Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
arXiv:2512.15880 · doi:10.1103/w6l4-mh6k
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.
arXiv comment5 pages, 1 figure. Comments are welcome
References in corpus (75)
- Improved Simulation of Stabilizer Circuits
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Quantum Resource Theories
- Characterizing Quantum Supremacy in Near-Term Devices
- A Theory of Fault-Tolerant Quantum Computation
- Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
- Improved classical simulation of quantum circuits dominated by Clifford gates
- Stabilizer Rényi entropy
- Quantum Supremacy and the Complexity of Random Circuit Sampling
- Simulation of quantum circuits by low-rank stabilizer decompositions
- Multifractal Scalings across the Many-Body Localization Transition
- Operational Resource Theory of Imaginarity
- 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
- Quantifying the Imaginarity of Quantum Mechanics
- 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
- Robustness of Magic and Symmetries of the Stabiliser Polytope
- Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
- Measurement-induced phase transitions in -dimensional stabilizer circuits
- Disentangling Scrambling and Decoherence via Quantum Teleportation
- 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
- Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
- Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
- Magic spreading in random quantum circuits
- Efficient quantum algorithms for stabilizer entropies
- Dynamical Magic Transitions in Monitored Clifford+T Circuits
- Typicality in random matrix product states
- Anticoncentration theorems for schemes showing a quantum speedup
- Real Randomized Benchmarking
- Efficient unitary designs with a system-size independent number of non-Clifford gates
- Learning t-doped stabilizer states
- Quantum advantage of unitary Clifford circuits with magic state inputs
- 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
- A single -gate makes distribution learning hard
- Stabilizer entropy in non-integrable quantum evolutions
- Thrifty shadow estimation: re-using quantum circuits and bounding tails
- Retrieving information from a black hole using quantum machine learning
- Entanglement Growth and Minimal Membranes in 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
- Spectral Properties Versus Magic Generation in -doped Random Clifford Circuits
- Independent stabilizer Rényi entropy and entanglement fluctuations in random unitary circuits
- Efficient learning of -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
- Quantum simulation from the bottom up: the case of rebits
- Impact of Clifford operations on non-stabilizing power and quantum chaos
- Disentangling magic states with classically simulable quantum circuits
- Qudit Shadow Estimation Based on the Clifford Group and the Power of a Single Magic Gate
- On the power quantum computation over real Hilbert spaces
- Operational interpretation of the Stabilizer Entropy
- Designs from magic-augmented Clifford circuits
- 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
- Analyzing the free states of one quantum resource theory as resource states of another
- A 3D lattice defect and efficient computations in topological MBQC
- On Computational Complexity of Unitary and State Design Properties