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:2510.08552

Single-Shot Universality in Quantum LDPC Codes via Code-Switching

Shi Jie Samuel Tan, Yifan Hong, Ting-Chun Lin, Michael J. Gullans, Min-Hsiu Hsieh

Published Oct 9, 2025• 0 citations
arXivHTMLPDF

Abstract

Code-switching is a powerful technique in quantum error correction that allows one to leverage the complementary strengths of different codes to achieve fault-tolerant universal quantum computation. However, existing code-switching protocols that encapsulate recent generalized lattice surgery approaches often either require many rounds of measurements to ensure fault-tolerance or suffer from low code rates. We present a single-shot, universal protocol that uses code-switching between high-rate quantum codes to perform fault-tolerant quantum computation. To our best knowledge, our work contains the first universal fault-tolerant quantum computation protocol that achieves what we term single-shot universality on high-rate codes that is characterized by (i) single-shot error correction, (ii) single-shot state preparation, as well as (iii) universal logical gates and logical measurements with constant depth circuits. We achieve this feat with single-shot code-switching between constant-rate 2D hypergraph product (HGP) codes and high-rate 3D HGP codes that can be viewed as a generalization of Bombin's dimensional jump for color codes and Hillmann et al.'s single-shot lattice surgery for higher-dimensional topological codes. In addition, we prove the fault-tolerance of our code-switching protocol under both the adversarial and local-stochastic noise models. We introduce a vastly simpler recipe to construct high-rate 3D HGP codes with transversal CCZ gates that grants immense flexibility in the choice of expander graphs and local codes, allowing us to expand the search space for codes with good parameters and interesting logical gates. Our work opens an alternative path towards universal fault-tolerant quantum computation with low space-time overhead by circumventing the need for magic state distillation.

DOI
10.48550/arxiv.2510.08552

Related papers

Transversal dimension jump for product qLDPC codes

Christine Li, John P. Preskill, Qian Xu

We introduce transversal dimension jump, a code-switching protocol for lifted product (LP) quantum low-density parity-check (qLDPC) codes across different chain-complex dimensions, enabling universal fault-tolerant quantum computation with low overhead. The construction leverages the product structure of LP codes to implement one-way transversal CNOTs between a 3D code and its 2D component codes, enabling teleportation-based switching with geometrically nonlocal gates. Combined with constant-depth CCZ gates in 3D LP codes and low-overhead transversal Clifford gates in 2D LP codes, this yields universal, high-rate quantum logical computation with high thresholds and low space-time costs. Beyond asymptotic schemes, we identify explicit 3D-2D LP code pairs supporting cup-product CCZ gates, including bivariate tricycle-bicycle families such as the $[[81,3,5]]$-$[[54,2,6]]$ pair, where the 3D tricycle codes admit depth-2 CCZ, weight-6 stabilizers, and pseudo-thresholds $\gtrsim 0.4\%$. As a byproduct, we show that the 3D codes enable highly efficient magic-state preparation: a single round of stabilizer measurements followed by depth-2 CCZ and postselection produces states with error $<10^{-9}$ and success probability $\sim 35\%$. Our results establish a native integration of qLDPC codes with complementary transversal gates-covering nearly all practically relevant families known so far-and open a broad design space for scalable, low-overhead universal quantum computation.

arXiv:2510.07269•Oct 8, 2025•0 citations

Minimizing the Number of Code Switching Operations in Fault-Tolerant Quantum Circuits

Erik Weilandt, Tom Peham, Robert Wille

Fault-tolerant quantum computers rely on Quantum Error-Correcting Codes (QECCs) to protect information from noise. However, no single error-correcting code supports a fully transversal and therefore fault-tolerant implementation of all gates required for universal quantum computation. Code switching addresses this limitation by moving quantum information between different codes that, together, support a universal gate set. Unfortunately, each switch is costly-adding time and space overhead and increasing the logical error rate. Minimizing the number of switching operations is, therefore, essential for quantum computations using code switching. In this work, we study the problem of minimizing the number of code switches required to run a given quantum circuit. We show that this problem can be solved efficiently in polynomial time by reducing it to a minimum-cut instance on a graph derived from the circuit. Our formulation is flexible and can incorporate additional considerations, such as reducing depth overhead by preferring switches during idle periods or biasing the compilation to favor one code over another. To the best of our knowledge, this is the first automated approach for compiling and optimizing code-switching-based quantum computations at the logical level.

