Fast classical simulation of qubit-qudit hybrid systems

TL;DR

This work adopts a block-simulation methodology applicable to qubit-qudit hybrid systems that interprets the statevector as a collection of blocks and applies gates without computing the entire circuit unitary.

Abstract

Simulating quantum circuits is a computationally intensive task that relies heavily on tensor products and matrix multiplications, which can be inefficient. Recent advancements, eliminate the need for tensor products and matrix multiplications, offering significant improvements in efficiency and parallelization. Extending these optimizations, we adopt a block-simulation methodology applicable to qubit-qudit hybrid systems. This method interprets the statevector as a collection of blocks and applies gates without computing the entire circuit unitary. Our method, a spiritual successor of the simulator QuDiet \cite{Chatterjee_2023}, utilizes this block-simulation method, thereby gaining major improvements over the simulation methods used by its predecessor. We exhibit that the proposed method is approximately 10$\times$ to 1000$\times$ faster than the state-of-the-art simulator for simulating multi-level quantum systems with various benchmark circuits.

Figures (10)

• Figure 1: Step 1 of the example circuit execution: The statevector of the initial state is taken into account as a single block.
• Figure 2: Step 2 of the example circuit execution: The statevector has been grouped into blocks based on the 3 dimensions of the qudit $q_1$.
• Figure 3: Step 3 of the example circuit execution: The grouped statevector is now being transformed into an appropriate matrix, such that further grouping is possible.
• Figure 4: Step 4 of the example circuit execution: The Hadamard operator is now being applied to the statevector as illustrated above.
• Figure 5: Step 5 of the example circuit execution: The resultant statevector at the end of the execution phase is now reconfigured into its initial form.