Application of a resource theory for magic states to fault-tolerant quantum computing

Abstract

Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. We first show that robustness of magic is a well-behaved magic monotone that operationally quantifies the classical simulation overhead for a Gottesman-Knill type scheme using ancillary magic states. Our framework subsequently finds immediate application in the task of synthesizing non-Clifford gates using magic states. When magic states are interspersed with Clifford gates, Pauli measurements and stabilizer ancillas - the most general synthesis scenario - then the class of synthesizable unitaries is hard to characterize. Our techniques can place non-trivial lower bounds on the number of magic states required for implementing a given target unitary. Guided by these results we have found new and optimal examples of such synthesis.

V2: Author's final copy. Minor corrections vs version 1. 5+5 pages, Supplementary Material available at http://tinyurl.com/jygz3zx

References in corpus (7)

• Quantum circuits of T-depth one
• Novel constructions for the fault-tolerant Toffoli gate
• Wigner function negativity and contextuality in quantum computation on rebits
• Universal quantum computation with little entanglement
• Catalysis and activation of magic states in fault tolerant architectures
• Classical simulatability, entanglement breaking, and quantum computation thresholds
• Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function

Cited by in corpus (181)

• Stabilizer Rényi entropy
• Quantifying nonstabilizerness of matrix product states
• Stabilizer entropies and nonstabilizerness monotones
• Measuring magic on a quantum processor
• Scalable measures of magic resource for quantum computers
• Circuit knitting with classical communication
• One-Shot Operational Quantum Resource Theory
• 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
• Measuring nonstabilizerness via multifractal flatness
• Computational power of one- and two-dimensional dual-unitary quantum circuits
• Nonstabilizerness determining the hardness of direct fidelity estimation
• Simulation of Qubit Quantum Circuits via Pauli Propagation
• 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
• Dynamical Entanglement
• Resource theory of quantum scrambling
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Non-stabilizerness versus entanglement in matrix product states
• Probabilistic transformations of quantum resources
• Complexity of frustration: a new source of non-local non-stabilizerness
• Stabilizer entropy dynamics after a quantum quench
• Entanglement-magic separation in hybrid quantum circuits
• Pseudomagic Quantum States
• Lower bound for the T count via unitary stabilizer nullity
• Quantum Entropy and Central Limit Theorem
• Magic in generalized Rokhsar-Kivelson wavefunctions
• Error mitigation and quantum-assisted simulation in the error corrected regime
• Learning quantum circuits of some $T$ gates
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding
• Fisher information universally identifies quantum resources
• Tight constraints on probabilistic convertibility of quantum states
• Stabilizer entropy in non-integrable quantum evolutions
• Quantum Magic and Multi-Partite Entanglement in the Structure of Nuclei
• Resource theory of quantum uncomplexity
• Retrieving information from a black hole using quantum machine learning
• Virtual quantum resource distillation
• Nonstabilizerness of Permutationally Invariant Systems
• Phase transition in Stabilizer Entropy and efficient purity estimation
• Magic of quantum hypergraph states
• Magic Resources of the Heisenberg Picture
• Exact solution of long-range stabilizer Rényi entropy in the dual-unitary XXZ model
• Quantifying non-stabilizerness via information scrambling
• Complexity of quantum circuits via sensitivity, magic, and coherence
• Hybrid Stabilizer Matrix Product Operator
• Quantifying dynamical magic with completely stabilizer preserving operations as free
• Probing quantum complexity via universal saturation of stabilizer entropies
• Doubly optimal parallel wire cutting without ancilla qubits
• Magic State Distillation from Entangled States
• Classical simulation of non-Gaussian fermionic circuits
• Mana and thermalization: probing the feasibility of near-Clifford Hamiltonian simulation
• Multi-object operational tasks for convex quantum resource theories
• Handbook for Quantifying Robustness of Magic
• Efficient mutual magic and magic capacity with matrix product states
• Stabilizer disentangling of conformal field theories
• One-Shot Yield-Cost Relations in General Quantum Resource Theories
• Quantum Non-Local Nonstabilizerness
• Magic Resource Can Enhance the Quantum Capacity of Channels
• Stabilizer entropy of quantum tetrahedra
• Effects of quantum resources on the statistical complexity of quantum circuits
• Chaos and magic in the dissipative quantum kicked top
• The role of cohomology in quantum computation with magic states
• Non-stabilizerness in kinetically-constrained Rydberg atom arrays
• Virtual quantum resource distillation: General framework and applications
• Entanglement and Stabilizer entropies of random bipartite pure quantum states
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Spectral Properties Versus Magic Generation in $T$-doped Random Clifford Circuits
• Quantum circuit compilation and hybrid computation using Pauli-based computation
• Characterisation of quantum betting tasks in terms of Arimoto mutual information
• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Pseudorandom density matrices
• Bridging magic and non-Gaussian resources via Gottesman-Kitaev-Preskill encoding
• Magic of Random Matrix Product States
• Stabilizer Testing and Magic Entropy via Quantum Fourier Analysis
• Long-range nonstabilizerness and phases of matter
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Stabilizer Rényi Entropy and Conformal Field Theory
• Coherence manipulation in asymmetry and thermodynamics
• On Groups in the Qubit Clifford Hierarchy
• Bridging Entanglement and Magic Resources within Operator Space
• Nonstabilizerness of a Boundary Time Crystal
• Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic
• Stability of classical shadows under gate-dependent noise
• Asymptotically Consistent Measures of General Quantum Resources: Discord, Non-Markovianity, and Non-Gaussianity
• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Extracting randomness from magic quantum states
• A nonstabilizerness monotone from stabilizerness asymmetry
