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:2412.16116 · Physical Review Letters

Kramers-Protected Hardware-Efficient Error Correction with Andreev Spin Qubits

Haoran Lu, Isidora Araya Day, Anton Akhmerov, Bernard van Heck, Valla Fatemi

Published Aug 21, 2025• 0 citations
arXivHTMLPDF

Abstract

We propose an architecture for bit-flip error correction of Andreev spins that is protected by Kramers' degeneracy. Specifically, we show that a coupling network of linear inductors and Andreev spin qubits results in a static Hamiltonian composed of the stabilizers of a bit-flip code. The electrodynamics of the many-body spin states also respect these stabilizers, and we show how reflectometry off a single coupled resonator can thereby accomplish their projective measurement. We further show how circuit-mediated spin couplings enable error correction operations and a complete set of single- and two-module logical quantum gates. The concept, which we dub the ``Ising molecule qubit,'' is experimentally feasible and provides a path for compact noise-biased qubits.

DOI
10.1103/lqf3-6r5z

Related papers

Kramers-Protected Hardware-Efficient Error Correction with Andreev Spin Qubits.

Hai Lu, Isidora Araya Day, Anton Akhmerov +2 more

We propose an architecture for bit-flip error correction of Andreev spins that is protected by Kramers' degeneracy. Specifically, we show that a coupling network of linear inductors and Andreev spin qubits results in a static Hamiltonian composed of the stabilizers of a bit-flip code. The electrodynamics of the many-body spin states also respect these stabilizers, and we show how reflectometry off a single coupled resonator can thereby accomplish their projective measurement. We further show how circuit-mediated spin couplings enable error correction operations and a complete set of single- and two-module logical quantum gates. The concept, which we dub the "Ising molecule qubit," is experimentally feasible and provides a path for compact noise-biased qubits.

•Nov 21, 2025•4 citations

A Resource-Efficient 4-Qubit Circuit for Bit-Flip Error Correction Using Feynman Gates

Dimitrios Gryllakis, Kyriakos Sgarbas

Abstract Quantum systems are inherently prone to errors caused by decoherence, noise, and imperfect gate operations. Effective error correction is essential to preserving quantum information, especially under hardware constraints. In this paper, we present a resource-efficient 4-qubit quantum circuit designed to detect and correct single-qubit bit-flip errors within a 3-qubit data block. The circuit uses Feynman (CNOT) and NOT gates alongside an ancillary qubit to implement full correction logic with minimal overhead. Compared to well-known approaches like the 9-qubit Shor code, our design achieves equivalent fidelity (100%) using fewer qubits, making it highly suitable for near-term quantum devices. Simulation results, obtained using IBM Quantum Composer and Qiskit, confirm the circuit’s correctness and reliability across all bit-flip scenarios. The design also introduces a reusable unitary block for efficient implementation. This work offers a scalable and practical solution to quantum error correction using minimal hardware resources.

Quantum Information and Computation•Aug 1, 2025•0 citations

Biased-noise qubits: a guide to efficient fault-tolerance using the hierarchy of errors

Diego Ruiz, Jérémie Guillaud, Christophe Vuillot +1 more

Qubits with strongly biased noise, in which phase-flip errors are orders of magnitude more frequent than bit-flips, arise both naturally, as in electron and nuclear spins, and by engineering, as in stabilized cat qubits. This noise structure holds the promise of reducing the daunting hardware overhead of fault-tolerant quantum computing, but exploiting it requires physical operations that do not convert frequent phase-flips into rare bit-flips. In this review, we analyze the most prominent fault-tolerant protocols for biased-noise qubits, organized according to the available set of such bias-preserving operations. When this set is restricted to the CZ gate together with preparation and measurement in the X basis, we show that the complexity of the required syndrome extraction gadgets essentially cancels the benefit of the noise bias: at experimentally relevant error rates, one may as well ignore the bias and rely on standard error correction designed for depolarizing noise. The situation changes drastically when a bias-preserving CX gate is available: the hierarchy of errors can then be reflected in the structure of the code, with frequent phase-flips corrected by a dedicated high-threshold code and rare bit-flips by concatenation with a high-rate code. The same hierarchy also enables hardware-efficient preparation of magic states. Finally, as a bias-preserving CX is forbidden in naturally biased platforms and challenging in engineered ones, we present a measurement-based architecture in which a high-fidelity quantum non-demolition readout of multi-qubit Pauli Z operators takes its place, extending these overhead reductions to a much broader range of physical platforms.

