Distributing Quantum Computations, Shot-wise

TL;DR

A methodological framework, termed shot-wise, which enables the distribution of shots for a single circuit across multiple QPUs, offering a robust and flexible approach to managing variability in quantum computing.

Abstract

NISQ (Noisy Intermediate-Scale Quantum) era constraints, high sensitivity to noise and limited qubit count, impose significant barriers on the usability of QPUs (Quantum Process Units) capabilities. To overcome these challenges, researchers are exploring methods to maximize the utility of existing QPUs despite their limitations. Building upon the idea that the execution of a quantum circuit's shots needs not to be treated as a singular monolithic unit, we propose a methodological framework, termed shot-wise, which enables the distribution of shots for a single circuit across multiple QPUs. Our framework features customizable policies to adapt to various scenarios. Additionally, it introduces a calibration method to pre-evaluate the accuracy and reliability of each QPU's output before the actual distribution process and an incremental execution mechanism for dynamically managing the shot allocation and policy updates. Such an approach enables flexible and fine-grained management of the distribution process, taking into account various user-defined constraints and (contrasting) objectives. Experimental findings show that while these strategies generally do not exceed the best individual QPU results, they maintain robustness and align closely with average outcomes. Overall, the shot-wise methodology improves result stability and often outperforms single QPU runs, offering a flexible approach to managing variability in quantum computing.

Figures (7)

• Figure 1: Diagram of the general strategy of heterogeneous quantum computation discussed in the text. Thin arrows connect steps in sequence, while thick arrows describe dependencies (with dashed line describing optional dependency).
• Figure 2: Diagram of the strategies considered in the numerical investigation of Section \ref{['sec:numres']}, as a specific instantiation of the general strategy depicted in Fig. \ref{['fig:diagram_strategy']}.
• Figure 3: Behavior of the Mean Square Hellinger distance on a fixed set of $10$ random circuits $\{U_c\}$ with $q=5$ qubits as a measure of unreliability for each QPU considered in this work, reported in Table \ref{['tab:QPUs']}.
• Figure 4: Results of single QPU executions (left part of the panels) and of the split and merged results from the full set of available QPUs (see text for details) in terms of the Hellinger distance ($d_H$, see Eq. \ref{['eq:Hellinger_def']}) from the ideal case. Points are slightly shifted on the horizontal axis for better readability. .
• Figure 5: Measured error for all circuits, divided by split and merge policy combinations while increasing the number of available QPUs. Each bar represents a specific combination of split and merge policies. The red bar corresponds to execute all the shots on a random QPU.