Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2111.01486 · IET Quantum Communication

Surface code design for asymmetric error channels

Utkarsh Azad, Aleksandra Lipińska, Shilpa Mahato, Rijul Sachdeva, Debasmita Bhoumik, Ritajit Majumdar

Published May 25, 2022• 6 citations
arXivHTMLPDF

Abstract

Abstract Surface codes are quantum error correcting codes typically defined on a 2D array of qubits. A [ d x , d z ] surface code design is being introduced, where d x ( d z ) represents the distance of the code for bit (phase) error correction, motivated by the fact that the severity of bit flip and phase flip errors in the physical quantum system is asymmetric. We present pseudo‐threshold and threshold values for the proposed surface code design for asymmetric error channels in the presence of various degrees of asymmetry of , errors in a depolarisation channel. We demonstrate that compared to symmetric surface codes, our asymmetric surface codes can provide almost double the pseudo‐threshold rates while requiring less than half the number of physical qubits in the presence of increasing asymmetry in the error channel. Our results show that for low degree of asymmetry, it is advantageous to increase d x along with d z . However, as the asymmetry of the channel increases, higher pseudo‐threshold is obtained with increasing d z when d x is kept constant at a low value. Additionally, we also show that the advantage in the pseudo‐threshold rates begins to saturate for any possible degree of asymmetry in the error channel as the surface code asymmetry is continued to be increased.

DOI
10.1049/qtc2.12042

Related papers

Quantum Codes for Asymmetric Channels: ZZZY Surface Codes

Diego Forlivesi, Lorenzo Valentini, Marco Chiani

We introduce surface ZZZY codes, a novel family of quantum error-correcting codes designed for asymmetric channels. Derived from standard surface codes through tailored modification of generators, ZZZY codes can be decoded by the minimum weight perfect matching (MWPM) algorithm with a suitable pre-processing phase. The resulting decoder exploits the information provided by the modified generators without introducing additional complexity. ZZZY codes demonstrate a significant performance advantage over surface codes when increasing the channel asymmetry, while maintaining the same correction capability over depolarizing channel.

arXiv:2409.10162•IEEE Communications Letters•Sep 5, 2024•5 citations

Asymmetric quantum error-correcting codes

L. B. Ioffe, Marc Mézard

The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error-correcting code that takes advantage of this asymmetry and shows good performance at a relatively small cost in redundancy, requiring less than a doubling of the number of physical qubits for error correction. This code is particularly adapted for building an efficient quantum memory.

arXiv:quant-ph/0606107•Physical Review A•Mar 29, 2007•170 citations

RESCUED: Robust Quantum Error Correction with Surface Code in Noisy Channels Using Ensemble Decoder

Saikat Barua, Syed Emad Uddin Shubha, Monika Rahman +2 more

The necessity for quantum error correction arises from the need to safeguard quantum information from errors induced by decoherence and other noise forms. However, the optimal decoding of quantum error-correcting codes is a computationally challenging task. In our research, we introduce an ensemble decoder that amalgamates the advantages of various decoders to attain lower logical error rates and the capability to decode multiple errors. We employed statistical methodologies to allocate a specific error syndrome to the decoder with the highest likelihood of accurate decoding. We applied diverse variants of the Noise model to simulate the impact of noise on transmitted quantum states accurately. The efficacy of the ensemble decoder was assessed in both Symmetric and Asymmetric Noise Models. In the Symmetric Noise Model, bit-flip and phase-flip errors are presumed to have equal probabilities, while in the Asymmetric Noise Model, these probabilities can vary. The comparison aimed to evaluate the ensemble decoder's proficiency in rectifying these error types compared to traditional decoding techniques. Our results indicate that the ensemble decoder surpasses conventional decoders in the Symmetric Noise model, particularly for higher code distances. It is also apparent that augmenting the lattice size diminishes the logical error rate and that threshold and pseudo-threshold values escalate with incremental changes in noise asymmetry. The study's findings underscore the substantial potential of the ensemble decoder in quantum error correction and communication realms.

IEEE International Conference on Telecommunications and Photonics (ICTP)•Dec 21, 2023•1 citation

Asymmetric quantum codes: constructions, bounds and performance

Pradeep Kiran Sarvepalli, Andreas Klappenecker, Martin Rötteler

Recently, quantum error-correcting codes have been proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit- and phase-flip errors. An example for a channel that exhibits such asymmetry is the combined amplitude damping and dephasing channel, where the probabilities of bit and phase flips can be related to relaxation and dephasing time, respectively. We study asymmetric quantum codes that are obtained from the Calderbank–Shor–Steane (CSS) construction. For such codes, we derive upper bounds on the code parameters using linear programming. A central result of this paper is the explicit construction of some new families of asymmetric quantum stabilizer codes from pairs of nested classical codes. For instance, we derive asymmetric codes using a combination of Bose–Chaudhuri–Hocquenghem (BCH) and finite geometry low-density parity-check (LDPC) codes. We show that the asymmetric quantum codes offer two advantages, namely to allow a higher rate without sacrificing performance when compared with symmetric codes and vice versa to allow a higher performance when compared with symmetric codes of comparable rates. Our approach is based on a CSS construction that combines BCH and finite geometry LDPC codes.

Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Mar 4, 2009•144 citations

Fault-tolerant quantum computing with three-dimensional surface codes

Michael Vasmer

Quantum computers are far more error-prone than their classical counterparts. Therefore, to build a quantum computer capable of running large-scale quantum algorithms, we must use the techniques of quantum error correction to ensure that the computer produces the correct output even when its components are unreliable. However, the resource requirements of building such a fault-tolerant quantum computer are currently prohibitive. Here, we examine the utility of using three-dimensional (3D) surface codes in a fault-tolerant quantum computer. This family of topological error-correcting codes is a generalization of the well-known 2D surface code to three spatial dimensions. We show that certain 3D surface codes have a transversal logical non-Clifford gate. In a quantum computing architecture, a non-Clifford gate is required to achieve computational universality. Transversal gates do not entangle qubits in different codes, so they are naturally fault tolerant because they do not spread errors. Next, we consider the problem of decoding 3D surface codes. In a quantum error-correcting code, we cannot observe the qubits directly, so we measure parity-check operators to gain information about the state of the code. Decoding is the problem of estimating what error has occurred given a list of unsatisfied parity checks. We observe that 3D surface codes offer asymmetric protection against bit-flip and phase-flip errors, but in both cases, we find that a threshold error rate exists below which we can suppress logical errors by increasing the size of the code. We use our results about logical gates and decoding to propose two fault-tolerant quantum computing architectures that utilize 3D surface codes. Finally, we compare the resource requirements of our architectures with the requirements of leading quantum computing architectures based on topological codes. We find that one of our architectures may be competitive with the leading architectures, depending on the properties of the physical systems used to build the qubits.

