Efficient certification of intractable quantum states with few Pauli measurements

• URL: http://arxiv.org/abs/2511.07300v1
• Date: Mon, 10 Nov 2025 17:01:51 GMT
• Title: Efficient certification of intractable quantum states with few Pauli measurements
• Authors: Sami Abdul Sater, Maxime Garnier, Thierry Martinez, Harold Ollivier, Ulysse Chabaud,
• Abstract summary: We introduce an efficient protocol for certifying Clifford-enhanced Product States.<n>Our protocol only requires single-qubit Pauli measurements together with efficient classical post-processing.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Verification of quantum computations is crucial as experiments advance toward fault-tolerant quantum computing. Yet, no efficient protocol exists for certifying states generated in the Magic-State Injection model -- the foundation of several fault-tolerant quantum computing architectures. Here, we introduce an efficient protocol for certifying Clifford-enhanced Product States, a large class of quantum states obtained by applying an arbitrary Clifford circuit to a product of single-qubit, possibly magic, states. Our protocol only requires single-qubit Pauli measurements together with efficient classical post-processing, and has efficient sample complexity in both the independent (i.i.d.) and adversarial (non-i.i.d.) settings. This fills a key gap between Pauli-based certification schemes for stabilizer or (hyper)graph states and general protocols demanding non-Pauli measurements or classically intractable information about the target state. Our work provides the first efficient, Pauli-only certification protocol for the Magic-State Injection model, leading to practical verification of universal quantum computation under minimal experimental assumptions.

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