Related papers: Finding Quantum Codes via Riemannian Optimization
We present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds…
In this paper, we address the problem of designing a quantum encoder that maximizes the minimum output purity of a given decohering channel, where the minimum is taken over all possible pure inputs. This problem is cast as a max-min…
We derive necessary and sufficient conditions for the approximate correctability of a quantum code, generalizing the Knill-Laflamme conditions for exact error correction. Our measure of success of the recovery operation is the worst-case…
Quantum error correction (QEC) is essential for reliable quantum information processing. Targeting a particular error channel, both the encoding and the recovery channel can be optimized through a biconvex optimization to give a…
Determining the ultimate limits of quantum communication, such as the quantum capacity of a channel and the distillable entanglement of a shared state, remains a central challenge in quantum information theory, primarily due to the…
Quantum computation promises to advance a wide range of computational tasks. However, current quantum hardware suffers from noise and is too small for error correction. Thus, accurately utilizing noisy quantum computers strongly relies on…
We present a simple and fast numerical procedure to search for good quantum codes for storing logical qubits in the presence of independent per-qubit noise. In a key departure from past work, we use the worst-case fidelity as the figure of…
The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum…
The Knill-Laflamme (KL) conditions distinguish exact quantum error correction codes, and it has played a critical role in the discovery of state-of-the-art codes. However, the family of exact codes is a very restrictive one and does not…
This paper investigates quantum error correction schemes for fully-correlated noise channels on an $n$-qubit system, where error operators take the form $W^{\otimes n}$, with $W$ being an arbitrary $2\times 2$ unitary operator. In previous…
Repetition code forms a fundamental basis for quantum error correction experiments. To date, it stands as the sole code that has achieved large distances and extremely low error rates. Its applications span the spectrum of evaluating…
Noise poses a challenge for any real-world implementation in quantum information science. The theory of quantum error correction deals with this problem via methods to encode and recover quantum information in a way that is resilient…
Quantum error correction (QEC) is an essential concept for any quantum information processing device. Typically, QEC is designed with minimal assumptions about the noise process; this generic assumption exacts a high cost in efficiency and…
Quantum error correction codes are usually designed to correct errors regardless of their physical origins. In large-scale devices, this is an essential feature. In smaller-scale devices, however, the main error sources are often…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
We present a protocol using machine learning (ML) to simultaneously optimize the quantum error-correcting code space and the corresponding recovery map in the framework of continuous-time quantum error correction. Given a Hilbert space and…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
Recent work on approximate quantum error correction (QEC) has opened up the possibility of constructing subspace codes that protect information with high fidelity in scenarios where perfect error correction is impossible. Motivated by this,…