Built on

A. Hatcher, Algebraic topology (2005)
2005
Earlier work this paper cites.
B. Eastin and E. Knill, Restrictions on transversal encoded quantum gate sets, Physical review letters 102
2009
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D. Gottesman, Fault-Tolerant Quantum Computation with Constant Overhead, Quantum Information and Computation 14
2013
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S. Bravyi and R. König, Classification of topologically protected gates for local stabilizer codes, Physical review letters 110
2013
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J.-P. Tillich and G. Zemor, Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2} (2013)
2013
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J. P. Tillich and G. Zemor, Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength, IEEE Transactions on Information Theory 60
2014
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H. Bombín, Dimensional jump in quantum error correction, New Journal of Physics 18
2016
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E. T. Campbell, A theory of single-shot error correction for adversarial noise, Quantum Science and Technology 4
2019
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G. V. Kalachev and P. A. Panteleev, On the minimum distance in one class of quantum ldpc codes, Intelligent systems. Theory and applications 24
2020
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J. Roffe, D. R. White, S. Burton, and E. Campbell, Decoding across the quantum low-density parity-check code landscape, Physical Review Research 2
2020
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C. Gidney, Stim: a fast stabilizer circuit simulator, Quantum 5
2021
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P. Panteleev and G. Kalachev, Asymptotically good quantum and locally testable classical ldpc codes, in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing (2022) pp. 375–388
2022
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A. Leverrier and G. Zémor, Quantum Tanner codes, arXiv preprint arXiv:2202.13641 10.48550/arxiv.2202.13641 (2022)
Original
2022
Earlier work this paper cites.
S. Gu, C. A. Pattison, and E. Tang, An efficient decoder for a linear distance quantum LDPC code, Proceedings of the Annual ACM Symposium on Theory of Computing , 919 (2022)
2022
Earlier work this paper cites.
I. Dinur, M.-H. H. Hsieh, T.-C. C. Lin, and T. Vidick, Good Quantum LDPC Codes with Linear Time Decoders, Proceedings of the Annual ACM Symposium on Theory of Computing , 905 (2022)
Original
2022
Earlier work this paper cites.
T.-C. Lin and M.-H. Hsieh, Good quantum LDPC codes with linear time decoder from lossless expanders, arXiv preprint arXiv:2203.03581 (2022)
Original
2022
Earlier work this paper cites.
L. Z. Cohen, I. H. Kim, S. D. Bartlett, and B. J. Brown, Low-overhead fault-tolerant quantum computing using long-range connectivity, Science Advances 8
2022
Earlier work this paper cites.
Lifted-product (lp) code, in The Error Correction Zoo , edited by V. V. Albert and P. Faist (2022)
2022
Earlier work this paper cites.

Similar

M. A. Tremblay, N. Delfosse, and M. E. Beverland, Constant-Overhead Quantum Error Correction with Thin Planar Connectivity, Physical Review Letters 129
2022
Cited alongside, same era.
G. Zhu, S. Sikander, E. Portnoy, A. W. Cross, and B. J. Brown, Non-clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum ldpc codes via higher symmetries, arXiv preprint arXiv:2310.16982 (2023)
Original
2023
Cited alongside, same era.
R. Wang, H.-K. Lin, and L. P. Pryadko, Abelian and non-abelian quantum two-block codes, in 2023 12th International Symposium on Topics in Coding (ISTC) (IEEE, 2023) pp. 1–5
2023
Cited alongside, same era.
Two-block group-algebra (2bga) codes, in The Error Correction Zoo , edited by V. V. Albert and P. Faist (2023)
2023
Cited alongside, same era.
S. Huang, T. Jochym-O’Connor, and T. J. Yoder, Homomorphic logical measurements, PRX Quantum 4

Then

Q. Xu, H. Zhou, G. Zheng, D. Bluvstein, J. P. B. Ataides, M. D. Lukin, and L. Jiang, Fast and parallelizable logical computation with homological product codes, Physical Review X 15
2025
Closest in time.
A. J. Malcolm, A. N. Glaudell, P. Fuentes, D. Chandra, A. Schotte, C. DeLisle, R. Haenel, A. Ebrahimi, J. Roffe, A. O. Quintavalle, S. J. Beale, N. R. Lee-Hone, and S. Simmons, Computing efficiently in qldpc codes (2025), arXiv:2502.07150 [quant-ph]
Original
2025
Closest in time.
T. J. Yoder, E. Schoute, P. Rall, E. Pritchett, J. M. Gambetta, A. W. Cross, M. Carroll, and M. E. Beverland, Tour de gross: A modular quantum computer based on bivariate bicycle codes, arXiv preprint arXiv:2506.03094 (2025)
Original
2025
Closest in time.
G. Zhang, Y. Zhu, X. Yuan, and Y. Li, Constant-overhead magic state injection into qldpc codes with error independence guarantees, arXiv preprint arXiv:2505.06981 (2025)
Original
2025
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2025

Transversal dimension jump for product qLDPC codes

Li, Christine, Preskill, John, Xu, Qian

Understand

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 $\gtrsim 0.4\%$.

