Quantum state preparation without coherent arithmetic - Paper Implementation Project

[zzz845zz]

Paper for Implementation

We (@zzz845zz, @venator2021, @eqs-kaist) aim to implement a quantum state preparation circuit based on Quantum State Preparation Without Coherent Arithmetic (arXiv:2210.14892). Specifically, we will construct a Gaussian state preparation circuit from Classiq’s MIT iQuHack 2025 challenge using the approach outlined in this paper.

$$\ket{x_0}_N = \ket{0}_N \rightarrow \sum_x \sqrt{G(x)} \ket{x}_N$$

Technical Approach

To implement amplitude encoding without coherent arithmetic, we construct the following three components, as described in Figure 1 of the paper:

• $U_{\text{sin}}$: Block encoding of the initial values.
• $U_f$: Function application via Quantum Eigenvalue Transformation (QET).
• $U_{\text{amp}}$: Amplitude amplification to increase the probability of the target state.

For each component, we follow Section 2 of the paper. In constructing $U_f$, we determine the QET rotation angles using pyqsp or other techniques. For evaluation, we verify correctness via state-vector simulation for small cases and perform resource estimation.

High-Level Example

• Applying $U_{\text{sin}}$ produces: block encoding of $\sum_x \sin(x/N) \ket{x}$
• Applying $U_f$ transforms it to: block encoding of $\sum_x f(x)\ket{x}$
• Applying $U_{\text{amp}}$ amplifies the probability of the desired state.

For Gaussian state preparation, we set f(x) to be the Gaussian function described in the MIT iQuHack 2025 challenge notebook.

[NadavClassiq]

Sounds great! If you will be able to implement it for an arbitrary exponential rate and resolution, it will be super cool :)

[vu1xan]

@zzz845zz is there a empty spot in your team ?

[zzz845zz]

@vu1xan Sorry, but unfortunately, our team doesn’t have an open slot.