Efficient Circuit Wire Cutting Based on Commuting Groups

TL;DR

This work proposes a new approach that can reduce subcircuit running overhead and significantly reduces the number of necessary subcircuits as well as the total number of shots.

Abstract

Current quantum devices face challenges when dealing with large circuits due to error rates as circuit size and the number of qubits increase. The circuit wire-cutting technique addresses this issue by breaking down a large circuit into smaller, more manageable subcircuits. However, the exponential increase in the number of subcircuits and the complexity of reconstruction as more cuts are made poses a great practical challenge. Inspired by ancilla-assisted quantum process tomography and the MUBs-based grouping technique for simultaneous measurement, we propose a new approach that can reduce subcircuit running overhead. The approach first uses ancillary qubits to transform all quantum input initializations into quantum output measurements. These output measurements are then organized into commuting groups for the purpose of simultaneous measurement, based on MUBs-based grouping. This approach significantly reduces the number of necessary subcircuits as well as the total number of shots. Lastly, we provide numerical experiments to demonstrate the complexity reduction.

Figures (7)

• Figure 1: An example of 3-qubit circuit cutting is depicted in \ref{['eq:three qubit example circuit cutting']}. The circuit is separated into two fragments, unitary $U$ and unitary $V$ by cutting at the a red cross mark. To construct the subcircuits, we need to measure the second qubit on the $M$ basis after $U$ and prepare the $M_r$ and $M_s$ states as the initial states for $V$.
• Figure 2: An Example of Classical/Quantum Input/Output: The state initialized as $\left|0\right\rangle$ represents the classical input $C_i(f_i)$, while states initialized as $M_r$ or $M_s$ are quantum inputs $Q_i(f_i)$. A qubit measured in the $Z$ basis constitutes a classical output $C_i(f_i)$, whereas measurements in several bases, denoted by $M$, are considered quantum outputs $Q_o(f_i)$.
• Figure 3: Transformation circuit of group $\{XY,YZ,ZX\}$. After transforming the circuit, running it once yields results for $\{XY, YZ, ZX\}$. Measuring the first qubit, the second qubit, and both the first and second qubits correspond to results for $YZ$, $ZX$, and $-XY$, respectively.
• Figure 4: An Example of Ancilla-Assisted Initialization. The left circuit involves initializing each qubit separately with $M_i^r$ and $M_i^s$, while the right circuit involves measuring each qubit in the $M_i$ basis. And $M_i = rM_i^r + sM_i^s$. The circuit on the left needs to be executed eight times to get the expectation value. However, by running the right circuit once, we can obtain the expectation value, which is much more convenient.
• Figure 5: Example of a subcircuit converted from Fig. \ref{['fig:QinQout']}. With the use of an ancilla qubit, we can convert quantum inputs into quantum outputs. This allows us to perform MUBs-based grouping on $M(f_j) = Qo(f_j) \otimes Qi(f_j)$.