# Error Thresholds for Arbitrary Pauli Noise

@article{Bausch2019ErrorTF, title={Error Thresholds for Arbitrary Pauli Noise}, author={Johannes Bausch and Felix Leditzky}, journal={ArXiv}, year={2019}, volume={abs/1910.00471} }

The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive. This in turn guarantees the existence of a quantum error correction code for noise modeled by that channel. Discretizing the single-qubit errors leads to the important family of Pauli quantum channels; curiously, multipartite entangled states can increase the threshold of these channels beyond the so-called hashing bound, anβ¦Β

## 15 Citations

### The XZZX surface code

- Computer Science, PhysicsNature Communications
- 2021

Focusing on the common situation where qubit dephasing is the dominant noise, this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable.

### Exploring super-additivity of coherent information of noisy quantum channels through Genetic algorithms

- Computer Science, Physics
- 2022

This work utilizes a neural network ansatz to represent quantum states and then applies an evolutionary optimization scheme to address the problem, suggesting that the Neural Network ansatz coupled with the evolutionary scheme is indeed a promising approach to non-trivial quantum codes of high coherent information.

### Exploring superadditivity of coherent information of noisy quantum channels through genetic algorithms

- Computer SciencePhysical Review A
- 2022

This work utilizes a neural network ansatz to represent quantum states and then applies an evolutionary optimization scheme to address the problem, suggesting that the Neural Network ansatz coupled with the evolutionary scheme is indeed a promising approach to non-trivial quantum codes of high coherent information.

### Entropic singularities give rise to quantum transmission

- PhysicsNature Communications
- 2021

This work shows non-additivity in a simple low-noise channel and proves a general theorem concerning positivity of a channelβs coherent information, and shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information.

### The platypus of the quantum channel zoo

- Computer Science2022 IEEE International Symposium on Information Theory (ISIT)
- 2022

A remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features is studied; the simplest example from this family, a qutrit-to-qutrit channel intuitively obtained by hybridizing together a simple degradable channel with a completely useless qubit channel is studied.

### Bounding the quantum capacity with flagged extensions

- MathematicsQuantum
- 2022

In this article we consider flagged extensions of convex combination of quantum channels, and find general sufficient conditions for the degradability of the flagged extension. An immediateβ¦

### Bounding Quantum Capacities via Partial Orders and Complementarity

- Computer ScienceIEEE Transactions on Information Theory
- 2023

Bounds on quantum capacities give operational limitations on superadditivity and the difference between capacities in terms of the information-theoretic properties of the complementary channel or state, and can be used as a new approach towards numerically bounding capacities.

### Noise Improvements in Quantum Simulations of sQED using Qutrits

- Physics
- 2022

We present an argument for the advantages of using qudits over qubits for scalar Quantum Electrodynamics in (1 + 1)d. We measure the mass gap using an out of time correlator as a function of noiseβ¦

### Leaking information to gain entanglement.

- Physics
- 2020

Entanglement lies at the root of quantum theory. It is a remarkable resource that is generally believed to diminish when entangled systems interact with their environment. On the contrary, we findβ¦

### Bounding quantum capacities via partial orders and complementarity

- Computer Science2022 IEEE International Symposium on Information Theory (ISIT)
- 2022

Borders on quantum capacities are given, including the quantum capacity and private capacity of a channel and the one-way distillable entanglement and private key of a bipartite state, to help to further understand the interplay between different capacities and give operational limitations on superadditivity properties.

## References

SHOWING 1-10 OF 69 REFERENCES

### QUANTUM-CHANNEL CAPACITY OF VERY NOISY CHANNELS

- Computer Science
- 1998

A family of additive quantum error-correcting codes whose capacities exceed those of quantum random coding (hashing) for very noisy channels are presented and a general relation between the capacity attainable by these concatenation schemes and the coherent information of the inner code states is derived.

### Graph-state basis for Pauli channels

- Computer Science
- 2011

Using graph state basis, it is shown that for a graph diagonal state passing through a Pauli channel the output state is diagonalizable and the joint output state of the system and ancilla is block diagonalizable.

### Quantum computations on a topologically encoded qubit

- Physics, Computer ScienceScience
- 2014

A quantum error-correcting code in which one qubit is encoded in entangled states distributed over seven trapped-ion qubits, which represents a fully functional instance of a topologically encoded qubit, or color code, and opens a route toward fault-tolerant quantum computing.

### Degenerate quantum codes for Pauli channels.

- Computer SciencePhysical review letters
- 2007

A heuristic for designing degenerate quantum codes for high noise rates is provided, which is applied to generate codes that can be used to communicate over almost any Pauli channel at rates that are impossible for a nondegenerate code.

### Ultrahigh Error Threshold for Surface Codes with Biased Noise.

- Computer SciencePhysical review letters
- 2018

It is shown that a simple modification of the surface code can exhibit an enormous gain in the error correction threshold for a noise model in which Pauli Z errors occur more frequently than X or Y errors, and that large efficiency gains can be found by appropriately tailoring codes and decoders to realistic noise models, even under the locality constraints of topological codes.

### Dephrasure Channel and Superadditivity of Coherent Information.

- PhysicsPhysical review letters
- 2018

The dephrasure channel is considered, which is the concatenation of a dephasing channel and an erasure channel, which finds nonadditivity of coherent information at the two-letter level, a substantial gap between the threshold for zero quantum capacity and zero single-letter coherent information, and positive quantum capacity for all complementary channels.

### Degenerate Codes and Capacities of Quantum Channels

- Computer Science
- 2017

This thesis outlines the work completed looking into the construction of good codes for the amplitude damping channel and the difficult problem of determining if a quantum channel has capacity; the ultimate use of QECCs in a sense.

### Fault-tolerant quantum computation against biased noise

- Physics
- 2008

We formulate a scheme for fault-tolerant quantum computation that works effectively against highly biased noise, where dephasing is far stronger than all other types of noise. In our scheme, theβ¦

### Noise tailoring for scalable quantum computation via randomized compiling

- Computer Science
- 2016

This work proposes a method for introducing independent random single-qubit gates into the logical circuit in such a way that the effective logical circuit remains unchanged and proves that this randomization tailors the noise into stochastic Pauli errors, which can dramatically reduce error rates while introducing little or no experimental overhead.

### Quantum and private capacities of low-noise channels

- Physics2017 IEEE Information Theory Workshop (ITW)
- 2017

It is found that, in the low noise regime, super-additivity and degenerate codes have negligible benefit for the quantum Capacity, and shielding does not improve the private capacity beyond the quantum capacity, in stark contrast to the situation when noisier channels are considered.