Stabilizer Tensor Networks with Magic State Injection

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.

5+7 pages, 3+5 figures

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• Bridging Entanglement and Magic Resources within Operator Space
• Fermionic Magic Resources of Quantum Many-Body Systems
• Disentangling magic states with classically simulable quantum circuits
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• Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states
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• Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States
• Limits of Clifford Disentangling in Tensor Network States
• GCAMPS: A Scalable Classical Simulator for Qudit Systems