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Phase transition in magic with random quantum circuits
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Phase transition in magic with random quantum circuits
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Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards efficient and practical fault-tolerant computation. We observe that a random stabilizer code subject to coherent errors exhibits a phase transition in magic, which we characterize through analytic, numeric and experimental probes. Below a critical error rate, stabilizer syndrome measurements remove the accumulated magic in the circuit, effectively protecting against coherent errors; above the critical error rate syndrome measurements concentrate magic. A better understanding of such rich behavior in the resource theory of magic could shed more light on origins of quantum speedup and pave pathways for more efficient magic state generation.
Forward citations
Cited by 6 Pith papers
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Taming Trotter Errors with Quantum Resources
Entanglement entropy bounds the variance of Trotter error downward, and magic drives the error kurtosis downward (Kur = α + βM, β<0 for large systems).
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Operator space fragmentation in perturbed Floquet-Clifford circuits
Perturbed random Floquet-Clifford circuits exhibit operator-space fragmentation into wall-separated sectors for p < 1, yielding exact local integrals of motion, tunable operator spreading length, an entanglement bottl...
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On the stabilizer complexity of Hawking radiation
In the PSSY model, the Wigner negativity (stabilizer magic) of Hawking radiation is O(1) before the Page time and grows as sqrt(2/pi) exp((S_max - S_2)/2) afterward; a similar formula is proposed for holographic state...
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Efficient witnessing and testing of magic in mixed quantum states
Efficient witnesses and testing algorithms based on stabilizer Rényi entropy certify and quantify magic in mixed states, with experimental demonstration on IonQ hardware showing robustness under strong noise.
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Magic and entanglement in 1+1-dimensional SU(2) lattice gauge theory
Tensor network calculation of magic and entanglement in SU(2) lattice gauge theory ground state shows a crossover from magic-rich to less-magic regime at g_star.
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Taming Trotter Errors with Quantum Resources
Higher entanglement entropy reduces variance of Trotter errors and higher magic reduces kurtosis, making error distributions more robust in quantum simulation.
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