Related papers: No ((n, k, d < 127)) code can violate the quantum …
Intersecting codes are a classical object in coding theory whose rank-metric analogue has recently been introduced. Although the definition formally parallels the Hamming-metric case, the structure and parameter constraints of rank-metric…
We demonstrate that a high fidelity approximation to $| \Psi_b \rangle$, the quantum superposition over all bit strings within Hamming distance $b$ of the codewords of a dimension-$k$ linear code over $\mathbb{Z}_2^n$, can be efficiently…
A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system.…
In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes"). By definition, a quasi code is a parametric approximate…
In this paper, we place bounds on when it is impossible to purify a noisy two-qubit state if all the gates used in the purification protocol are subject to adversarial local, independent, noise. It is found that the gate operations must be…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
Quantum theory imposes fundamental limitations to the amount of information that can be carried by any quantum system. On the one hand, Holevo bound rules out the possibility to encode more information in a quantum system than in its…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
Many physical systems considered promising qubit candidates are not, in fact, two-level systems. Such systems can leak out of the preferred computational states, leading to errors on any qubits that interact with leaked qubits. Without…
In certain approaches to quantum computing the operations between qubits are non-deterministic and likely to fail. For example, a distributed quantum processor would achieve scalability by networking together many small components;…
Many current quantum error-correcting codes that achieve full fault tolerance suffer from having low ratios of logical to physical qubits and significant overhead. This makes them difficult to implement on current noisy intermediate-scale…
Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while…
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
It is important to protect quantum information against decoherence and operational errors, and quantum error-correcting (QEC) codes are the keys to solving this problem. Of course, just the existence of codes is not efficient. It is…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
We study the quantum security of key-alternating ciphers (KAC), a natural multi-round generalization of the Even--Mansour construction. KAC abstracts the round structure of practical block ciphers as public permutations interleaved with key…
Recent advancements in quantum computing have enabled practical use of quantum error detecting and correcting codes. However, current architectures and future proposals of quantum computer design suffer from limited qubit counts,…
There is an advantage in simultaneously transmitting both classical and quantum information over a quantum channel compared to sending independent transmissions. The successful implementation of simultaneous transmissions of quantum and…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
I consider the theory of quantum error correcting code (QECC) where each quantum particle has more than two possible eigenstates. In this higher spin system, I report an explicit QECC that is related to the symmetry group ${\Bbb…