Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On universality of hardware-efficient ansatzes

Hokuto Iwakiri, Keita Kanno

TL;DR

The paper addresses whether hardware-efficient ansatzes (HEA) used in near-term quantum computing are classically simulable. It analyzes two concrete HEA families, HEA(R_y{-}R_z, Ladder_CZ) and HEA(R_y, Ladder_CNOT), and proves universality results by constructing polynomial-depth representations of universal gate sets within these HEAs. Specifically, HEA(R_y{-}R_z, Ladder_CZ) is strictly universal, while HEA(R_y, Ladder_CNOT) is computationally universal, implying that simulating these HEAs is BQP-hard (and thus unlikely to be classically efficient unless the PH collapses). The work provides explicit circuit decompositions, depth bounds, and ancilla-assisted constructions to realize H, T, CZ, and CNOT gates within these frameworks, strengthening the case for quantum advantage in HEA-based tasks and guiding future exploration of other HEA architectures.

Abstract

The hardware-efficient ansatz (HEA) is one of the most important class of parametrized quantum circuits for near-term applications of quantum computing. We show that the problem of simulating some major classes of the HEA is BQP-complete by explicitly demonstrating that any relevant quantum circuit can be efficiently represented as an HEA circuit of those classes.

On universality of hardware-efficient ansatzes

TL;DR

The paper addresses whether hardware-efficient ansatzes (HEA) used in near-term quantum computing are classically simulable. It analyzes two concrete HEA families, HEA(R_y{-}R_z, Ladder_CZ) and HEA(R_y, Ladder_CNOT), and proves universality results by constructing polynomial-depth representations of universal gate sets within these HEAs. Specifically, HEA(R_y{-}R_z, Ladder_CZ) is strictly universal, while HEA(R_y, Ladder_CNOT) is computationally universal, implying that simulating these HEAs is BQP-hard (and thus unlikely to be classically efficient unless the PH collapses). The work provides explicit circuit decompositions, depth bounds, and ancilla-assisted constructions to realize H, T, CZ, and CNOT gates within these frameworks, strengthening the case for quantum advantage in HEA-based tasks and guiding future exploration of other HEA architectures.

Abstract

The hardware-efficient ansatz (HEA) is one of the most important class of parametrized quantum circuits for near-term applications of quantum computing. We show that the problem of simulating some major classes of the HEA is BQP-complete by explicitly demonstrating that any relevant quantum circuit can be efficiently represented as an HEA circuit of those classes.

Paper Structure

This paper contains 24 sections, 3 theorems, 36 equations, 19 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Definition of HEA
  4. Strict and computational universality
  5. Strict universality
  6. Computational universality
  7. Universality of families of quantum circuits
  8. Results
  9. Decomposition into a product of unitary layers
  10. $\mathrm{HEA}(R_y\text{-}R_z,Ladder_\text{CZ})$
  11. $\mathrm{HEA}(R_y,Ladder_\mathrm{CNOT})$
  12. Universality
  13. $\mathrm{HEA}(R_y\text{-}R_z,Ladder_\text{CZ})$
  14. Single-qubit gates $H$ and $T$
  15. Two-qubit gate $\mathrm{CNOT}$
  16. ...and 9 more sections

Key Result

Theorem 3.1

The circuit family $\mathrm{HEA}(R_y\text{-}R_z,Ladder_\text{CZ})$ is strictly universal.

Figures (19)

  • Figure 1: The general structure of hardware-efficient ansatz.
  • Figure 2: The Ry-Rz-CZ ansatz.
  • Figure 3: $N$-qubit ladder of CZ. Since CZs are mutually commutative, unlike the $CNOT$ ladder, the structure does not change whether even or odd.
  • Figure 4: The Ry-CNOT ansatz.
  • Figure 5: Left side is a $(2i)$-qubit ladder of $CNOT$ and Right side is a $(2i+1)$-qubit ladder of CNOT.
  • ...and 14 more figures

Theorems & Definitions (4)

  • Theorem 3.1
  • Theorem 3.2
  • Proposition : \ref{['prop:order-of-CNOT-ladder']}
  • proof