- #Qudit quantum error correction transversal t gate pdf
- #Qudit quantum error correction transversal t gate code
Single-error-correcting codes of the same lengths. The specific application of these codes to universal quantum computation based on qubit fusion is also discussed. This construction is presented generally for qudits of any dimension.
#Qudit quantum error correction transversal t gate code
They prove that there can't be a gate set that works on a non trivial quantum code space C that is also universal and the gates are transversal. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. Error code blocks (Cp ) that support a transversal T (/8) gate (or corrections. OurĬodes have larger code dimensions than the previously known In the article they talk about the importance of transversal encoded gates for fault tolerant quantum computing. All circuits for both computation and error correction are transversal. Single-error-correcting quantum codes that can be used for both cases. the gate called T in this thesis is transversal for the 5,1,3 code. Of decay process, and for bosonic systems,we consider the qudit amplitudeĭamping channel obtained by truncating the Fock basis of the bosonic modes to aĬertain maximum occupation number. Quantum computing promises to leverage aspects of quantum mechanics to solve. For multi-level atoms, we consider a natural kind Quantum error-correcting codes adapted to amplitude damping channels for higherĭimensional systems (qudits). For example, an X gate implemented in a spin resonance system requires perfect timing. As a result, perfect accuracy is required for correct operation. These are unitary transformations operating on a continuous parameter space, unlike classical digital computers.
#Qudit quantum error correction transversal t gate pdf
(c) Four virtual layers of surface codes have space to fold one qudit or two qubits (left), use a resource state for code conversion (center), or store two qudits or four qubits (right).Authors: Markus Grassl, Linghang Kong, Zhaohui Wei, Zhang-Qi Yin, Bei Zeng Download PDF Abstract: Traditional quantum error-correcting codes are designed for the depolarizingĬhannel modeled by generalized Pauli errors occurring with equal probability.Īmplitude damping channels model, in general, the decay process of a multilevelĪtom or energy dissipation of a bosonic system at zero temperature. Quantum gates, building blocks of QC, can also introduce errors. These implementations further simplify if qubits are not returned to their initial orientation. Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. We decompose C X gates into H and C Z gates (inset), and implement C Z gates with nearest-neighbor two-qubit gates that depend on the relative orientations of qubit pairs in every qudit. 1 can be implemented with nearest-neighbor two-qubit gates, but the C X gate is more complicated. We derive transversal Clifford operations for CSS codes over nice. This layout of data and ancilla qubits in 2 × 2 clusters also can be operated as four stacked qubit surface codes. Transversal operations are the simplest way to implement fault-tolerant quantum gates. (a) A stacked pair of four-dimensional qudit surface codes on a planar qudit lattice (left) can be implemented on a planar qubit lattice (right) by embedding each qudit in a pair of physical qubits. Universal quantum computation on a planar qubit lattice. We achieve and improve this result by constructing two families of folded surface codes with transversal Clifford gates. This construct, like any logical T-gate circuit using no functional ancillas, is not fault tolerant nor even pieceably fault tolerant. However, the equivalence does imply the existence of constant-depth circuit implementations of logical Clifford gates on folded surface codes. A logical Z exp (i Z / 2) gate for the 5-qubit code. A formal equivalence exists between color codes and folded surface codes, but it does not guarantee the transferability of any of these favorable properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and correct errors, while color codes have transversal Clifford gates and better code efficiency in the number of physical qubits needed to achieve a given code distance. Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties.
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