相关论文: No quantum Ramsey theorem for stabilizer codes
Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the…
The calculating of the coherent information is a fundamental step in obtaining the quantum capacity of a quantum channel. We introduce orthogonal and complete code basis to evaluate the coherent information per channel use when the input is…
This paper is motivated by the computer-generated nonadditive ((5,6,2)) code described in an article by Rains, Hardin, Shor and Sloane. We describe a theory of non-stabilizer codes of which the nonadditive code of Rains et al is an example.…
We present a simple protocol for certifying graph states in quantum networks using stabiliser measurements. The certification statements can easily be applied to different protocols using graph states. We see for example how it can be used…
There is a connection between classical codes, highly entangled pure states (called k-uniform or absolutely maximally entangled (AME) states), and quantum error correcting codes (QECCs). This leads to a systematic method to construct…
We provide a generalization of quantum polar codes to quantum channels with qudit-input, achieving the symmetric coherent information of the channel. Our scheme relies on a channel combining and splitting construction, where a two-qudit…
In this paper, we study the problem of learning an unknown quantum circuit of a certain structure. If the unknown target is an $n$-qubit Clifford circuit, we devise an efficient algorithm to reconstruct its circuit representation by using…
The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational…
Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing. We present a no-go theorem that places very strong limitations on the potential of such schemes for…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the quantum space $M_2$. Secondly, we apply the theory of…
We generalize the polynomial-time outcome-complete simulation algorithm for stabilizer circuits in arXiv:2309.08676 to track global phases exactly, yielding what we call phased outcome-complete simulation. The original algorithm enabled…
Verification of NISQ era quantum devices demands fast classical simulation of large noisy quantum circuits. We present an algorithm based on the stabilizer formalism that can efficiently simulate noisy stabilizer circuits. Additionally, the…
Gottesman-Knill theorem states that computations on stabilizer circuits can be simulated on a classical computer, conventional simulation algorithms extensively use linear algebra over bit strings. For instance, given a non-adaptive…
We find a scaling reduction in the stabilizer rank of the twelve-qubit tensored $T$ gate magic state. This lowers its asymptotic bound to $2^{\sim 0.463 t}$ for multi-Pauli measurements on $t$ magic states, improving over the best…
We investigate the problem of predicting the output behavior of unknown quantum channels. Given query access to an $n$-qubit channel $E$ and an observable $O$, we aim to learn the mapping \begin{equation*} \rho \mapsto \mathrm{Tr}(O…
Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…
Noise forms a central obstacle to effective quantum information processing. Recent experimental advances have enabled the tailoring of noise properties through Pauli twirling, transforming arbitrary noise channels into Pauli channels. This…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…
The stabilizer ZX-calculus is a rigorous graphical language for reasoning about quantum mechanics.The language is sound and complete: a stabilizer ZX-diagram can be transformed into another one if and only if these two diagrams represent…