11 papers · ranked by Valyu relevance
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Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction1,2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against…
J. Pablo Bonilla Ataides, David K. Tuckett, Stephen D. Bartlett, Steven T. Flammia + 1 more
'Steven T. Flammia' 'Benjamin J. Brown'] Performing large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. The challenge is to design practical quantum error-correcting codes that perform well against realistic noise using modest resources.…
Utkarsh Azad, Aleksandra Lipińska, Shilpa Mahato, Rijul Sachdeva + 2 more
'Debasmita Bhoumik' 'Ritajit Majumdar'] Surface codes are quantum error correcting codes typically defined on 2D array of qubits. In this paper, a [dx, dz] surface code design is being introduced, where dx(dz) represents the distance of the code for bit (phase) error correction, motivated by the fact that the severity…
Fang Zhang, Jianxin Chen, Giuliano Benenti
Error correction is an essential part of the theory of quantum computation. However, new quantum computation students may find the theories of error correction and fault tolerance daunting, or they may be stuck with theoretical/outdated schemes (such as the one in the original proof of the threshold theorem by Aharonov…
Craig Gidney, Michael Newman, Peter Brooks, Cody Jones
One of the biggest obstacles to building a large scale quantum computer is the high qubit cost of protecting quantum information. For two-dimensional architectures, the surface code has long been the leading candidate quantum memory, but can require upwards of a thousand physical qubits per logical qubit to reach…
Nicolas Delfosse
The family of hyperbolic surface codes is one of the rare families of quantum LDPC codes with non-zero rate and unbounded minimum distance. First, we introduce a family of hyperbolic color codes. This produces a new family of quantum LDPC codes with nonzero rate and with minimum distance logarithmic in the blocklength.…
Asmae Benhemou, Kaavya Sahay, Lingling Lao, Benjamin J. Brown
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced by the depolarising noise model. The decoder is obtained by mapping the syndrome…
Avaz Naghipour, M. A. Jafarizadeh, S. Shahmorad
This paper presents four new classes of binary quantum codes with minimum distance 3 and 4, namely Class-I, Class-II, Class-III and Class-IV. The classes Class-I and Class-II are constructed based on self-dual orientable embeddings of the complete graphs K4r+1 and K4s and by current graphs and rotation schemes. The…
J. Conrad, C. Chamberland, N. P. Breuckmann, B. M. Terhal
We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small stellated dodecahedron code can be located on the edges respectively…
Nicolas Delfosse
We propose a new strategy to decode color codes, which is based on the projection of the error onto three surface codes. This provides a method to transform every decoding algorithm of surface codes into a decoding algorithm of color codes. Applying this idea to a family of hexagonal color codes, with the perfect…
Cristiano Torezzan, Sueli I. R. Costa, Vinay A. Vaishampayan
—A new class of spherical codes is constructed by selecting a finite subset of flat tori from a foliation of the unit sphere S 2L−1 ⊂ R 2L and designing a structured codebook on each torus layer. The resulting spherical code can be the image of a lattice restricted to a specific hyperbox in R L in each layer. Group…