• Stoquasticity in circuit QED
• Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond
• Interplay of entanglement structures and stabilizer entropy in spin models
• Sufficient condition for universal quantum computation using bosonic circuits
• Quantifying fermionic nonlinearity of quantum circuits
• The non-stabilizerness of fermionic Gaussian states
• Limitations of Classically-Simulable Measurements for Quantum State Discrimination
• Pauli-based model of quantum computation with higher-dimensional systems
• Stabilizer ground states for simulating quantum many-body physics: theory, algorithms, and applications
• Geometric-Like imaginarity: quantification and state conversion
• Fermionic Magic Resources of Quantum Many-Body Systems
• Faster Born probability estimation via gate merging and frame optimisation
• Efficient witnessing and testing of magic in mixed quantum states
• Quantum Ruzsa Divergence to Quantify Magic
• Optimal wire cutting with classical communication
• Unlocking early fault-tolerant quantum computing with mitigated magic dilution
• Rademacher complexity of noisy quantum circuits
• Maximal Magic for Two-qubit States
• Computing quantum magic of state vectors
• Clifford operations and homological codes for rotors and oscillators
• Building Qutrit Diagonal Gates from Phase Gadgets
• Automatic Test Pattern Generation for Robust Quantum Circuit Testing
• Non-stabilizerness in quantum-enhanced metrological protocols
• Non-stabilizerness of Neural Quantum States
• Counting stabiliser codes for arbitrary dimension
• Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
• Prepare-and-Magic: Semi-Device Independent Magic Certification in the Prepare-and-Measure Scenario
• Resource Theory of Non-absolute Separability
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• The Hadamard gate cannot be replaced by a resource state in universal quantum computation
• Quantum Circuit Design using a Progressive Widening Enhanced Monte Carlo Tree Search
• Black Box Work Extraction and Composite Hypothesis Testing
• Role of quantum state texture in probing resource theories and quantum phase transition
• Faster computation of nonstabilizerness
• Unified Framework for Calculating Convex Roof Resource Measures
• A trace distance-based geometric analysis of the stabilizer polytope for few-qubit systems
• Unconditional quantum magic advantage in shallow circuit computation
• Local spreading of stabilizer Rényi entropy in a brickwork random Clifford circuit
• Covariant influences for finite discrete dynamical systems
• Hidden variable model for quantum computation with magic states on qudits of any dimension
• Quantifying the imaginarity via different distance measures
• One-Shot Static Entanglement Cost of Bipartite Quantum Channels
• Polynomial T-depth Quantum Solvability of Noisy Binary Linear Problem: From Quantum-Sample Preparation to Main Computation
• Wigner's Theorem for stabilizer states and quantum designs
• Choi-Defined Resource Theories
• Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version)
• Projective robustness for quantum channels and measurements and their operational significance
• Extending Classically Simulatable Bounds of Clifford Circuits with Nonstabilizer States via Framed Wigner Functions
• Wasserstein Complexity of Quantum Circuits
• Minimizing the negativity of quantum circuits in overcomplete quasiprobability representations
• Fundamental limits on concentrating and preserving tensorized quantum resources
• Rise and fall of nonstabilizerness via random measurements
• Quantum coherence with incomplete set of pointers and corresponding wave-particle duality
• Nonstabilizerness and Error Resilience in Noisy Quantum Circuits
• Experimentally validated quantum-secure federated learning over a multi-user quantum network
• Improving quantum channel discrimination with resourceful states
• Multi-object operational tasks for measurement incompatibility
• Analyzing the free states of one quantum resource theory as resource states of another
• Perspectives on Utilization of Measurements in Quantum Algorithms
• Robustness of Magic in the quantum Ising chain via Quantum Monte Carlo tomography
• Invested and Potential Magic Resources in Measurement-Based Quantum Computation
• Invariant Off-Diagonality: SICs as Equicoherent Quantum States
• Low Overhead Qutrit Magic State Distillation
• Scalable projected entangled-pair state representation of random quantum circuit states
• Grand Unification of All Discrete Wigner Functions on $d\times d$ Phase Space
• Non-stabilizerness and entanglement from cat-state injection
• Enhancement of non-Stabilizerness within Indefinite Causal Order
• Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
• Spectral signatures of nonstabilizerness and criticality in infinite matrix product states
• Stabilizer Rényi Entropy for Translation-Invariant Matrix Product States
• Complexity of Quantum Trajectories
• Quantifying magic via quantum $(\alpha ,\beta )$ Jensen-Shannon divergence
• Circuit cutting with classical side information
• Sampling-based quasiprobability simulation for fault-tolerant quantum error correction on the surface codes under coherent noise
• Characterization of non-adaptive Clifford channels
• Halving the cost of quantum multiplexed rotations
• Coherence-induced deep thermalization transition in random permutation quantum dynamics
• On the Hardness of Measuring Magic
• Simulation of quantum computation with magic states via Jordan-Wigner transformations
• General entropic constraints on CSS codes within magic distillation protocols
• Harvesting stabilizer entropy and non-locality from a quantum field
• Van Hove singularities in stabilizer entropy densities
• Scalable protocol to coherence estimation from scarce data: Theory and experiment
• Mathematical methods for resource-based type theories
• A Study on Stabilizer Rényi Entropy Estimation using Machine Learning
• No-cost Bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing
• Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction
• Constructing all qutrit controlled Clifford+T gates in Clifford+T
• Equivalence of Stabilizer and Shannon Rényi Entropies: Exact Results for Quantum Critical Chains
• Gottesman-Knill Limit on One-way Communication Complexity: Tracing the Quantum Advantage down to Magic Resources
• Symmetry-Accelerated Classical Simulation of Clifford-Dominated Circuits
• On the extremal points of the $\Lambda$-polytopes and classical simulation of quantum computation with magic states