Dissipationless topological quantum computation for Majorana objects in sparse-dense mixed encoding process
arXiv:2407.11544 · doi:10.1103/PhysRevA.110.022609
Abstract
Topological quantum computation based on Majorana objects is subject to a significant challenge because at least some of the two-qubit quantum gates rely on the fermion (either charge or spin) parity of the qubits. This dependency renders the quantum operations involving these gates probabilistic when attempting to advance quantum processes within the quantum circuit model. Such an approach leads to significant information loss whenever measurements yield the undesired fermion parity. To resolve the problem of wasting information, we devise topological operations that allow for the non-dissipative correction of information from undesired fermion parity to the desired one. We will use the sparse-dense mixed encoding process for the controlled-NOT gate as an example to explain how corrections can be implemented without affecting the quantum information carried by the computational qubits. This correction process can be applied {to} either the undesired input qubits or the fermion parity-dependent quantum gates, and it works for both Majorana-zero-mode-based and Majorana-edge-mode-based topological quantum computation.
9 pages, 5 figures, accepted by PRA
References in corpus (69)
- Topological Insulators
- Topological insulators and superconductors
- Quantum Spin Hall Effect in Graphene
- Fault-tolerant quantum computation by anyons
- Non-Abelian Anyons and Topological Quantum Computation
- Topological Order and the Quantum Spin Hall Effect
- Anyons in an exactly solved model and beyond
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- Unpaired Majorana fermions in quantum wires
- Topological Insulators in Three Dimensions
- Elementary gates for quantum computation
- Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
- Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
- Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
- Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
- Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
- Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
- A generic new platform for topological quantum computation using semiconductor heterostructures
- Non-abelian statistics of half-quantum vortices in p-wave superconductors
- Measurement-based quantum computation with cluster states
- Non-Abelian statistics and topological quantum information processing in 1D wire networks
- Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
- Majorana Zero Modes and Topological Quantum Computation
- Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
- An Electronic Mach-Zehnder Interferometer
- Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
- Observation of Majorana fermions with spin selective Andreev reflection in the vortex of topological superconductor
- Majorana mode in vortex core of Bi2Te3/NbSe2 topological insulator-superconductor heterostructure
- Chiral Topological Superconductor From the Quantum Hall State
- Quasihole States Realize -Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
- Flux-controlled quantum computation with Majorana fermions
- Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
- Topological Quantum Computation Based on Chiral Majorana Fermions
- Measurement-Only Topological Quantum Computation
- Continuous quantum measurement of a double dot
- Multiple topological states in iron-based superconductors
- Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State
- Direct measurement of the coherence length of edge states in the Integer Quantum Hall Regime
- Controlling non-Abelian statistics of Majorana fermions on Majorana dimer lattices
- Observation of half-integer level shift of vortex bound states in an iron-based superconductor
- Charge detection enables free-electron quantum computation
- Signature of Dispersing 1D Majorana Channels in an Iron-based Superconductor
- Non-Majorana Origin of the Half-Quantized Conductance Plateau in Quantum Anomalous Hall Insulator and Superconductor Hybrid Structures
- Soft Superconducting Gap in Semiconductor Majorana Nanowires
- Introduction to topological quantum computation with non-Abelian anyons
- A new Majorana platform in an Fe-As bilayer superconductor
- Atomic line defects and zero-energy end states in monolayer Fe(Te,Se) high-temperature superconductors
- Hunting for Majoranas
- Edge Channel Interference Controlled by Landau Level Filling
- Unexpected finite-bias visibility dependence in an electronic Mach Zehnder interferometer
- Quantized conductance of Majorana zero mode in the vortex of the topological superconductor (Li0.84Fe0.16)OHFeSe
- Non-Abelian Majorana Doublets in Time-Reversal Invariant Topological Superconductor
- A mechanism of conductance plateau without 1D chiral Majorana fermions
- Parity independence of the zero-bias conductance peak in a nanowire based topological superconductor-quantum dot hybrid device
- Theory of Majorana zero modes in unconventional superconductors
- Parity meter for charge qubits: an efficient quantum entangler
- Tuning decoherence with a voltage probe
- Topologically protected quantum gates for computation with non-Abelian anyons in the Pfaffian quantum Hall state
- Controlled-NOT for multiparticle qubits and topological quantum computation based on parity measurements
- Universal fault-tolerant measurement-based quantum computation
- Fibonacci Topological Superconductor
- Dzyaloshinskii-Moriya Interaction and Spiral Order in Spin-orbit Coupled Optical Lattices
- Majorana spintronics
- Parity detection and entanglement with a Mach-Zehnder interferometer
- Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation
- Universal topological quantum computation with strongly correlated Majorana edge modes
- Quantum Computation by Spin Parity Measurements with Encoded Spin Qubits
- Deterministic topological quantum gates for Majorana qubits without ancillary modes
- Intrinsic chiral topological superconductor thin films