Related papers: Lower Bounds on Pauli Manipulation Detection Codes
A Bounded-Degree Low-Rank Parity-Check (BD-LRPC) code is a rank-metric code that admits a parity-check matrix whose support is generated by a set of powers of an element. This specific structure of the parity-check matrix was employed to…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
Surface codes are the most promising candidates for fault-tolerant quantum computation. Single qudit errors are typically modelled as Pauli operators, to which general errors are converted via randomizing methods. In this Letter, we…
Complex orthogonal designs (CODs) are used to construct space-time block codes. COD $\mathcal{O}_z$ with parameter $[p, n, k]$ is a $p \times n$ matrix, where nonzero entries are filled by $\pm z_i$ or $\pm z^*_i$, $i = 1, 2,..., k$, such…
Just as the Hamming weight spectrum of a linear block code sheds light on the performance of a maximum likelihood decoder, the pseudo-weight spectrum provides insight into the performance of a linear programming decoder. Using properties of…
We introduce the notion of fault-tolerant quantum metrology to overcome noise beyond our control -- associated with sensing the parameter, by reducing the noise in operations under our control -- associated with preparing and measuring…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…
Remarkable experimental advances in quantum computing are exemplified by recent announcements of impressive average gate fidelities exceeding 99.9% for single-qubit gates and 99% for two-qubit gates. Although these high numbers engender…
Suppose that $P$ is a property that may be satisfied by a random code $C \subset \Sigma^n$. For example, for some $p \in (0,1)$, ${P}$ might be the property that there exist three elements of $C$ that lie in some Hamming ball of radius…
Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not…
One often encounters the curse of dimensionality in the application of dynamic programming to determine optimal policies for controlled Markov chains. In this paper, we provide a method to construct sub-optimal policies along with a bound…
The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or non-identical quantum noise. In this work, we…
The error threshold for fault tolerant quantum computation with concatenated encoding of qubits is penalized by internal communication overhead. Many quantum computation proposals rely on nearest-neighbour communication, which requires…
Let $C$ be a linear code of length $n$ and dimension $k$ over the finite field $\mathbb{F}_{q^m}$. The trace code $\mathrm{Tr}(C)$ is a linear code of the same length $n$ over the subfield $\mathbb{F}_q$. The obvious upper bound for the…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli…
We obtain a query lower bound for quantum algorithms solving the phase estimation problem. Our analysis generalizes existing lower bound approaches to the case where the oracle Q is given by controlled powers Q^p of Q, as it is for example…
The intrinsic probabilistic nature of quantum systems makes error correction or mitigation indispensable for quantum computation. While current error-correcting strategies focus on correcting errors in quantum states or quantum gates, these…
The performance of low-density parity-check (LDPC) codes at high signal-to-noise ratios (SNRs) is known to be limited by the presence of certain sub-graphs that exist in the Tanner graph representation of the code, for example trapping sets…
Quantum code surgery offers a flexible, low-overhead framework for executing logical measurements within quantum error-correcting codes. It encompasses several fault-tolerant logical computation schemes, including parallel surgery,…