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Comparing Algorithms for Loading Classical Datasets into Quantum Memory

Andriy Miranskyy, Mushahid Khan, Udson Mendes

TL;DR

This paper tackles the challenge of loading classical data into quantum memory by framing statevector preparation as a multi-attribute optimization problem. It introduces a five-attribute criterion (circuit depth, qubit count, classical runtime, dense vs sparse statevector representation, and circuit alterability) and uses Pareto optimization to compare dense and sparse loading algorithms, highlighting inherent trade-offs. The study demonstrates that, for dense statevectors, the Pareto front reduces to two practical options (Unitary and Zhang'21a), while for sparse statevectors, NR-group and Zhang'22b prevail, with suitability depending on hardware and application (online vs offline). Overall, the work provides a structured, scalable methodology to select data-loading algorithms as quantum hardware evolves and online data-adaptation becomes more important.

Abstract

Quantum computers are gaining importance in various applications like quantum machine learning and quantum signal processing. These applications face significant challenges in loading classical datasets into quantum memory. With numerous algorithms available and multiple quality attributes to consider, comparing data loading methods is complex. Our objective is to compare (in a structured manner) various algorithms for loading classical datasets into quantum memory (by converting statevectors to circuits). We evaluate state preparation algorithms based on five key attributes: circuit depth, qubit count, classical runtime, statevector representation (dense or sparse), and circuit alterability. We use the Pareto set as a multi-objective optimization tool to identify algorithms with the best combination of properties. To improve comprehension and speed up comparisons, we also visually compare three metrics (namely, circuit depth, qubit count, and classical runtime). We compare seven algorithms for dense statevector conversion and six for sparse statevector conversion. Our analysis reduces the initial set of algorithms to two dense and two sparse groups, highlighting inherent trade-offs. This comparison methodology offers a structured approach for selecting algorithms based on specific needs. Researchers and practitioners can use it to help select data-loading algorithms for various quantum computing tasks.

Comparing Algorithms for Loading Classical Datasets into Quantum Memory

TL;DR

This paper tackles the challenge of loading classical data into quantum memory by framing statevector preparation as a multi-attribute optimization problem. It introduces a five-attribute criterion (circuit depth, qubit count, classical runtime, dense vs sparse statevector representation, and circuit alterability) and uses Pareto optimization to compare dense and sparse loading algorithms, highlighting inherent trade-offs. The study demonstrates that, for dense statevectors, the Pareto front reduces to two practical options (Unitary and Zhang'21a), while for sparse statevectors, NR-group and Zhang'22b prevail, with suitability depending on hardware and application (online vs offline). Overall, the work provides a structured, scalable methodology to select data-loading algorithms as quantum hardware evolves and online data-adaptation becomes more important.

Abstract

Quantum computers are gaining importance in various applications like quantum machine learning and quantum signal processing. These applications face significant challenges in loading classical datasets into quantum memory. With numerous algorithms available and multiple quality attributes to consider, comparing data loading methods is complex. Our objective is to compare (in a structured manner) various algorithms for loading classical datasets into quantum memory (by converting statevectors to circuits). We evaluate state preparation algorithms based on five key attributes: circuit depth, qubit count, classical runtime, statevector representation (dense or sparse), and circuit alterability. We use the Pareto set as a multi-objective optimization tool to identify algorithms with the best combination of properties. To improve comprehension and speed up comparisons, we also visually compare three metrics (namely, circuit depth, qubit count, and classical runtime). We compare seven algorithms for dense statevector conversion and six for sparse statevector conversion. Our analysis reduces the initial set of algorithms to two dense and two sparse groups, highlighting inherent trade-offs. This comparison methodology offers a structured approach for selecting algorithms based on specific needs. Researchers and practitioners can use it to help select data-loading algorithms for various quantum computing tasks.
Paper Structure (8 sections, 2 figures, 1 table)

This paper contains 8 sections, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Quality attributes
  3. Crude algorithm comparison
  4. Dense statevector representation
  5. Sparse statevector representation
  6. Alterable circuits
  7. A note on multi-qubit gate count
  8. Summary

Figures (2)

  • Figure 1: Relation between the order of circuit depth (labelled "order of depth"), classical runtime (labelled "order of runtime"), and qubit count (labelled "order of qubits") for algorithms operating on dense statevector representation. Red spheres represent algorithms in the Pareto set; blue tetrahedra --- those not in the set.
  • Figure 2: Relation between the order of circuit depth (labelled "order of depth"), classical runtime (labelled "order of runtime"), and qubit count (labelled "order of qubits") for algorithms operating on sparse statevector representation. We demonstrate various combinations of $n$ and $r$ to illustrate how fast growth is with these two factors. Red spheres represent algorithms in the Pareto set; blue tetrahedra --- those not in the set.