Related papers: Comparison of 2D topological codes and their decod…
We generalize a construction of non-binary quantum LDPC codes over $\F_{2^m}$ due to \cite{KHIS11a} and apply it in particular to toric codes. We obtain in this way not only codes with better rates than toric codes but also improve…
Quantum error correction (QEC) is crucial for realizing scalable quantum technologies, and topological quantum error correction (TQEC) has emerged as the most experimentally advanced paradigm of QEC. Existing homological and topological…
In this paper, we propose how to simply construct a pair of linear codes for the BB84 quantum key distribution protocol. This protocol allows unconditional security in the presence of an eavesdropper, and the pair of linear codes is used…
Mapping a quantum algorithm to any practical large-scale quantum computer will require a sequence of compilations and optimizations. At the level of fault-tolerant encoding, one likely requirement of this process is the translation into a…
Topological error-correcting codes, such as surface codes and color codes, are promising because quantum operations are realized by two-dimensionally (2D) arrayed quantum bits (qubits). However, physical wiring of electrodes to qubits is…
Despite the evident necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings of topological quantum logic gates had arguably remained shaky, both regarding their physical realization as well…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
A recently developed theory for eliminating decoherence and design constraints in quantum computers, ``encoded recoupling and decoupling'', is shown to be fully compatible with a promising proposal for an architecture enabling scalable…
We present a topological approach to lifting a quantum CSS code. In previous work, we proposed lifting a CSS code by constructing covering spaces over its 2D simplicial complex representation, known as the Tanner cone-complex. This idea was…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…
In this paper, we propose an efficient decoding algorithm for short low-density parity check (LDPC) codes by carefully combining the belief propagation (BP) decoding and order statistic decoding (OSD) algorithms. Specifically, a modified BP…
Quantum low-density parity-check codes are promising candidates for quantum error correcting codes as they might offer more resource-efficient alternatives to surface code architectures. In particular, bivariate bicycle codes have recently…
The minimum weight matching (MWM) and maximum likelihood decoding (MLD) are two widely used and distinct decoding strategies for quantum error correction. For a given syndrome, the MWM decoder finds the most probable physical error…
We find that the overlapping of a topological quantum color code state, representing a quantum memory, with a factorized state of qubits can be written as the partition function of a 3-body classical Ising model on triangular or Union Jack…
For finite coupling lengths, terminated spatially coupled low-density parity-check (SC-LDPC) codes show a non-negligible rate-loss. In this paper, we investigate if this rate loss can be mitigated by tail-biting SC-LDPC codes in conjunction…
Product constructions constitute a powerful method for generating quantum CSS codes, yielding celebrated examples such as toric codes and asymptotically good low-density parity check (LDPC) codes. Since a CSS code is fully described by a…
In our recent paper entitled "Quantum Quasi-Cyclic Low-Density Parity-Check codes" [ICIC 2009. LNCS 5754], it was claimed that some new quantum codes can be constructed via the CSS encoding/decoding approach with various lengths and rates.…
Quantum based systems are a relatively new research area for that different modelling languages including process calculi are currently under development. Encodings are often used to compare process calculi. Quality criteria are used then…
We construct toric codes on various high-dimensional manifolds. Assuming a conjecture in geometry we find families of quantum CSS stabilizer codes on $N$ qubits with logarithmic weight stabilizers and distance $N^{1-\epsilon}$ for any…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…