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Analyzing Quantum Circuit Depth Reduction with Ancilla Qubits in MCX Gates

Ahmad Bennakhi, Paul Franzon, Gregory T. Byrd

TL;DR

The paper analyzes depth-reduction strategies for MCX gates on NISQ hardware using ancilla qubits, focusing on Recursion and V-Chain as the dominant approaches in Qiskit-like decompositions. It shows that V-Chain methods provide predictable, near-linear depth reductions that scale to about 10 control qubits, while Recursion exhibits superlinear depth growth beyond roughly 8 controls; Recursion remains viable at very small MCX sizes with a single ancilla. Qubit mapping and topology significantly influence achievable depth reductions, with fully connected layouts offering the lowest depth but being impractical for real devices. The findings argue for prioritizing v-chain-based strategies in hardware-aware compilation to enable reliable execution of large MCX circuits on current and near-term quantum processors.

Abstract

This paper aims to give readers a high-level overview of the different MCX depth reduction techniques that utilize ancilla qubits. We also exhibit a brief analysis of how they would perform under different quantum topological settings. The techniques examined are recursion and v-chain, as they are the most commonly used techniques in the most popular quantum computing libraries, Qiskit. The target audience of this paper is people who do not have intricate mathematical or physics knowledge related to quantum computing.

Analyzing Quantum Circuit Depth Reduction with Ancilla Qubits in MCX Gates

TL;DR

The paper analyzes depth-reduction strategies for MCX gates on NISQ hardware using ancilla qubits, focusing on Recursion and V-Chain as the dominant approaches in Qiskit-like decompositions. It shows that V-Chain methods provide predictable, near-linear depth reductions that scale to about 10 control qubits, while Recursion exhibits superlinear depth growth beyond roughly 8 controls; Recursion remains viable at very small MCX sizes with a single ancilla. Qubit mapping and topology significantly influence achievable depth reductions, with fully connected layouts offering the lowest depth but being impractical for real devices. The findings argue for prioritizing v-chain-based strategies in hardware-aware compilation to enable reliable execution of large MCX circuits on current and near-term quantum processors.

Abstract

This paper aims to give readers a high-level overview of the different MCX depth reduction techniques that utilize ancilla qubits. We also exhibit a brief analysis of how they would perform under different quantum topological settings. The techniques examined are recursion and v-chain, as they are the most commonly used techniques in the most popular quantum computing libraries, Qiskit. The target audience of this paper is people who do not have intricate mathematical or physics knowledge related to quantum computing.
Paper Structure (10 sections, 1 equation, 8 figures, 2 tables, 2 algorithms)

This paper contains 10 sections, 1 equation, 8 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Significance
  3. MCX Ancilla Qubits
  4. MCX Depth Reduction Techniques
  5. Recursion
  6. Qubit Mapping
  7. V-Chain
  8. Other Approaches
  9. Depth Reduction in Different Topologies
  10. Conclusion

Figures (8)

  • Figure 1: A decomposed circuit of a 3-controlled MCX gate.
  • Figure 2: A 5-controlled MCX gate decomposed using recursion and an extra ancilla qubit. The second iteration is to account for the dirty ancilla qubit's effect.
  • Figure 3: A 10-controlled MCX gate would utilize some control qubits to fulfill its function. The colored boxes represent the repeated quantum circuit components due to the recursion process. This case is simple enough to demonstrate the workings of Algorithm 1.
  • Figure 4: V-chain implementation of a 5-controlled MCX gate, using three ancilla qubits. The green box encapsulates the process of flipping the target qubit, while the red box encapsulates the reversion of the ancilla qubits.
  • Figure 5: Dirty V-chain MCX gate decomposition
  • ...and 3 more figures