Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInduced Weights on Quotient Modules and an Application to Error Correction in Coherent Networks
76
0
0.0
(
0
)
Authors
Eimear Byrne
Ask ChatGPT about the research
No Arabic abstract
We consider distance functions on a quotient module $M/K$ induced by distance functions on a module $M$. We define error-correction for codes in $M/K$ with respect to induced distance functions. For the case that the metric is induced by a homogeneous weight, we derive analogues of the Plotkin and Elias-Bassalygo bounds and give their asymptot
rate research
Read More
We study the performance of quantum error correction codes(QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the most promising surface code, we find that the detection-induced coherent error will result in undetected error terms, which will accumulate and evolve into logical errors. However, we show that this kind of errors will be alleviated by increasing the code size, akin to eliminating other types of errors discussed previously. We also find that with detection-induced coherent errors, the exact surface code becomes an approximate QECC.
Let m and n be any integers with n>m>=2. Using just the entropy function it is possible to define a partial order on S_mn (the symmetric group on mn letters) modulo a subgroup isomorphic to S_m x S_n. We explore this partial order in the case m=2, n=3, where thanks to the outer automorphism the quotient space is actually isomorphic to a parabolic quotient of S_6. Furthermore we show that in this case it has a fairly simple algebraic description in terms of elements of the group ring.
We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault tolerant quantum error correcting circuit for a $d=3$ Steane and surface code. We find that the output distributions are markedly different for the two error models, showing that no simple mapping between the two error models exists. Coherent errors create very broad and heavy-tailed failure distributions. This suggests that they are susceptible to outlier events and that mean statistics, such as pseudo-threshold estimates, may not provide the key figure of merit. This provides further statistical insight into why coherent errors can be so harmful for quantum error correction. These output probability distributions may also provide a useful metric that can be utilized when optimizing quantum error correcting codes and decoding procedures for purely coherent errors.
Quantum-enhanced measurements hold the promise to improve high-precision sensing ranging from the definition of time standards to the determination of fundamental constants of nature. However, quantum sensors lose their sensitivity in the presence of noise. To protect them, the use of quantum error correcting codes has been proposed. Trapped ions are an excellent technological platform for both quantum sensing and quantum error correction. Here we present a quantum error correction scheme that harnesses dissipation to stabilize a trapped-ion qubit. In our approach, always-on couplings to an engineered environment protect the qubit against spin- or phase flips. Our dissipative error correction scheme operates in a fully autonomous manner without the need to perform measurements or feedback operations. We show that the resulting enhanced coherence time translates into a significantly enhanced precision for quantum measurements. Our work constitutes a stepping stone towards the paradigm of self-correcting quantum information processing.
A sort of planar tensor networks with tensor constraints is investigated as a model for holography. We study the greedy algorithm generated by tensor constraints and propose the notion of critical protection (CP) against the action of greedy algorithm. For given tensor constraints, a CP tensor chain can be defined. We further find that the ability of quantum error correction (QEC), the non-flatness of entanglement spectrum (ES) and the correlation function can be quantitatively evaluated by the geometric structure of CP tensor chain. Four classes of tensor networks with different properties of entanglement is discussed. Thanks to tensor constraints and CP, the correlation function is reduced into a bracket of Matrix Production State and the result agrees with the one in conformal field theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
