics

3. Mario Berta Aachen

   RWTH Aachen University · Imperial College London

   Affiliation as printed

   Imperial College London

   RWTH Aachen University