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Quantum Skip Gates: Coherently Conditioned Subroutines in Iterative Quantum Algorithms

Kym Derriman

TL;DR

The paper introduces Quantum Skip Gate (QSG), a unitary primitive that coherently conditionally executes or skips an expensive subroutine $U_B$ based on the outcome of a cheaper $U_A$, without collapsing coherence. By encoding the skip condition into a dedicated ancilla and using purely quantum control, QSG integrates seamlessly into iterative algorithms such as Grover searches, with a swap-out variant to curb depth growth. Experimental results on IBM hardware and noise-model simulations show substantial improvements in success-per-oracle efficiency and reductions in $U_B$ calls, especially at moderate oracle depths; swap-out further enhances depth management, extending the practical utility of coherent skip. These findings demonstrate practical resource management in near-term quantum algorithms and point to broader applications in adaptive quantum circuits and metrology where conditional execution saves runtime and mitigates noise.

Abstract

The Quantum Skip Gate (QSG) is a unitary circuit primitive that coherently superposes the execution and omission of an expensive quantum subroutine based on the outcome of a cheaper preceding subroutine, without mid-circuit measurement or loss of coherence. By using a control qubit and an internal flag, QSG enables conditional quantum logic entirely within a unitary framework. We demonstrate QSG experimentally in a Grover-style search on IBM quantum hardware with four data qubits and three Grover iterations, where it reduces costly subroutine calls by 9 to 25 percent and achieves 31 to 61 percent higher success-per-oracle efficiency relative to a fixed-order baseline. Noise-model simulations further confirm and strengthen these gains, reaching improvements of up to 45 percent when using an optimized swap-out design. These results show that coherently conditioned subroutines provide practical resource management, significantly reducing runtime cost and noise accumulation in near-term quantum algorithms.

Quantum Skip Gates: Coherently Conditioned Subroutines in Iterative Quantum Algorithms

TL;DR

The paper introduces Quantum Skip Gate (QSG), a unitary primitive that coherently conditionally executes or skips an expensive subroutine based on the outcome of a cheaper , without collapsing coherence. By encoding the skip condition into a dedicated ancilla and using purely quantum control, QSG integrates seamlessly into iterative algorithms such as Grover searches, with a swap-out variant to curb depth growth. Experimental results on IBM hardware and noise-model simulations show substantial improvements in success-per-oracle efficiency and reductions in calls, especially at moderate oracle depths; swap-out further enhances depth management, extending the practical utility of coherent skip. These findings demonstrate practical resource management in near-term quantum algorithms and point to broader applications in adaptive quantum circuits and metrology where conditional execution saves runtime and mitigates noise.

Abstract

The Quantum Skip Gate (QSG) is a unitary circuit primitive that coherently superposes the execution and omission of an expensive quantum subroutine based on the outcome of a cheaper preceding subroutine, without mid-circuit measurement or loss of coherence. By using a control qubit and an internal flag, QSG enables conditional quantum logic entirely within a unitary framework. We demonstrate QSG experimentally in a Grover-style search on IBM quantum hardware with four data qubits and three Grover iterations, where it reduces costly subroutine calls by 9 to 25 percent and achieves 31 to 61 percent higher success-per-oracle efficiency relative to a fixed-order baseline. Noise-model simulations further confirm and strengthen these gains, reaching improvements of up to 45 percent when using an optimized swap-out design. These results show that coherently conditioned subroutines provide practical resource management, significantly reducing runtime cost and noise accumulation in near-term quantum algorithms.

Paper Structure

This paper contains 25 sections, 19 equations, 2 figures, 3 tables.

Table of Contents

  1. Quantum Skip Gates
  2. Formal Description of Quantum Skip Gate (QSG)
  3. Register Structure
  4. Initial State Preparation
  5. Application of Inexpensive Subroutine and Flag Encoding
  6. Conditional Skip Logic
  7. Controlled Application of $U_B$
  8. Swap-Based Realization of Conditional Skip
  9. Flag Setting and Ancilla Uncomputation
  10. Overall Unitary of One QSG Layer
  11. Embedding QSG in Grover Search
  12. Operational Picture
  13. Grover Layering and Skip-Aware Iteration
  14. Low-Cost Implementation of the Skip Condition
  15. Swap-Out Realization of the Expensive Subroutine
  16. ...and 10 more sections

Figures (2)

  • Figure 1: Generalized structure of the quantum skip gate (QSG). The control qubit $C$ and data registers $x_A$, $x_B$ are initialized in superposition. A subroutine $U_A$ marks $x_A$, and a controlled Toffoli-style gate encodes the skip condition $C \land f_A$ into an ancilla $a$. The subroutine $U_B$ is applied to $x_B$ only if $a = 0$ and skipped when $a = 1$. The ancilla is uncomputed to restore coherence. The depth-optimized swap-out realization is omitted.
  • Figure 2: High-level diagram of the Quantum Skip Gate applied within a Grover-style circuit. The control qubit $C$, data registers $x_A$ and $x_B$, flag qubits $f_A$, $f_B$, and ancilla $a$ are shown. Oracle $\mathcal{O}_A$ always runs, and $\mathcal{O}_B$ is conditionally executed depending on the conjunction $C \wedge f_A$, computed into $a$ via RCCX. Grover diffusion $D$ follows. This sketch omits low-level optimizations such as the swap-out construction.