The Efficient Preparation of Normal Distributions in Quantum Registers

2020/09/30 by Arthur G. Rattew, Yue Sun, Pierre Minssen +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Bounded function #Computer engineering #Computer science #Engineering #Leverage (statistics) #Mathematics #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum computer #Quantum mechanics #Quantum-Dot Cellular Automata #Qubit #Range (aeronautics) #Reduction (mathematics) #Reuse #Theoretical computer science #quant-ph

paper · pdf · doi:10.22331/q-2021-12-23-609

published as Quantum 5, 609 (2021) · Accepted in Quantum on 2021-12-14. Minor fixes

arxiv created 2021/12/17 · openalex publication_date 2021/12/23 · arxiv updated 2021/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The efficient preparation of input distributions is an important problem in obtaining quantum advantage in a wide range of domains. We propose a novel quantum algorithm for the efficient preparation of arbitrary normal distributions in quantum registers. To the best of our knowledge, our work is the first to leverage the power of Mid-Circuit Measurement and Reuse (MCMR), in a way that is broadly applicable to a range of state-preparation problems. Specifically, our algorithm employs a repeat-until-success scheme, and only requires a constant-bounded number of repetitions in expectation. In the experiments presented, the use of MCMR enables up to a 862.6x reduction in required qubits. Furthermore, the algorithm is provably resistant to both phase-flip and bit-flip errors, leading to a first-of-its-kind empirical demonstration on real quantum hardware, the MCMR-enabled Honeywell System Models H0 and H1-2.

Citations

• Wavefunction preparation and resampling using a quantum computer
• Creating superpositions that correspond to efficiently integrable probability distributions
• Addition on a Quantum Computer
• On the product of semi-groups of operators
• Quantum-state preparation with universal gate decompositions
• Elementary gates for quantum computation
• Quantum support vector machine for big data classification
• Optimal computation with non-unitary quantum walks
• Quantum Neuron: an elementary building block for machine learning on quantum computers
• Quantum Computing in the NISQ era and beyond
• Optimizing Quantum Circuits for Arithmetic
• Quantum Generative Adversarial Networks for Learning and Loading Random Distributions
• Quantum Computation and Quantum Information
• Efficient Quantum Circuits for Accurate State Preparation of Smooth, Differentiable Functions
• Demonstration of the trapped-ion quantum CCD computer architecture