Related papers: Constructions and Noise Threshold of Hyperbolic Su…
The complete quantum theory of closed superstrings is constructed using string diagrams endowed with metric having constant curvature $-1$. The elementary string diagrams are equipped with the analytic local coordinates induced from the…
Topological error correction codes are promising candidates to protect quantum computations from the deteriorating effects of noise. While some codes provide high noise thresholds suitable for robust quantum memories, others allow…
We consider a notion of relative homology (and cohomology) for surfaces with two types of boundaries. Using this tool, we study a generalization of Kitaev's code based on surfaces with mixed boundaries. This construction includes both…
The surface code is a prominent topological error-correcting code exhibiting high fault-tolerance accuracy thresholds. Conventional schemes for error correction with the surface code place qubits on a planar grid and assume native CNOT…
We demonstrate that the performance of quantum error correction can be improved with noise-aware decoders that are calibrated to the likelihood of physical error configurations in a device. We show that noise-aware decoding increases the…
Using algebraic geometry codes we give a polynomial construction of quantum codes with asymptotically non-zero rate and relative distance.
The code-capacity threshold of a scalable quantum error correcting stabilizer code can be expressed as a thermodynamic phase transition of a corresponding random-bond Ising model. Here we study the XY and XZZX surface codes under…
Surface codes$\unicode{x2014}$leading candidates for quantum error correction (QEC)$\unicode{x2014}$and entanglement phases$\unicode{x2014}$a key notion for many-body quantum dynamics$\unicode{x2014}$have heretofore been unrelated. Here, we…
We present a fault-tolerant universal quantum computing architecture based on a code concatenation of biased-noise qubits and the parity architecture. The parity architecture can be understood as an LDPC code tailored specifically to obtain…
Information obtained from noise characterization of a quantum device can be used in classical decoding algorithms to improve the performance of quantum error-correcting codes. Focusing on the surface code under local (i.e. single-qubit)…
In this work we introduce two code families, which we call the heavy hexagon code and heavy square code. Both code families are implemented by assigning physical data and ancilla qubits to both vertices and edges of low degree graphs. Such…
Qubit shuttling promises to advance some quantum computing platforms to the qubit register sizes needed for effective quantum error correction (QEC), but also introduces additional errors whose impact must be evaluated. The established…
It is well known that quantum codes can be constructed by means of classical symplectic dual-containing codes. This paper considers a family of two-generator quasi-cyclic codes and derives sufficient conditions for these codes to be…
We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts…
We define several quantitative measures of the robustness of a quantum gate against noise. Exact analytic expressions for the robustness against depolarizing noise are obtained for all unitary quantum gates, and it is found that the…
As quantum circuits become more integrated and complex, additional error sources that were previously insignificant start to emerge. Consequently, the fidelity of quantum gates benchmarked under pristine conditions falls short of predicting…
Color codes present distinct advantages for fault-tolerant quantum computing, such as high encoding rates and the transversal implementation of Clifford gates. However, existing matching-based decoders for the color codes such as the…
Current approaches for building quantum computing devices focus on two-level quantum systems which nicely mimic the concept of a classical bit, albeit enhanced with additional quantum properties. However, rather than artificially limiting…
Topological quantum codes are favored because they allow qubit layouts that are suitable for practical implementation. An $N$-qubit topological code can be decoded by minimum-weight perfect matching (MWPM) with complexity…
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…