quant-pharXiv:2607.20143•Jul 23, 2026•0 citations

Detecting bit-flip errors in a logical qubit using stabilizer measurements

Diego Ristè, Stefano Poletto, Meng-Zi Huang +4 more

Quantum data are susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction to actively protect against both. In the smallest error correction codes, the information in one logical qubit is encoded in a two-dimensional subspace of a larger Hilbert space of multiple physical qubits. For each code, a set of non-demolition multi-qubit measurements, termed stabilizers, can discretize and signal physical qubit errors without collapsing the encoded information. Here using a five-qubit superconducting processor, we realize the two parity measurements comprising the stabilizers of the three-qubit repetition code protecting one logical qubit from physical bit-flip errors. While increased physical qubit coherence times and shorter quantum error correction blocks are required to actively safeguard the quantum information, this demonstration is a critical step towards larger codes based on multiple parity measurements.

arXiv:1411.5542•Nature Communications•Apr 29, 2015•261 citations

Experimental demonstration of continuous quantum error correction

William P. Livingston, Machiel Blok, Emmanuel Flurin +3 more

The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction. Typically, quantum error correction is executed in discrete rounds, using entangling gates and projective measurement on ancillary qubits to complete each round of error correction. Here we use direct parity measurements to implement a continuous quantum bit-flip correction code in a resource-efficient manner, eliminating entangling gates, ancillary qubits, and their associated errors. An FPGA controller actively corrects errors as they are detected, achieving an average bit-flip detection efficiency of up to 91%. Furthermore, the protocol increases the relaxation time of the protected logical qubit by a factor of 2.7 over the relaxation times of the bare comprising qubits. Our results showcase resource-efficient stabilizer measurements in a multi-qubit architecture and demonstrate how continuous error correction codes can address challenges in realizing a fault-tolerant system.

arXiv:2107.11398•Nature Communications•Apr 28, 2022•73 citations

Autonomous Quantum Error Correction of Spin-Oscillator Hybrid Qubits

Sungjoo Cho, Ju-yeon Gyhm, Hyukjoon Kwon +1 more

We propose a novel measurement-free scheme for stabilizing a spin-oscillator hybrid qubit via autonomous quantum error correction. The engineered Lindbladian renders the code space into an attractive steady-state subspace, realized by coupling the storage mode to a rapidly cooled bath through a controlled beam-splitter and spin-dependent displacement interactions. The continuous variable-discrete variable hybrid approach to autonomous quantum error correction preserves the hardware efficiency of conventional dissipation engineering while simplifying the required system-bath coupling. The construction is compatible with simple logical gates and leverages primitives already demonstrated in experimental platforms, such as trapped-ion systems, suggesting a practical route to hardware-efficient, noise-biased logical qubits without repeated syndrome measurements and feedforward.

