In this paper, we deal with quantum information decoding. Quantum codes are a known technique for correcting errors of quantum information caused by noise or operational errors and one of the most popular types of codes is the so-called stabilizer code. Various implementation methods have been proposed to encode information into a stabilizer code, but there have been few studies on decoding to extract the original information from the code words. In this paper, we propose a decoding method for stabilizer codes using dissipation dynamics and show that the original information can be extracted from the code words.
In this paper, we deal with quantum information decoding. Quantum codes are a known technique for correcting errors of quantum information caused by noise or operational errors and one of the most popular types of codes is the so-called stabilizer code. Various implementation methods have been proposed to encode information into a stabilizer code, but there have been few studies on decoding to extract the original information from the code words. In this paper, we propose a decoding method for stabilizer codes using dissipation dynamics and show that the original information can be extracted from the code words.
This paper proposes an improved quantum coding method based on Markovian dissipative dynamics that is robust against thermal noise. A method for correcting information errors is indispensable for the practical use of quantum information devices, and stabilizer codes for quantum systems have been devised. One of the quantum coding methods, namely, quantum coding based on Markovian dissipative dynamics, has a favorable feature that it does not require strict time control, however it is known that these methods are susceptible to thermal noise. In this paper, we propose a quantum coding method that incorporates a new mechanism to correct the disturbance of the quantum state caused by thermal noise into the quantum coding method using dissipative dynamics. We also analyze the stability of the proposed quantum dynamics in the quantum state corresponding to the target code word. Numerical experiments confirm the effectiveness of the proposed method.
In order to ensure reliable quantum information processing in realistic noisy devices, it is necessary to resort to suitable error correction and avoidance strategies. A key aspect of these techniques is how the relevant information is logically mapped (encoded) in the noise-protected codewords. Here, we study how to engineer Markov dynamics that transfers the desired information from an "upload" subsystem to the target error-correcting or noiseless quantum code, effectively acting as a dissipative quantum encoder. Dissipative encoders offer advantages with respect to standard unitary encoding protocols based on quantum circuits, as they can associate the target states to non-trivial basins of attraction, and thus tolerate more general initializations in the upload qubits. In particular, we show that devising continuous-time dissipative encoders requires the target code to be invariant, making this task more delicate as compared to its discrete-time counterpart. Nonetheless, we show how this is always possible for stabilizer quantum error-correcting codes.
Quantum error-correcting codes are used to protect quantum information from decoherence. A raw state is mapped, by an encoding circuit, to a codeword so that the most likely quantum errors from a noisy quantum channel can be removed after a decoding process.A good encoding circuit should have some desired features, such as low depth, few gates, and so on. In this paper, we show how to practically implement an encoding circuit of gate complexity O(n(n - k + c)/ log n) for an [[n, k; c]] quantum stabilizer code with the help of c pairs of maximally-entangled states. For the special case of an [[n, k]] stabilizer code with c = 0, the encoding complexity is O(n(n-k)/ log n), which is previously known to be O(n2/ log n). For c > 0, this suggests that the benefits from shared entanglement come at an additional cost of encoding complexity.Finally we discuss decoding of entanglement-assisted quantum stabilizer codes and extend previously known computational hardness results on decoding quantum stabilizer codes.
We present a method for implementing stabilizer-based codes with encoding schemes of the operator quantum error correction paradigm, e.g., the ``standard'' five-qubit and CSS codes, on solid-state qubits with Ising or XY-type interactions. Using pulse sequences, we show how to dynamically generate the effective dynamics of the stabilizer Hamiltonian, the sum of an appropriate set of stabilizer operators for a given code. Within this approach, the encoded states (ground states of the stabilizer Hamiltonian) can be prepared without measurements and preserved against both the time evolution governed by the original qubit Hamiltonian, and errors caused by local sources.
We study attendant properties of the following system: Error Correcting Codes In Quantum Theory, Scheme For Reducing Decoherence In Quantum Computer Memory, Correcting Quantum Computer Errors, Qubits Based On Quantum Spins, Nine-Qubit State Is A Set Of Three Groups, Repeated Quantum Error Correction On A Continuously Encoded Qubit, Active Error Correction On A Continuously Protected Logical Qubit, Correction Of Errors In Encoded Quantum States, Connection Between The Observers Will Typically Be Subject To Disturbances That Can Disrupt The Entanglement, Reconstruct The Original Qubit From The Unchanged Pair, Quantum Error Correction That Extends The Lifetime Of Quantum Information, Error Correction Under Different Types Of Noise Key words: Quantum error correction, Qubit, Noise The full paper: http://www.iiste.org/PDFshare/APTA-PAGENO-548811-555137.pdf
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 noise types, they often require substantial resources, making them impractical for near-term quantum devices. Approximate quantum error correction provides an alternative by tailoring codes to specific noise environments, reducing resource demands while still maintaining noise-robustness. Dynamical codes, including Floquet codes, introduce a dynamic approach to quantum error correction, employing time-dependent operations to stabilize logical qubits. In this work, we combine the flexibility of dynamical codes with the versatility of approximate quantum error correction to offer a promising avenue for addressing dominant noise in quantum systems. We construct several approximate dynamical codes using the recently developed strategic code framework. As a special case, we recover the approximate static codes widely studied in the existing literature. By analyzing these approximate dynamical codes through semidefinite programming, we establish the uniqueness and robustness of the optimal encoding, decoding, and check measurements. We also develop a temporal Petz recovery map suited to approximate dynamical codes.