Stabilizer Tensor Networks with Magic State Injection

TL;DR

This paper enhances Stabilizer Tensor Networks with magic state injection, enabling efficient classical simulation of large quantum circuits with many non-Clifford gates, surpassing previous exponential scaling limitations.

Contribution

Introduces a magic state injection method into STNs, significantly improving their ability to simulate large quantum circuits with many non-Clifford operations.

Findings

Efficient simulation of random T-doped Clifford circuits up to 200 qubits.

Simulation of 4000-qubit, 320 T-gate circuits with the new framework.

Polynomial scaling in computational cost for circuits with up to N T-gates.

Abstract

This work augments the recently introduced Stabilizer Tensor Network (STN) protocol with magic state injection, reporting a new framework with significantly enhanced ability to simulate circuits with an extensive number of non-Clifford operations. Specifically, for random $T$-doped $N$-qubit Clifford circuits the computational cost of circuits prepared with magic state injection scales as $\mathcal{O}(\text{poly}(N))$ when the circuit has $t \lesssim N$ $T$-gates compared to an exponential scaling for the STN approach, which is demonstrated in systems of up to $200$ qubits. In the case of the Hidden Bit Shift circuit, a paradigmatic benchmarking system for extended stabilizer methods with a tunable amount of magic, we report that our magic state injected STN framework can efficiently simulate $4000$ qubits and $320$ $T$-gates. These findings provide a promising outlook for the use of this protocol in the classical modelling of quantum circuits that are conventionally difficult to simulate efficiently.