Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks

Abstract

We investigate the statistical properties of orthogonal, or real, Clifford circuits doped with magic and imaginary resources. By developing the Weingarten calculus for the real Clifford group, we derive the exact overlap distribution of real stabilizer states, identifying a new universality class: the orthogonal Clifford Porter-Thomas distribution. We prove that local real architectures recover this global statistic in logarithmic depth. Furthermore, we uncover a sharp hierarchy in resource requirements: while retrieving Haar statistics necessitates a polylogarithmic amount of magic states, recovering the full unitary Clifford statistics requires only a single phase gate.

5 pages, 1 figure. Comments are welcome

References in corpus (52)

• Stabilizer Rényi entropy
• Linear growth of quantum circuit complexity
• Wigner function negativity and contextuality in quantum computation on rebits
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• A general framework for randomized benchmarking
• Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Resource theory of imaginarity: Quantification and state conversion
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Quantum Chaos is Quantum
• Measuring nonstabilizerness via multifractal flatness
• Phase transition in magic with random quantum circuits
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Magic spreading in random quantum circuits
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Efficient quantum algorithms for stabilizer entropies
• Dynamical Magic Transitions in Monitored Clifford+T Circuits
• Learning t-doped stabilizer states
• Unitary-invariant witnesses of quantum imaginarity
• Resource Theory of Imaginarity: New Distributed Scenarios
• Unscrambling Quantum Information with Clifford decoders
• Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits
• Thrifty shadow estimation: re-using quantum circuits and bounding tails
• A single $T$-gate makes distribution learning hard
• Stabilizer entropy in non-integrable quantum evolutions
• Retrieving information from a black hole using quantum machine learning
• Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits
• Probing quantum complexity via universal saturation of stabilizer entropies
• Pseudorandom unitaries are neither real nor sparse nor noise-robust
• Stabilizer Tensor Networks with Magic State Injection
• Anticoncentration and state design of random tensor networks
• Independent stabilizer Rényi entropy and entanglement fluctuations in random unitary circuits
• Spectral Properties Versus Magic Generation in $T$-doped Random Clifford Circuits
• Efficient learning of $t$-doped stabilizer states with single-copy measurements
• Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• Nonstabilizerness dynamics in many-body localized systems
• Quantum Complexity and Chaos in Many-Qudit Doped Clifford Circuits
• Stability of classical shadows under gate-dependent noise
• Disentangling magic states with classically simulable quantum circuits
• Impact of Clifford operations on non-stabilizing power and quantum chaos
• Qudit Shadow Estimation Based on the Clifford Group and the Power of a Single Magic Gate
• Designs from magic-augmented Clifford circuits
• Operational interpretation of the Stabilizer Entropy
• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• Universal distributions of overlaps from generic dynamics in quantum many-body systems
• Non-Clifford Cost of Random Unitaries
• Classical simulability of Clifford+T circuits with Clifford-augmented matrix product states
• Multi-state imaginarity and coherence in qubit systems
• Universality in the Anticoncentration of Noisy Quantum Circuits at Finite Depths
• A 3D lattice defect and efficient computations in topological MBQC
• Analyzing the free states of one quantum resource theory as resource states of another
• On Computational Complexity of Unitary and State Design Properties

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