quant-pharXiv:2512.04170•Dec 5, 2025•0 citations

Single-shot preparation of hypergraph product codes via dimension jump

Yifan Hong

Quantum error correction is a fundamental primitive of fault-tolerant quantum computing. But in order for error correction to proceed, one must first prepare the codespace of the underlying error-correcting code. A popular method for encoding quantum low-density parity-check codes is transversal initialization, where one begins in a product state and measures a set of stabilizer generators. In the presence of measurement errors however, this procedure is generically not fault-tolerant, and so one typically needs to repeat the measurements many times, resulting in a deep initialization circuit. We present a protocol that prepares the codespace of constant-rate hypergraph product codes in constant depth with O(n) spatial overhead, and we show that the protocol is robust even in the presence of measurement errors. Our construction is inspired by dimension-jumping in topological codes and leverages two properties that arise from the homological product of codes. We provide some improvements to lower the spatial overhead and discuss applications to fault-tolerant architectures.

arXiv:2410.05171•Quantum•Oct 7, 2025•3 citations

Constant-Overhead Addressable Gates via Single-Shot Code Switching

Louis Golowich, Kathleen Chang, Guanyu Zhu

It is a major challenge to perform addressable and parallel logical operations on constant-rate quantum LDPC (qLDPC) codes. Indeed, the overhead of targeting specific logical qubits represents a crucial bottleneck in many quantum fault-tolerance schemes. We introduce fault-tolerant protocols for performing various addressable as well as parallel logical operations with constant space-time overhead, on a family of constant-rate and polynomial-distance qLDPC codes. Specifically, we construct gadgets for a large class of permutations of logical qubits. We apply these logical permutations to construct gadgets for applying a targeted Hadamard (or $CNOT$) gate on any chosen logical qubit (pair). We also construct gadgets for preparing logical code states, and for applying Hadamard gates on all logical qubits in a codeblock. All of our gadgets use constant quantum space-time overhead along with polynomially bounded classical computation. Prior protocols for such operations required larger overhead, or else relied on codes with certain symmetries that lack known asymptotic constructions. Our codes are given by tensor products of classical codes constructed from lossless expander graphs. Our core technical contribution is a constant-overhead code-switching procedure between 2- and 3-dimensional product codes, which generalizes Bombin's dimensional jump (arXiv:1412.5079). We prove that all of our gadgets exhibit a constant threshold under locally stochastic noise. Along the way, we develop a small-set flip decoder for high-dimensional product codes from lossless expanders. Our techniques yield additional interesting consequences, such as single-shot state preparation of 2-dimensional product codes with constant space-time overhead. We also propose a method for performing parallel non-Clifford gates by extending our techniques to codes supporting transversal application of such gates.

arXiv:2510.06760•Oct 8, 2025•0 citations

Addressable gate-based logical computation with quantum LDPC codes

Laura Pecorari, Francesco Paolo Guerci, Hugo Perrin +1 more

Quantum computing relies on quantum error correction for high-fidelity logical operations, but scaling to achieve near-term quantum utility is highly resource-intensive. High-rate quantum LDPC codes can reduce error correction overhead, yet realizing high-rate fault-tolerant computation with these codes remains a central challenge. Apart of the lattice surgery approach, standard schemes for realizing logical gates have so far been restricted to performing global operations on all logical qubits at the same time. Another approach relies on low-rate code switching methods. In this work, we introduce a gate-based protocol for addressable single- and multi-qubit Clifford operations on individual logical qubits encoded within one or more quantum LDPC codes. Our scheme leverages logical transversal operations via an auxiliary Bacon-Shor code to perform logical operations with constant time overhead enabled by teleportation. We demonstrate the implementation of an overcomplete logical Clifford gate set and perform numerical simulations to evaluate the error-correction performance of our protocol. Finally, we observe that our scheme can be integrated with magic state cultivation protocols to achieve universal, gate-based, and fully addressable quantum computation.

quant-pharXiv:2511.06124•Nov 11, 2025•0 citations

Universal Weakly Fault-Tolerant Quantum Computation via Code Switching in the [[8,3,2]] Code

