Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Reducing Mid-Circuit Measurements via Probabilistic Circuits

Yanbin Chen, Innocenzo Fulginiti, Christian B. Mendl

TL;DR

Mid-circuit measurements impose significant hardware and classical feedback overhead in dynamic quantum circuits. The authors present a static optimization that replaces certain mid-circuit measurement snippets with probabilistic circuit components, enabled by extending Quantum Constant Propagation (QCP) with a compile-time analysis and a purity test to identify pure-input cases. They model circuit uncertainty through ensembles and probabilistic gates, showing a polynomial-time optimization in the number of qubits $n$, gates $g$, maximum controls $c$, and mid-circuit measurements $m$. Demonstrations on two dynamic circuits illustrate substantial reductions in runtime overhead and a shift from dynamic to static execution components, with potential practical impact for quantum hardware efficiency and error-correction workflows.

Abstract

Mid-circuit measurements and measurement-controlled gates are supported by an increasing number of quantum hardware platforms and will become more relevant as an essential building block for quantum error correction. However, mid-circuit measurements impose significant demands on the quantum hardware due to the required signal analysis and classical feedback loop. This work presents a static circuit optimization algorithm that can substitute some of these measurements with an equivalent circuit with randomized gate applications. Our method uses ideas from constant propagation to classically precompute measurement outcome probabilities. Our proposed optimization is efficient, as its runtime scales polynomially on the number of qubits and gates of the circuit.

Reducing Mid-Circuit Measurements via Probabilistic Circuits

TL;DR

Mid-circuit measurements impose significant hardware and classical feedback overhead in dynamic quantum circuits. The authors present a static optimization that replaces certain mid-circuit measurement snippets with probabilistic circuit components, enabled by extending Quantum Constant Propagation (QCP) with a compile-time analysis and a purity test to identify pure-input cases. They model circuit uncertainty through ensembles and probabilistic gates, showing a polynomial-time optimization in the number of qubits , gates , maximum controls , and mid-circuit measurements . Demonstrations on two dynamic circuits illustrate substantial reductions in runtime overhead and a shift from dynamic to static execution components, with potential practical impact for quantum hardware efficiency and error-correction workflows.

Abstract

Mid-circuit measurements and measurement-controlled gates are supported by an increasing number of quantum hardware platforms and will become more relevant as an essential building block for quantum error correction. However, mid-circuit measurements impose significant demands on the quantum hardware due to the required signal analysis and classical feedback loop. This work presents a static circuit optimization algorithm that can substitute some of these measurements with an equivalent circuit with randomized gate applications. Our method uses ideas from constant propagation to classically precompute measurement outcome probabilities. Our proposed optimization is efficient, as its runtime scales polynomially on the number of qubits and gates of the circuit.
Paper Structure (16 sections, 4 theorems, 8 equations, 9 figures, 2 algorithms)

This paper contains 16 sections, 4 theorems, 8 equations, 9 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Compile time for quantum circuits
  4. Runtime for quantum circuits
  5. Mid-circuit measurement
  6. Static and dynamic circuit
  7. Quantum Constant Propagation
  8. Method
  9. Uncertainty of quantum system
  10. Probabilistic circuit
  11. Purity test
  12. Put everything together
  13. Asymptotic analysis
  14. Demonstrating examples
  15. Related works
  16. ...and 1 more sections

Key Result

lemma 3.1

For two circuits $C_{1}$ and $C_{2}$, it holds that $\|C_{1} \cdot C_{2}\|^{\star} = \|C_{1}\|^{\star} \cdot \|C_{2}\|^{\star}$ and $\|C_{1} \otimes C_{2}\|^{\star} = \|C_{1}\|^{\star} \otimes \|C_{2}\|^{\star}$.

Figures (9)

  • Figure 1: Example of mid-circuit measurement elimination, where $\ket{\Phi} = \frac{1}{\sqrt{2}}(\ket{00} + \ket{11})$ and $\ket{\Psi}$ is an arbitrary two-qubit state.
  • Figure 2: Illustration of a mid-circuit measurement.
  • Figure 3: Example of a dynamic component in a quantum circuit.
  • Figure 4: The dynamic circuit in \ref{['ex:toy_mid_circ_elim']}.
  • Figure 5: The circuit diagram of the probabilistic gate $U(p)$.
  • ...and 4 more figures

Theorems & Definitions (22)

  • Example 1.1
  • Remark
  • Definition 3.1: The ensemble of circuits
  • Example 3.1
  • Definition 3.2: Probabilistic quantum gate
  • Definition 3.3: Compilation of probabilistic gate
  • Definition 3.4: Probabilistic quantum circuit
  • Example 3.2
  • Remark
  • Definition 3.5
  • ...and 12 more