•Dec 28, 2019•2 citations

Disparity Surface Code: Optimizing Error Correction in Quantum Networks

Tianjie Hu, Jindi Wu, Qun Li

Practical quantum computing requires error rates much lower than those achievable with physical qubits. Surface codes provide a reliable method to implement logical qubits using physical qubits. However, when these physical qubits are transmitted within quantum networks, their error rates can vary due to differences in the routing paths. Our experimental results indicate that the geometric arrangement of these physical qubits within a surface code significantly impacts its logical error rate. In this paper, we address this issue by proposing disparity surface codes, which are a group of geometric configurations for surface codes that adapt them for transmission within quantum networks. For a distance-$d$disparity surface code, only$d$physical qubits need to be transmitted with low error rates, and we identify multiple equivalent choices for selecting these$d$qubits. Additionally, we propose Di-MWPM, a new decoder designed to exploit physical error rate disparity for enhanced error correction. Results demonstrate that disparity surface codes maintain favorable performance in different network scenarios, even under high noise conditions. Our Di-MWPM decoder achieves improved Pauli-error thresholds.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•1 citation
Abstract Surface codes are quantum error correcting codes typically defined on a 2D array of qubits. A [ d x , d z ] surface code design is being introduced, where d x ( d z ) represents the distance of the code for bit (phase) error correction, motivated by the fact that the severity of bit flip and phase flip errors in the physical quantum system is asymmetric. We present pseudo‐threshold and threshold values for the proposed surface code design for asymmetric error channels in the presence of various degrees of asymmetry of , errors in a depolarisation channel. We demonstrate that compared to symmetric surface codes, our asymmetric surface codes can provide almost double the pseudo‐threshold rates while requiring less than half the number of physical qubits in the presence of increasing asymmetry in the error channel. Our results show that for low degree of asymmetry, it is advantageous to increase d x along with d z . However, as the asymmetry of the channel increases, higher pseudo‐threshold is obtained with increasing d z when d x is kept constant at a low value. Additionally, we also show that the advantage in the pseudo‐threshold rates begins to saturate for any possible degree of asymmetry in the error channel as the surface code asymmetry is continued to be increased.
We introduce surface ZZZY codes, a novel family of quantum error-correcting codes designed for asymmetric channels. Derived from standard surface codes through tailored modification of generators, ZZZY codes can be decoded by the minimum weight perfect matching (MWPM) algorithm with a suitable pre-processing phase. The resulting decoder exploits the information provided by the modified generators without introducing additional complexity. ZZZY codes demonstrate a significant performance advantage over surface codes when increasing the channel asymmetry, while maintaining the same correction capability over depolarizing channel.
The necessity for quantum error correction arises from the need to safeguard quantum information from errors induced by decoherence and other noise forms. However, the optimal decoding of quantum error-correcting codes is a computationally challenging task. In our research, we introduce an ensemble decoder that amalgamates the advantages of various decoders to attain lower logical error rates and the capability to decode multiple errors. We employed statistical methodologies to allocate a specific error syndrome to the decoder with the highest likelihood of accurate decoding. We applied diverse variants of the Noise model to simulate the impact of noise on transmitted quantum states accurately. The efficacy of the ensemble decoder was assessed in both Symmetric and Asymmetric Noise Models. In the Symmetric Noise Model, bit-flip and phase-flip errors are presumed to have equal probabilities, while in the Asymmetric Noise Model, these probabilities can vary. The comparison aimed to evaluate the ensemble decoder's proficiency in rectifying these error types compared to traditional decoding techniques. Our results indicate that the ensemble decoder surpasses conventional decoders in the Symmetric Noise model, particularly for higher code distances. It is also apparent that augmenting the lattice size diminishes the logical error rate and that threshold and pseudo-threshold values escalate with incremental changes in noise asymmetry. The study's findings underscore the substantial potential of the ensemble decoder in quantum error correction and communication realms.
Recently, quantum error-correcting codes have been proposed that capitalize on the fact that many physical error models lead to a significant asymmetry between the probabilities for bit- and phase-flip errors. An example for a channel that exhibits such asymmetry is the combined amplitude damping and dephasing channel, where the probabilities of bit and phase flips can be related to relaxation and dephasing time, respectively. We study asymmetric quantum codes that are obtained from the Calderbank–Shor–Steane (CSS) construction. For such codes, we derive upper bounds on the code parameters using linear programming. A central result of this paper is the explicit construction of some new families of asymmetric quantum stabilizer codes from pairs of nested classical codes. For instance, we derive asymmetric codes using a combination of Bose–Chaudhuri–Hocquenghem (BCH) and finite geometry low-density parity-check (LDPC) codes. We show that the asymmetric quantum codes offer two advantages, namely to allow a higher rate without sacrificing performance when compared with symmetric codes and vice versa to allow a higher performance when compared with symmetric codes of comparable rates. Our approach is based on a CSS construction that combines BCH and finite geometry LDPC codes.
Quantum computers are far more error-prone than their classical counterparts. Therefore, to build a quantum computer capable of running large-scale quantum algorithms, we must use the techniques of quantum error correction to ensure that the computer produces the correct output even when its components are unreliable. However, the resource requirements of building such a fault-tolerant quantum computer are currently prohibitive. Here, we examine the utility of using three-dimensional (3D) surface codes in a fault-tolerant quantum computer. This family of topological error-correcting codes is a generalization of the well-known 2D surface code to three spatial dimensions. We show that certain 3D surface codes have a transversal logical non-Clifford gate. In a quantum computing architecture, a non-Clifford gate is required to achieve computational universality. Transversal gates do not entangle qubits in different codes, so they are naturally fault tolerant because they do not spread errors. Next, we consider the problem of decoding 3D surface codes. In a quantum error-correcting code, we cannot observe the qubits directly, so we measure parity-check operators to gain information about the state of the code. Decoding is the problem of estimating what error has occurred given a list of unsatisfied parity checks. We observe that 3D surface codes offer asymmetric protection against bit-flip and phase-flip errors, but in both cases, we find that a threshold error rate exists below which we can suppress logical errors by increasing the size of the code. We use our results about logical gates and decoding to propose two fault-tolerant quantum computing architectures that utilize 3D surface codes. Finally, we compare the resource requirements of our architectures with the requirements of leading quantum computing architectures based on topological codes. We find that one of our architectures may be competitive with the leading architectures, depending on the properties of the physical systems used to build the qubits.
Practical quantum computing requires error rates much lower than those achievable with physical qubits. Surface codes provide a reliable method to implement logical qubits using physical qubits. However, when these physical qubits are transmitted within quantum networks, their error rates can vary due to differences in the routing paths. Our experimental results indicate that the geometric arrangement of these physical qubits within a surface code significantly impacts its logical error rate. In this paper, we address this issue by proposing disparity surface codes, which are a group of geometric configurations for surface codes that adapt them for transmission within quantum networks. For a distance-ddddisparity surface code, onlydddphysical qubits need to be transmitted with low error rates, and we identify multiple equivalent choices for selecting thesedddqubits. Additionally, we propose Di-MWPM, a new decoder designed to exploit physical error rate disparity for enhanced error correction. Results demonstrate that disparity surface codes maintain favorable performance in different network scenarios, even under high noise conditions. Our Di-MWPM decoder achieves improved Pauli-error thresholds.