Shixin Wu, Dawei Zhong, Todd A. Brun +1 more

Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a fault-tolerant code-switching protocol between two versions of the $[[8, 3, 2]]$ code. One version supports weakly fault-tolerant single-qubit Clifford gates, while the other supports a logical $\overline{\mathrm{CCZ}}$ gate via transversal $T/T^\dagger$ together with logical $\overline{\mathrm{CZ}}$, $\overline{\mathrm{CNOT}}$, and $\overline{\mathrm{SWAP}}$ gates. Because both codes have distance 2, the protocol operates in a postselected, error-detecting regime: single faults lead to detectable outcomes, and accepted runs exhibit quadratic suppression of logical error rates. This yields a universal scheme for postselected fault-tolerant computation. We validate the protocol numerically through simulations of state preparation, code switching, and a three-logical-qubit implementation of Grover's search.

quant-pharXiv:2603.15610•Physical Review Research•Mar 17, 2026•0 citations
Code-switching is a powerful technique in quantum error correction that allows one to leverage the complementary strengths of different codes to achieve fault-tolerant universal quantum computation. However, existing code-switching protocols that encapsulate recent generalized lattice surgery approaches often either require many rounds of measurements to ensure fault-tolerance or suffer from low code rates. We present a single-shot, universal protocol that uses code-switching between high-rate quantum codes to perform fault-tolerant quantum computation. To our best knowledge, our work contains the first universal fault-tolerant quantum computation protocol that achieves what we term single-shot universality on high-rate codes that is characterized by (i) single-shot error correction, (ii) single-shot state preparation, as well as (iii) universal logical gates and logical measurements with constant depth circuits. We achieve this feat with single-shot code-switching between constant-rate 2D hypergraph product (HGP) codes and high-rate 3D HGP codes that can be viewed as a generalization of Bombin's dimensional jump for color codes and Hillmann et al.'s single-shot lattice surgery for higher-dimensional topological codes. In addition, we prove the fault-tolerance of our code-switching protocol under both the adversarial and local-stochastic noise models. We introduce a vastly simpler recipe to construct high-rate 3D HGP codes with transversal CCZ gates that grants immense flexibility in the choice of expander graphs and local codes, allowing us to expand the search space for codes with good parameters and interesting logical gates. Our work opens an alternative path towards universal fault-tolerant quantum computation with low space-time overhead by circumventing the need for magic state distillation.
We introduce transversal dimension jump, a code-switching protocol for lifted product (LP) quantum low-density parity-check (qLDPC) codes across different chain-complex dimensions, enabling universal fault-tolerant quantum computation with low overhead. The construction leverages the product structure of LP codes to implement one-way transversal CNOTs between a 3D code and its 2D component codes, enabling teleportation-based switching with geometrically nonlocal gates. Combined with constant-depth CCZ gates in 3D LP codes and low-overhead transversal Clifford gates in 2D LP codes, this yields universal, high-rate quantum logical computation with high thresholds and low space-time costs. Beyond asymptotic schemes, we identify explicit 3D-2D LP code pairs supporting cup-product CCZ gates, including bivariate tricycle-bicycle families such as the [[81,3,5]][[81,3,5]][[81,3,5]]-[[54,2,6]][[54,2,6]][[54,2,6]] pair, where the 3D tricycle codes admit depth-2 CCZ, weight-6 stabilizers, and pseudo-thresholds ≳0.4%\gtrsim 0.4\%≳0.4%. As a byproduct, we show that the 3D codes enable highly efficient magic-state preparation: a single round of stabilizer measurements followed by depth-2 CCZ and postselection produces states with error <10−9<10^{-9}<10−9 and success probability ∼35%\sim 35\%∼35%. Our results establish a native integration of qLDPC codes with complementary transversal gates-covering nearly all practically relevant families known so far-and open a broad design space for scalable, low-overhead universal quantum computation.
Fault-tolerant quantum computers rely on Quantum Error-Correcting Codes (QECCs) to protect information from noise. However, no single error-correcting code supports a fully transversal and therefore fault-tolerant implementation of all gates required for universal quantum computation. Code switching addresses this limitation by moving quantum information between different codes that, together, support a universal gate set. Unfortunately, each switch is costly-adding time and space overhead and increasing the logical error rate. Minimizing the number of switching operations is, therefore, essential for quantum computations using code switching. In this work, we study the problem of minimizing the number of code switches required to run a given quantum circuit. We show that this problem can be solved efficiently in polynomial time by reducing it to a minimum-cut instance on a graph derived from the circuit. Our formulation is flexible and can incorporate additional considerations, such as reducing depth overhead by preferring switches during idle periods or biasing the compilation to favor one code over another. To the best of our knowledge, this is the first automated approach for compiling and optimizing code-switching-based quantum computations at the logical level.
