Estimating Non-Stabilizerness Dynamics Without Simulating It

• URL: http://arxiv.org/abs/2405.06054v1
• Date: Thu, 9 May 2024 18:57:55 GMT
• Title: Estimating Non-Stabilizerness Dynamics Without Simulating It
• Authors: Alessio Paviglianiti, Guglielmo Lami, Mario Collura, Alessandro Silva,
• Abstract summary: Iterative Clifford Circuit Renormalization (I CCR) is designed to efficiently handle the dynamics of non-stabilizerness in quantum circuits. I CCR embeds the complex dynamics of non-stabilizerness in the flow of an effective initial state. We implement the I CCR algorithm to evaluate the non-stabilizerness dynamics for systems of size up to N = 1000.
• Score: 43.80709028066351
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We introduce the Iterative Clifford Circuit Renormalization (ICCR), a novel technique designed to efficiently handle the dynamics of non-stabilizerness (a.k.a. quantum magic) in generic quantum circuits. ICCR iteratively adjusts the starting circuit, transforming it into a Clifford circuit where all elements that can alter the non-stabilizerness, such as measurements or T gates, have been removed. In the process the initial state is renormalized in such a way that the new circuit outputs the same final state as the original one. This approach embeds the complex dynamics of non-stabilizerness in the flow of an effective initial state, enabling its efficient evaluation while avoiding the need for direct and computationally expensive simulation of the original circuit. The initial state renormalization can be computed explicitly using an approximation that can be systematically improved. We implement the ICCR algorithm to evaluate the non-stabilizerness dynamics for systems of size up to N = 1000. We validate our method by comparing it to tensor networks simulations. Finally, we employ the ICCR technique to study a magic purification circuit, where a measurement-induced transition is observed.

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