Universal resources for quantum computing
arXiv:2303.03715 · doi:10.1088/1572-9494/ad07d6
Abstract
Unravelling the source of quantum computing power has been a major goal in the field of quantum information science. In recent years, the quantum resource theory (QRT) has been established to characterize various quantum resources, yet their roles in quantum computing tasks still require investigation. The so-called universal quantum computing model (UQCM), e.g., the circuit model, has been the main framework to guide the design of quantum algorithms, creation of real quantum computers etc. In this work, we combine the study of UQCM together with QRT. We find on one hand, using QRT can provide a resource-theoretic characterization of a UQCM, the relation among models and inspire new ones, and on the other hand, using UQCM offers a framework to apply resources, study relation among resources and classify them. We develop the theory of universal resources in the setting of UQCM, and find a rich spectrum of UQCMs and the corresponding universal resources. Depending on a hierarchical structure of resource theories, we find models can be classified into families. In this work, we study three natural families of UQCMs in details: the amplitude family, the quasi-probability family, and the Hamiltonian family. They include some well known models, like the measurement-based model and adiabatic model, and also inspire new models such as the contextual model we introduce. Each family contains at least a triplet of models, and such a succinct structure of families of UQCMs offers a unifying picture to investigate resources and design models. It also provides a rigorous framework to resolve puzzles, such as the role of entanglement vs. interference, and unravel resource-theoretic features of quantum algorithms.
References in corpus (100)
- Quantum entanglement
- Non-Abelian Anyons and Topological Quantum Computation
- The density-matrix renormalization group in the age of matrix product states
- Quantum Teleportation is a Universal Computational Primitive
- Quantum Coherence as a Resource
- Adiabatic Quantum Computing
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Quantum Algorithms Revisited
- Quantum Resource Theories
- Quantum fingerprinting
- Hidden Variables and the Two Theorems of John Bell
- Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
- A Theory of Fault-Tolerant Quantum Computation
- Classification of Gapped Symmetric Phases in 1D Spin Systems
- Operational Resource Theory of Coherence
- Measuring Quantum Coherence with Entanglement
- On the Power of One Bit of Quantum Information
- Classifying quantum phases using Matrix Product States and PEPS
- Simulating Hamiltonian dynamics with a truncated Taylor series
- Efficient quantum algorithms for simulating sparse Hamiltonians
- On the role of entanglement in quantum computational speed-up
- Contextuality for preparations, transformations, and unsharp measurements
- Contextuality supplies the magic for quantum computation
- Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
- The Resource Theory of Stabilizer Computation
- Universal computation by multi-particle quantum walk
- The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
- Quantum advantage with shallow circuits
- A limit on nonlocality in any world in which communication complexity is not trivial
- Negative Quasi-Probability as a Resource for Quantum Computation
- The general structure of quantum resource theories
- Transforming quantum operations: quantum supermaps
- Hudson's Theorem for finite-dimensional quantum systems
- Quantum channels and memory effects
- The fundamental limit on the rate of quantum dynamics: the unified bound is tight
- Negativity and contextuality are equivalent notions of nonclassicality
- PEPS as ground states: degeneracy and topology
- Simulation of quantum circuits by low-rank stabilizer decompositions
- Most quantum states are too entangled to be useful as computational resources
- The General Quantum Interference Principle and the Duality Computer
- Novel schemes for measurement-based quantum computation
- Contextuality in Measurement-based Quantum Computation
- All Entangled Quantum States Are Nonlocal
- Estimating outcome probabilities of quantum circuits using quasiprobabilities
- Kochen-Specker Contextuality
- Computational power of correlations
- Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
- Symmetry-protected phases for measurement-based quantum computation
- Quantifying Superposition
- Memory effects in quantum channel discrimination
- Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries
- Operational one-to-one mapping between coherence and entanglement measures
- Unified derivations of measurement-based schemes for quantum computation
- A review of Quantum Cellular Automata
- Quantum computation on the edge of a symmetry-protected topological order
- Are random pure states useful for quantum computation?
- Quantifying quantum speedups: improved classical simulation from tighter magic monotones
- Quantum circuits cannot control unknown operations
- Universal quantum computation with little entanglement
- Simple universal models capture all classical spin physics
- Contextuality and Wigner function negativity in qubit quantum computation
- Quantum computational capability of a 2D valence bond solid phase
- Universal Quantum Hamiltonians
- Classical simulation versus universality in measurement based quantum computation
- A computationally universal phase of quantum matter
- Instantaneous measurement of non-local variables
- Hierarchy of universal entanglement in 2D measurement-based quantum computation
- Computational Power of Symmetry-Protected Topological Phases
- Fundamentals of universality in one-way quantum computation
- The Impossibility Of Secure Two-Party Classical Computation
- Resource theories of communication
- Quantum Computing with black-box Subroutines
- Hamiltonian Quantum Cellular Automata in 1D
- Quantum simulators, continuous-time automata, and translationally invariant systems
- Quantum interference as a resource for quantum speedup
- Revisiting the simulation of quantum Turing machines by quantum circuits
- A universally programmable Quantum Cellular Automaton
- Changing the circuit-depth complexity of measurement-based quantum computation with hypergraph states
- Measurement-based classical computation
- Qudit quantum computation on matrix product states with global symmetry
- A Quantitative Measure of Interference
- Fast Universal Quantum Computation with Railroad-switch Local Hamiltonians
- Symmetry-Protected Topological Entanglement
- Spin-1/2 particles moving on a 2D lattice with nearest-neighbor interactions can realize an autonomous quantum computer
- Universal 2-local Hamiltonian Quantum Computing
- Adiabatic and Hamiltonian computing on a 2D lattice with simple 2-qubit interactions
- Time Independent Universal Computing with Spin Chains: Quantum Plinko Machine
- Coherence makes quantum systems 'magical'
- A quantum computer only needs one universe
- A comparative study of universal quantum computing models: towards a physical unification
- No nonlocal box is universal
- A prototype of quantum von Neumann architecture
- Bounds on Instantaneous Nonlocal Quantum Computation
- General conditions for universality of Quantum Hamiltonians
- Popescu-Rohrlich correlations imply efficient instantaneous nonlocal quantum computation
- Universal Quantum Computation by Scattering in the Fermi-Hubbard Model
- Quantum Fine-Grained Entropy
- Superposition and Entanglement from Quantum Scope
- Quantum Cellular Automata
- A local model of quantum Turing machines