Quantum error correction is a fundamental primitive of fault-tolerant quantum computing. But in order for error correction to proceed, one must first prepare the codespace of the underlying error-correcting code. A popular method for encoding quantum low-density parity-check codes is transversal initialization, where one begins in a product state and measures a set of stabilizer generators. In the presence of measurement errors however, this procedure is generically not fault-tolerant, and so one typically needs to repeat the measurements many times, resulting in a deep initialization circuit. We present a protocol that prepares the codespace of constant-rate hypergraph product codes in constant depth with O(n) spatial overhead, and we show that the protocol is robust even in the presence of measurement errors. Our construction is inspired by dimension-jumping in topological codes and leverages two properties that arise from the homological product of codes. We provide some improvements to lower the spatial overhead and discuss applications to fault-tolerant architectures.
It is a major challenge to perform addressable and parallel logical operations on constant-rate quantum LDPC (qLDPC) codes. Indeed, the overhead of targeting specific logical qubits represents a crucial bottleneck in many quantum fault-tolerance schemes. We introduce fault-tolerant protocols for performing various addressable as well as parallel logical operations with constant space-time overhead, on a family of constant-rate and polynomial-distance qLDPC codes. Specifically, we construct gadgets for a large class of permutations of logical qubits. We apply these logical permutations to construct gadgets for applying a targeted Hadamard (or CNOTCNOTCNOT) gate on any chosen logical qubit (pair). We also construct gadgets for preparing logical code states, and for applying Hadamard gates on all logical qubits in a codeblock. All of our gadgets use constant quantum space-time overhead along with polynomially bounded classical computation. Prior protocols for such operations required larger overhead, or else relied on codes with certain symmetries that lack known asymptotic constructions. Our codes are given by tensor products of classical codes constructed from lossless expander graphs. Our core technical contribution is a constant-overhead code-switching procedure between 2- and 3-dimensional product codes, which generalizes Bombin's dimensional jump (arXiv:1412.5079). We prove that all of our gadgets exhibit a constant threshold under locally stochastic noise. Along the way, we develop a small-set flip decoder for high-dimensional product codes from lossless expanders. Our techniques yield additional interesting consequences, such as single-shot state preparation of 2-dimensional product codes with constant space-time overhead. We also propose a method for performing parallel non-Clifford gates by extending our techniques to codes supporting transversal application of such gates.
Quantum computing relies on quantum error correction for high-fidelity logical operations, but scaling to achieve near-term quantum utility is highly resource-intensive. High-rate quantum LDPC codes can reduce error correction overhead, yet realizing high-rate fault-tolerant computation with these codes remains a central challenge. Apart of the lattice surgery approach, standard schemes for realizing logical gates have so far been restricted to performing global operations on all logical qubits at the same time. Another approach relies on low-rate code switching methods. In this work, we introduce a gate-based protocol for addressable single- and multi-qubit Clifford operations on individual logical qubits encoded within one or more quantum LDPC codes. Our scheme leverages logical transversal operations via an auxiliary Bacon-Shor code to perform logical operations with constant time overhead enabled by teleportation. We demonstrate the implementation of an overcomplete logical Clifford gate set and perform numerical simulations to evaluate the error-correction performance of our protocol. Finally, we observe that our scheme can be integrated with magic state cultivation protocols to achieve universal, gate-based, and fully addressable quantum computation.
Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a fault-tolerant code-switching protocol between two versions of the [[8,3,2]][[8, 3, 2]][[8,3,2]] code. One version supports weakly fault-tolerant single-qubit Clifford gates, while the other supports a logical CCZ‾\overline{\mathrm{CCZ}}CCZ gate via transversal T/T†T/T^\daggerT/T† together with logical CZ‾\overline{\mathrm{CZ}}CZ, CNOT‾\overline{\mathrm{CNOT}}CNOT, and SWAP‾\overline{\mathrm{SWAP}}SWAP gates. Because both codes have distance 2, the protocol operates in a postselected, error-detecting regime: single faults lead to detectable outcomes, and accepted runs exhibit quadratic suppression of logical error rates. This yields a universal scheme for postselected fault-tolerant computation. We validate the protocol numerically through simulations of state preparation, code switching, and a three-logical-qubit implementation of Grover's search.