quant-pharXiv:2604.11145•Apr 14, 2026•0 citations
We propose an architecture for bit-flip error correction of Andreev spins that is protected by Kramers' degeneracy. Specifically, we show that a coupling network of linear inductors and Andreev spin qubits results in a static Hamiltonian composed of the stabilizers of a bit-flip code. The electrodynamics of the many-body spin states also respect these stabilizers, and we show how reflectometry off a single coupled resonator can thereby accomplish their projective measurement. We further show how circuit-mediated spin couplings enable error correction operations and a complete set of single- and two-module logical quantum gates. The concept, which we dub the ``Ising molecule qubit,'' is experimentally feasible and provides a path for compact noise-biased qubits.
We propose an architecture for bit-flip error correction of Andreev spins that is protected by Kramers' degeneracy. Specifically, we show that a coupling network of linear inductors and Andreev spin qubits results in a static Hamiltonian composed of the stabilizers of a bit-flip code. The electrodynamics of the many-body spin states also respect these stabilizers, and we show how reflectometry off a single coupled resonator can thereby accomplish their projective measurement. We further show how circuit-mediated spin couplings enable error correction operations and a complete set of single- and two-module logical quantum gates. The concept, which we dub the "Ising molecule qubit," is experimentally feasible and provides a path for compact noise-biased qubits.
Abstract Quantum systems are inherently prone to errors caused by decoherence, noise, and imperfect gate operations. Effective error correction is essential to preserving quantum information, especially under hardware constraints. In this paper, we present a resource-efficient 4-qubit quantum circuit designed to detect and correct single-qubit bit-flip errors within a 3-qubit data block. The circuit uses Feynman (CNOT) and NOT gates alongside an ancillary qubit to implement full correction logic with minimal overhead. Compared to well-known approaches like the 9-qubit Shor code, our design achieves equivalent fidelity (100%) using fewer qubits, making it highly suitable for near-term quantum devices. Simulation results, obtained using IBM Quantum Composer and Qiskit, confirm the circuit’s correctness and reliability across all bit-flip scenarios. The design also introduces a reusable unitary block for efficient implementation. This work offers a scalable and practical solution to quantum error correction using minimal hardware resources.
Qubits with strongly biased noise, in which phase-flip errors are orders of magnitude more frequent than bit-flips, arise both naturally, as in electron and nuclear spins, and by engineering, as in stabilized cat qubits. This noise structure holds the promise of reducing the daunting hardware overhead of fault-tolerant quantum computing, but exploiting it requires physical operations that do not convert frequent phase-flips into rare bit-flips. In this review, we analyze the most prominent fault-tolerant protocols for biased-noise qubits, organized according to the available set of such bias-preserving operations. When this set is restricted to the CZ gate together with preparation and measurement in the X basis, we show that the complexity of the required syndrome extraction gadgets essentially cancels the benefit of the noise bias: at experimentally relevant error rates, one may as well ignore the bias and rely on standard error correction designed for depolarizing noise. The situation changes drastically when a bias-preserving CX gate is available: the hierarchy of errors can then be reflected in the structure of the code, with frequent phase-flips corrected by a dedicated high-threshold code and rare bit-flips by concatenation with a high-rate code. The same hierarchy also enables hardware-efficient preparation of magic states. Finally, as a bias-preserving CX is forbidden in naturally biased platforms and challenging in engineered ones, we present a measurement-based architecture in which a high-fidelity quantum non-demolition readout of multi-qubit Pauli Z operators takes its place, extending these overhead reductions to a much broader range of physical platforms.
Quantum data are susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction to actively protect against both. In the smallest error correction codes, the information in one logical qubit is encoded in a two-dimensional subspace of a larger Hilbert space of multiple physical qubits. For each code, a set of non-demolition multi-qubit measurements, termed stabilizers, can discretize and signal physical qubit errors without collapsing the encoded information. Here using a five-qubit superconducting processor, we realize the two parity measurements comprising the stabilizers of the three-qubit repetition code protecting one logical qubit from physical bit-flip errors. While increased physical qubit coherence times and shorter quantum error correction blocks are required to actively safeguard the quantum information, this demonstration is a critical step towards larger codes based on multiple parity measurements.
The storage and processing of quantum information are susceptible to external noise, resulting in computational errors. A powerful method to suppress these effects is quantum error correction. Typically, quantum error correction is executed in discrete rounds, using entangling gates and projective measurement on ancillary qubits to complete each round of error correction. Here we use direct parity measurements to implement a continuous quantum bit-flip correction code in a resource-efficient manner, eliminating entangling gates, ancillary qubits, and their associated errors. An FPGA controller actively corrects errors as they are detected, achieving an average bit-flip detection efficiency of up to 91%. Furthermore, the protocol increases the relaxation time of the protected logical qubit by a factor of 2.7 over the relaxation times of the bare comprising qubits. Our results showcase resource-efficient stabilizer measurements in a multi-qubit architecture and demonstrate how continuous error correction codes can address challenges in realizing a fault-tolerant system.
We propose a novel measurement-free scheme for stabilizing a spin-oscillator hybrid qubit via autonomous quantum error correction. The engineered Lindbladian renders the code space into an attractive steady-state subspace, realized by coupling the storage mode to a rapidly cooled bath through a controlled beam-splitter and spin-dependent displacement interactions. The continuous variable-discrete variable hybrid approach to autonomous quantum error correction preserves the hardware efficiency of conventional dissipation engineering while simplifying the required system-bath coupling. The construction is compatible with simple logical gates and leverages primitives already demonstrated in experimental platforms, such as trapped-ion systems, suggesting a practical route to hardware-efficient, noise-biased logical qubits without repeated syndrome measurements and feedforward.