Efficient mutual magic and magic capacity with matrix product states

Abstract

Stabilizer Rényi entropies (SREs) probe the non-stabilizerness (or magic) of many-body systems and quantum computers. Here, we introduce the mutual von-Neumann SRE and magic capacity, which can be efficiently computed in time $O(N{\chi }^3)$ for matrix product states (MPSs) of bond dimension $\chi$. We find that mutual SRE characterizes the critical point of ground states of the transverse-field Ising model, independently of the chosen local basis. Then, we relate the magic capacity to the anti-flatness of the Pauli spectrum, which quantifies the complexity of computing SREs. The magic capacity characterizes transitions in the ground state of the Heisenberg and Ising model, randomness of Clifford+T circuits, and distinguishes typical and atypical states. Finally, we make progress on numerical techniques: we design two improved Monte-Carlo algorithms to compute the mutual $2$-SRE, overcoming limitations of previous approaches based on local update. We also give improved statevector simulation methods for Bell sampling and SREs with $O(8^{N/2})$ time and $O(2^N)$ memory, which we demonstrate for $24$ qubits. Our work uncovers improved approaches to study the complexity of quantum many-body systems.

arXiv comment13+10 pages, 6+9 figures

References in corpus (63)

• Fault-tolerant quantum computation by anyons
• Scaling of Entanglement close to a Quantum Phase Transitions
• Improved Simulation of Stabilizer Circuits
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Quantum Resource Theories
• Logical quantum processor based on reconfigurable atom arrays
• The ITensor Software Library for Tensor Network Calculations
• A Theory of Fault-Tolerant Quantum Computation
• Stabilizer Codes and Quantum Error Correction
• The Resource Theory of Stabilizer Computation
• Instantaneous non-local computation of low T-depth quantum circuits
• The Heisenberg Representation of Quantum Computers
• Direct Fidelity Estimation from Few Pauli Measurements
• Restrictions on Transversal Encoded Quantum Gate Sets
• Application of a resource theory for magic states to fault-tolerant quantum computing
• Stabilizer Rényi entropy
• Simulation of quantum circuits by low-rank stabilizer decompositions
• Many-body quantum magic
• Quantifying nonstabilizerness of matrix product states
• Stabilizer entropies and nonstabilizerness monotones
• Scalable measures of magic resource for quantum computers
• Measuring magic on a quantum processor
• Schur-Weyl Duality for the Clifford Group with Applications: Property Testing, a Robust Hudson Theorem, and de Finetti Representations
• Conformal field theories are magical
• Many-body magic via Pauli-Markov chains -- from criticality to gauge theories
• Quantum Chaos is Quantum
• Stabilizer entropies are monotones for magic-state resource theory
• Magic-state resource theory for the ground state of the transverse-field Ising model
• Nonstabilizerness via matrix product states in the Pauli basis
• Aspects of capacity of entanglement
• Measuring nonstabilizerness via multifractal flatness
• Phase transition in magic with random quantum circuits
• 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
• Resource theory of quantum scrambling
• Efficient unitary designs with a system-size independent number of non-Clifford gates
• Non-stabilizerness versus entanglement in matrix product states
• Learning t-doped stabilizer states
• Entanglement-magic separation in hybrid quantum circuits
• Critical behaviors of non-stabilizerness in quantum spin chains
• Magic in generalized Rokhsar-Kivelson wavefunctions
• Learning efficient decoders for quasi-chaotic quantum scramblers
• Characterization of an operational quantum resource in a critical many-body system
• Learning quantum circuits of some $T$ gates
• Nonstabilizerness in U(1) lattice gauge theory
• Magic-induced computational separation in entanglement theory
• Bell sampling from quantum circuits
• Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model
• Magic Resources of the Heisenberg Picture
• Stabilizer disentangling of conformal field theories
• Quantum Non-Local Nonstabilizerness
• Non-equilibrium quantum Monte Carlo algorithm for stabilizer Renyi entropy in spin systems
• Knots, links, and long-range magic
• Interplay of entanglement structures and stabilizer entropy in spin models
• A nonstabilizerness monotone from stabilizerness asymmetry
• Efficient distributed inner product estimation via Pauli sampling
• Quantum State Designs with Clifford Enhanced Matrix Product States
• Anticoncentration and nonstabilizerness spreading under ergodic quantum dynamics
• Evaluating many-body stabilizer Rényi entropy by sampling reduced Pauli strings: singularities, volume law, and nonlocal magic
• Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States
• Universal Spreading of Nonstabilizerness and Quantum Transport

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• Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
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