编码-解码量子电路中的错误韧性相变

Simple scheme for encoding and decoding a qubit in unknown state for various topological codes

We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and Haah 3D code. The protocol is local whenever in a given code the crossings between the logical operators consist of next neighbour pairs, which holds for the above codes. For subsystem code we also present scheme in a noisy case, where we allow for bit and phase-flip errors on qubits as well as state preparation and syndrome measurement errors. Similar scheme can be built for t…

通过读出后解码对基于奇偶编码的退火进行纠错

Error correction of parity-encoding-based annealing through post-readout decoding

本研究针对奇偶编码量子退火中冗余自旋导致的效率与成本问题，提出在读出后加入经典解码纠错，并通过Monte Carlo模拟验证其可恢复逻辑信息、提升方案可行性。

Blind encoding into qudits

We consider the problem of encoding classical information into unknown qudit states belonging to any basis, of a maximal set of mutually unbiased bases, by one party and then decoding by another party who has perfect knowledge of the basis. Working with qudits of prime dimensions, we point out a no-go theorem that forbids shift operations on arbitrary unknown states. We then provide the necessary conditions for reliable encoding/decoding.

Recursive Encoding and Decoding of Noiseless Subsystem and Decoherence Free Subspace

When the environmental disturbace to a quantum system has a wavelength much larger than the system size, all qubits localized within a small area are under action of the same error operators. Noiseless subsystem and decoherence free subspace are known to correct such collective errors. We construct simple quantum circuits, which implement these collective error correction codes, for a small number $n$ of physical qubits. A single logical qubit is encoded with $n=3$ and $n=4$, while two logical qubits are encoded with $n=5$. The recursive relations among the subspaces employed in noiseless subs…

编码-解码量子电路中的蝴蝶效应

A Butterfly Effect in Encoding-Decoding Quantum Circuits

本文研究了含噪编码-解码量子电路中的信息置乱，利用$\mathcal{A}$-OTOC推导出解析表达式，发现热力学极限下微小噪声会引发宏观信息置乱的蝴蝶效应，且该效应可能广泛存在。

编码解码电路中魔术相变的理论

Theory of Magic Phase Transitions in Encoding-Decoding Circuits

本研究揭示了编码解码电路中魔术相变的本质，表明其是误差抗性阈值的直接表现，而非独立临界现象。

How to Counteract Systematic Errors in Quantum State Transfer

In the absence of errors, the dynamics of a spin chain, with a suitably engineered local Hamiltonian, allow the perfect, coherent transfer of a quantum state over large distances. Here, we propose encoding and decoding procedures to recover perfectly from low rates of systematic errors. The encoding and decoding regions, located at opposite ends of the chain, are small compared to the length of the chain, growing linearly with the size of the error. We also describe how these errors can be identified, again by only acting on the encoding and decoding regions.

A Scheme of Concatenated Quantum Code to Protect against both Computational Error and an Erasure

We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding for quantum graph codes are done, which will provide the protection against the occurrence of computational errors (external code). As internal code is used encoding and decoding via scheme of GHZ states for protection against the occurrence of one quantum erasure.

Distributing entanglement with separable states: assessment of encoding and decoding imperfections

Entanglement can be distributed using a carrier which is always separable from the rest of the systems involved. Up to now, this effect has predominantly been analyzed in the case where the carrier-system interactions take the form of ideal unitary operations, thus leaving untested its robustness against either non-unitary or unitary errors. We address this issue by considering the effect of incoherent dynamics acting alongside imperfect unitary interactions. In particular, we determine the restrictions that need to be placed on the interaction time, as well as the strength of the incoherent d…

New encoding schemes for quantum authentication

We study the potential of general quantum operations, Trace-Preserving Completely-Positive Maps (TPCPs), as encoding and decoding mechanisms in quantum authentication protocols. The study shows that these general operations do not offer significant advantage over unitary encodings. We also propose a practical authentication protocol based on the use of two successive unitary encodings.

Optimal Circuit-Level Decoding for Surface Codes

Surface codes exploit topological protection to increase error resilience in quantum computing devices and can in principle be implemented in existing hardware. They are one of the most promising candidates for active error correction, not least due to a polynomial-time decoding algorithm which admits one of the highest predicted error thresholds. We consider the dependence of this threshold on underlying assumptions including different noise models, and analyze the performance of a minimum weight perfect matching (MWPM) decoding compared to a mathematically optimal maximum likelihood (ML) dec…

Quantum error correcting codes and one-way quantum computing: Towards a quantum memory

For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation can be performed faster than the typical decoherence time of the underlying system. The computational model underlying the one-way quantum computer, which has been introduced by Hans Briegel and Robert Raussendorf, provides a suitable concept for a fast implementation of quantum error correcting codes. It is shown explicitly in this article is how encoding a…

Resilience of hybrid optical angular momentum qubits to turbulence

Recent schemes to encode quantum information into the total angular momentum of light, defining rotation-invariant hybrid qubits composed of the polarization and orbital angular momentum degrees of freedom, present interesting applications for quantum information technology. However, there remains the question as to how detrimental effects such as random spatial perturbations affect these encodings. Here, we demon- strate that alignment-free quantum communication through a turbulent channel based on hybrid qubits can be achieved with unit transmission fidelity. In our experiment, alignment-fre…

高性能线性速率LDPC量子码的单次解码

Single-Shot Decoding of Linear Rate LDPC Quantum Codes with High Performance

本文基于四维双曲流形镶嵌构造了一类线性速率LDPC量子码，通过Coxeter群表示和拓扑覆盖实现构造，证明编码速率下界为13/72，并展示了低复杂度并行解码方案在含综合征噪声的单次解码中达到约4%阈值。