GCAMPS: A Scalable Classical Simulator for Qudit Systems

TL;DR

This paper extends the CAMPS method to simulate higher-dimensional qudit systems, specifically qutrits, achieving significant speedups and enabling classical simulation of previously intractable quantum problems.

Contribution

The work generalizes the CAMPS simulation technique to qudits, demonstrating improved performance and broader applicability for classical simulation of complex quantum systems.

Findings

Qutrit systems benefit from similar or greater speedups compared to qubits.

The extended GCAMPS simulator can handle problems previously intractable with classical methods.

Benchmarking shows increased difficulty of simulating qutrits with tensor networks, highlighting the method's effectiveness.

Abstract

Classical simulations of quantum systems are notoriously difficult computational problems, with conventional state vector and tensor network methods restricted to quantum systems that feature only a small number of qudits. The recently introduced Clifford Augmented Matrix Product State (CAMPS) method offer scalability and efficiency by combining both tensor network and stabilizer simulation techniques and leveraging their complementary advantages. This hybrid simulation method has indeed demonstrated significant improvements in simulation performance for qubit circuits. Our work generalises the CAMPS method to higher quantum degrees of freedom -- qudit simulation, resulting in a generalised CAMPS (GCAMPS). Benchmarking this extended simulator on quantum systems with three degrees of freedom, i.e. qutrits, we show that similar to the case of qubits, qutrit systems also benefit from a comparable speedup using these techniques. Indeed, we see a greater improvement with qutrit simulation compared to qubit simulation on the same $T$-doped random Clifford benchmarking circuit as a result of the increased difficulty of conventional qutrit simulation using tensor networks. This extension allows for the classical simulation of problems that were previously intractable without access to a quantum device and will open new avenues to study complex many-body physics and to develop efficient methods for quantum information processing.