Quasi-exact quantum computation
arXiv:1910.00038 · doi:10.1103/PhysRevResearch.2.033116
Abstract
We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding exact codes, serving as its fixed points. The computation with a quasi-exact code cannot realize any logical gate to arbitrary accuracy. To overcome this, the notion of quasi-exact universality is proposed, which makes quasi-exact quantum computation a feasible model especially for executing moderate-size algorithms. We find that the incompatibility between universality and transversality of the set of logical gates does not persist in the quasi-exact scenario. A class of covariant quasi-exact codes is defined which proves to support transversal and quasi-exact universal set of logical gates for . This work opens the possibility of quantum computation with quasi-exact universality, transversality, and fault tolerance.
References in corpus (36)
- Non-Abelian Anyons and Topological Quantum Computation
- The density-matrix renormalization group in the age of matrix product states
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Classification of Gapped Symmetric Phases in 1D Spin Systems
- Classifying quantum phases using Matrix Product States and PEPS
- Distance measures to compare real and ideal quantum processes
- Restrictions on Transversal Encoded Quantum Gate Sets
- Stabilizer Formalism for Operator Quantum Error Correction
- A Unified and Generalized Approach to Quantum Error Correction
- Novel schemes for measurement-based quantum computation
- Universal fault-tolerant quantum computation with only transversal gates and error correction
- Classification of topologically protected gates for local stabilizer codes
- Quantum computation with Turaev-Viro codes
- General conditions for approximate quantum error correction and near-optimal recovery channels
- Valence bond solids for SU(n) spin chains: exact models, spinon confinement, and the Haldane gap
- Fault-tolerant logical gates in quantum error-correcting codes
- Using concatenated quantum codes for universal fault-tolerant quantum gates
- A simple approach to approximate quantum error correction based on the transpose channel
- Computational Power of Symmetry-Protected Topological Phases
- On topological phases of spin chains
- Quantum Error Correcting Codes in Eigenstates of Translation-Invariant Spin Chains
- Z_3 symmetry-protected topological phases in the SU(3) AKLT model
- Protected gates for topological quantum field theories
- Continuous groups of transversal gates for quantum error correcting codes from finite clock reference frames
- From symmetry-protected topological order to Landau order
- Entanglement in an SU(n) Valence-Bond-Solid State
- Algebraic and information-theoretic conditions for operator quantum error-correction
- Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit
- Quantum Circuits for Measuring Levin-Wen Operators
- Towards a Unified Framework for Approximate Quantum Error Correction
- Qudit quantum computation on matrix product states with global symmetry
- Quantum Origami: Transversal Gates for Quantum Computation and Measurement of Topological Order
- Approximate simulation of quantum channels
- Perturbative quantum error correction
- Topological qubits from valence bond solids
Cited by in corpus (15)
- Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem
- Error Correction of Quantum Reference Frame Information
- New perspectives on covariant quantum error correction
- Near-optimal covariant quantum error-correcting codes from random unitaries with symmetries
- Optimal Universal Quantum Error Correction via Bounded Reference Frames
- Approximate symmetries and quantum error correction
- A comparative study of universal quantum computing models: towards a physical unification
- A prototype of quantum von Neumann architecture
- Complexity and order in approximate quantum error-correcting codes
- Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes
- Extracting Error Thresholds through the Framework of Approximate Quantum Error Correction Condition
- Quantum resource theory of coding for error correction
- Approximate Quantum Codes From Long Wormholes
- State-adaptive quantum error correction and fault-tolerant quantum computing
- Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout