Scalable measures of magic resource for quantum computers

Abstract

Non-stabilizerness or magic resource characterizes the amount of non-Clifford operations needed to prepare quantum states. It is a crucial resource for quantum computing and a necessary condition for quantum advantage. However, quantifying magic resource beyond a few qubits has been a major challenge. Here, we introduce efficient measures of magic resource for pure quantum states with a sampling cost that is independent of the number of qubits. Our method uses Bell measurements over two copies of a state, which we implement in experiment together with a cost-free error mitigation scheme. We show the transition of classically simulable stabilizer states into intractable quantum states on the IonQ quantum computer. For applications, we efficiently distinguish stabilizer and non-stabilizer states with low measurement cost even in the presence of experimental noise. Further, we propose a variational quantum algorithm to maximize our measure via the shift-rule. Our algorithm can be free of barren plateaus even for highly expressible variational circuits. Finally, we experimentally demonstrate a Bell measurement protocol for the stabilizer Rényi entropy as well as the Wallach-Meyer entanglement measure. Our results pave the way to understand the non-classical power of quantum computers, quantum simulators and quantum many-body systems.

arXiv comment23 pages, 10 figures

References in corpus (66)

• Quantum Computing in the NISQ era and beyond
• Double-slit photoelectron interference in strong-field ionization of the neon dimer
• Fault-tolerant quantum computation by anyons
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Barren plateaus in quantum neural network training landscapes
• Quantum Communication
• Quantum Teleportation is a Universal Computational Primitive
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum Circuit Learning
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Improved Simulation of Stabilizer Circuits
• Measuring entanglement entropy through the interference of quantum many-body twins
• Quantum thermalization through entanglement in an isolated many-body system
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• A Theory of Fault-Tolerant Quantum Computation
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Contextuality supplies the magic for quantum computation
• Probing entanglement entropy via randomized measurements
• Roads towards fault-tolerant universal quantum computation
• Quantum advantage in learning from experiments
• Noise tailoring for scalable quantum computation via randomized compiling
• Hybrid quantum-classical algorithms and quantum error mitigation
• Global entanglement in multiparticle systems
• The Resource Theory of Stabilizer Computation
• Quantum Natural Gradient
• Universal Quantum Estimator
• Direct estimations of linear and non-linear functionals of a quantum state
• Application of a resource theory for magic states to fault-tolerant quantum computing
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• Quantum certification and benchmarking
• Local random quantum circuits are approximate polynomial-designs
• Trading classical and quantum computational resources
• Stabilizer Rényi entropy
• Simulation of quantum circuits by low-rank stabilizer decompositions
• Estimating outcome probabilities of quantum circuits using quasiprobabilities
• The SWAP test and the Hong-Ou-Mandel effect are equivalent
• The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)
• Mitigating depolarizing noise on quantum computers with noise-estimation circuits
• Estimating the gradient and higher-order derivatives on quantum hardware
• Many-body quantum magic
• Wigner function negativity and contextuality in quantum computation on rebits
• Capacity and quantum geometry of parametrized quantum circuits
• Lower bounds on the non-Clifford resources for quantum computations
• Quantifying the magic of quantum channels
• Quantifying quantum speedups: improved classical simulation from tighter magic monotones
• Quantifying magic for multi-qubit operations
• 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
• Simple Mitigation of Global Depolarizing Errors in Quantum Simulations
• Quantum Algorithmic Measurement
• Conformal field theories are magical
• Quantum Chaos is Quantum
• Theoretical and Experimental Perspectives of Quantum Verification
• Catalysis and activation of magic states in fault tolerant architectures
• Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics
• Measurement cost of metric-aware variational quantum algorithms
• Efficient unitary designs with a system-size independent number of non-Clifford gates
• Transitions in Entanglement Complexity in Random Circuits
• Learning and Testing Algorithms for the Clifford Group
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding
• Rényi squashed entanglement, discord, and relative entropy differences
• Natural parameterized quantum circuit

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