A simpler Gaussian state-preparation

2025/08/06 by Kuklinski, Parker, Rempfer, Benjamin, Obenland, Kevin +1 · 1 citation
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2508.03987

Abstract

The ability to efficiently state-prepare Gaussian distributions is critical to the success of numerous quantum algorithms. The most popular algorithm for this subroutine (Kitaev-Webb) has favorable polynomial resource scaling, however it faces enormous resource overheads making it functionally impractical. In this paper, we present a new, more intuitive method which uses exactly n-1 rotations, (n-1)(n-2)/2 two-qubit controlled rotations, and \lfloor(n-1)/2\rfloor ancilla to state-prepare an n-qubit Gaussian state. We then apply optimizations to the circuit to render it linear in T-depth. This method can be extended to state-preparations of complex functions with polynomial phase.

Citations

• The State Preparation of Multivariate Normal Distributions using Tree Tensor Network
• Efficient explicit circuit for quantum state preparation of piecewise continuous functions
• Quantum sampling algorithms for quantum state preparation and matrix block-encoding
• Initial state preparation for quantum chemistry on quantum computers
• An Efficient Quantum Factoring Algorithm
• Efficient Quantum State Preparation with Walsh Series
• Improved quantum algorithms for linear and nonlinear differential equations
• Practical considerations for the preparation of multivariate Gaussian states on quantum computers
• Low-overhead constructions for the fault-tolerant Toffoli gate
• Wavefunction preparation and resampling using a quantum computer
• Efficient state preparation for a register of quantum bits
• Creating superpositions that correspond to efficiently integrable probability distributions

Cited by

• Logarithmic-depth quantum state preparation of polynomials

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