State Dependent Optimization with Quantum Circuit Cutting

TL;DR

The paper tackles mitigating noise and gate counts in quantum circuits by extending ISDO to circuit cutting through MSDO and biased observable selection, all within an SDO framework. It also introduces non-separate circuit cutting (NSCC) to address scalability, enabling gate optimization without full circuit separation. Through simulations on QAOA, QFT, and BV circuits, the authors demonstrate consistent fidelity improvements and substantial reductions in the average gate count per term (AGT) when using SDO with circuit cutting, and provide competitive gains with NSCC. The work offers a practical pathway to improve near-term quantum algorithm execution by combining state-aware optimization with flexible circuit decomposition strategies.

Abstract

Quantum circuits can be reduced through optimization to better fit the constraints of quantum hardware. One such method, initial-state dependent optimization (ISDO), reduces gate count by leveraging knowledge of the input quantum states. Surprisingly, we found that ISDO is broadly applicable to the downstream circuits produced by circuit cutting. Circuit cutting also requires measuring upstream qubits and has some flexibility of selection observables to do reconstruction. Therefore, we propose a state-dependent optimization (SDO) framework that incorporates ISDO, our newly proposed measure-state dependent optimization (MSDO), and a biased observable selection strategy. Building on the strengths of the SDO framework and recognizing the scalability challenges of circuit cutting, we propose non-separate circuit cutting-a more flexible approach that enables optimizing gates without fully separating them. We validate our methods on noisy simulations of QAOA, QFT, and BV circuits. Results show that our approach consistently mitigates noise and improves overall circuit performance, demonstrating its promise for enhancing quantum algorithm execution on near-term hardware.

Figures (4)

• Figure 1: Framework of circuit cutting with state-dependent optimization (SDO): Assuming we need to run a three-qubit circuit on a two-qubit device, circuit cutting can be used to divide it into two-qubit subcircuits. The SDO framework can further reduce gates, making certain subcircuits easier to execute.
• Figure 2: Illustrations of ISDO on RZZ gate. For the RZZ gate, two input qubits are equivalent.
• Figure 3: Example of measure-state dependent optimization (MSDO). Measuring the first qubit in the Z observable is equivalent to measuring in the Z observable while separately extracting the results corresponding to $\ket{0}$ and $\ket{1}$ using two circuits. Then, by applying the inverse of ISDO, we obtain two circuits with fewer gates.
• Figure 4: AGT of two-qubit gates versus the number of subcircuits for different QAOA configurations. The best situation is for each circuit to have fewer subcircuits and a lower AGT. In the case of uncut (red star) and cut (blue square), there are either too many gates or too many subcircuits. The non-separate circuit cutting (NSCC) (orange round) provides an intermediate solution.