Related papers: Lee Weight for Nonbinary Quantum Error Correction
By utilizing quantum mechanical effects, such as superposition and entanglement, quantum metrology promises higher precision than the classical strategies. It is, however, practically challenging to realize the quantum advantages. This is…
Quantum weight reduction procedures ease the implementation of quantum codes by sparsifying them, resulting in low-weight checks and low-degree qubits. However, to date, only few quantum weight reduction methods have been explored. In this…
In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. We concatenate alternant codes with any linear code achieving…
We introduce a notion of nuclear numerical range defined as the set of expectation values of a given operator $A$ among normalized pure states, which belong to the nucleus of an auxiliary operator $Z$. This notion proves to be applicable to…
I develop methods for analyzing quantum error-correcting codes, and use these methods to construct an infinite class of codes saturating the quantum Hamming bound. These codes encode $k=n-j-2$ qubits in $n=2^j$ qubits and correct $t=1$…
I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011) for…
We derive bounds on general quantum error correcting codes against the displacement noise channel. The bounds limit the distances attainable by codes and also apply in an approximate setting. Our main result is a quantum analogue of the…
The bit-wise unequal error protection problem, for the case when the number of groups of bits $\ell$ is fixed, is considered for variable length block codes with feedback. An encoding scheme based on fixed length block codes with erasures…
We provide a new approach to error mitigation for quantum chemistry simulation that uses a Bravyi-Kitaev Superfast encoding to implement a quantum error detecting code within the fermionic encoding. Our construction has low-weight parity…
We present a simple proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code (QECC) with its ability to achieve a universal set of transversal logical gates. Our derivation employs…
Solving non-Hermitian quantum many-body systems on a quantum computer by minimizing the variational energy is challenging as the energy can be complex. Here, based on energy variance, we propose a variational method for solving the…
We give a lower bound on the probability of error in quantum state discrimination. The bound is a weighted sum of the pairwise fidelities of the states to be distinguished.
We present several results on quantum codes over general alphabets (that is, in which the fundamental units may have more than 2 states). In particular, we consider codes derived from finite symplectic geometry assumed to have additional…
Error-correction process has to be carried out periodically to prevent accumulation of errors in fault-tolerant quantum computation. It is believed that the best choice to get maximum threshold value is carrying out an error-correction…
Cumulative weight enumerators of random linear codes are introduced, their asymptotic properties are studied, and very sharp thresholds are exhibited; as a consequence, it is shown that the asymptotic Gilbert-Varshamov bound is a very sharp…
To implement fault-tolerant quantum computation with continuous variables, Gottesman-Kitaev-Preskill (GKP) qubits have been recognized as an important technological element. However, the analog outcome of GKP qubits, which includes…
Efficient decoding to estimate error locations from outcomes of syndrome measurement is the prerequisite for quantum error correction. Decoding in presence of circuit-level noise including measurement errors should be considered in case of…
This article describes a {\em nonstandard} quantum group that may be used to derive a positive formula for the plethysm problem, just as the standard (Drinfeld-Jimbo) quantum group can be used to derive the positive Littlewood-Richardson…
We use affine variety codes and their subfield-subcodes for obtaining quantum stabilizer codes via the CSS code construction. With this procedure, we get codes with good parameters and a code whose parameters exceed the CSS quantum…
Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. Practical implementations of these algorithms, despite offering certain levels of robustness against systematic errors, show a decline…