Built on

A. Hatcher, Algebraic topology (2005)
2005
Earlier work this paper cites.
B. Eastin and E. Knill, Restrictions on transversal encoded quantum gate sets, Physical review letters 102
2009
Earlier work this paper cites.
D. Gottesman, Fault-Tolerant Quantum Computation with Constant Overhead, Quantum Information and Computation 14
2013
Earlier work this paper cites.
S. Bravyi and R. König, Classification of topologically protected gates for local stabilizer codes, Physical review letters 110
2013
Earlier work this paper cites.
J.-P. Tillich and G. Zemor, Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2} (2013)
2013
Earlier work this paper cites.
J. P. Tillich and G. Zemor, Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength, IEEE Transactions on Information Theory 60
2014
Earlier work this paper cites.
H. Bombín, Dimensional jump in quantum error correction, New Journal of Physics 18
2016
Earlier work this paper cites.
E. T. Campbell, A theory of single-shot error correction for adversarial noise, Quantum Science and Technology 4
2019
Earlier work this paper cites.
G. V. Kalachev and P. A. Panteleev, On the minimum distance in one class of quantum ldpc codes, Intelligent systems. Theory and applications 24
2020
Earlier work this paper cites.
J. Roffe, D. R. White, S. Burton, and E. Campbell, Decoding across the quantum low-density parity-check code landscape, Physical Review Research 2
2020
Earlier work this paper cites.
C. Gidney, Stim: a fast stabilizer circuit simulator, Quantum 5
2021
Earlier work this paper cites.
P. Panteleev and G. Kalachev, Asymptotically good quantum and locally testable classical ldpc codes, in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing (2022) pp. 375–388
2022
Earlier work this paper cites.
A. Leverrier and G. Zémor, Quantum Tanner codes, arXiv preprint arXiv:2202.13641 10.48550/arxiv.2202.13641 (2022)
Original
2022
Earlier work this paper cites.
S. Gu, C. A. Pattison, and E. Tang, An efficient decoder for a linear distance quantum LDPC code, Proceedings of the Annual ACM Symposium on Theory of Computing , 919 (2022)
2022
Earlier work this paper cites.
I. Dinur, M.-H. H. Hsieh, T.-C. C. Lin, and T. Vidick, Good Quantum LDPC Codes with Linear Time Decoders, Proceedings of the Annual ACM Symposium on Theory of Computing , 905 (2022)
Original
2022
Earlier work this paper cites.
T.-C. Lin and M.-H. Hsieh, Good quantum LDPC codes with linear time decoder from lossless expanders, arXiv preprint arXiv:2203.03581 (2022)
Original
2022
Earlier work this paper cites.
L. Z. Cohen, I. H. Kim, S. D. Bartlett, and B. J. Brown, Low-overhead fault-tolerant quantum computing using long-range connectivity, Science Advances 8
2022
Earlier work this paper cites.
Lifted-product (lp) code, in The Error Correction Zoo , edited by V. V. Albert and P. Faist (2022)
2022
Earlier work this paper cites.

Similar

M. A. Tremblay, N. Delfosse, and M. E. Beverland, Constant-Overhead Quantum Error Correction with Thin Planar Connectivity, Physical Review Letters 129
2022
Cited alongside, same era.
G. Zhu, S. Sikander, E. Portnoy, A. W. Cross, and B. J. Brown, Non-clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum ldpc codes via higher symmetries, arXiv preprint arXiv:2310.16982 (2023)
Original
2023
Cited alongside, same era.
R. Wang, H.-K. Lin, and L. P. Pryadko, Abelian and non-abelian quantum two-block codes, in 2023 12th International Symposium on Topics in Coding (ISTC) (IEEE, 2023) pp. 1–5
2023
Cited alongside, same era.
Two-block group-algebra (2bga) codes, in The Error Correction Zoo , edited by V. V. Albert and P. Faist (2023)
2023
Cited alongside, same era.
S. Huang, T. Jochym-O’Connor, and T. J. Yoder, Homomorphic logical measurements, PRX Quantum 4

Then

Q. Xu, H. Zhou, G. Zheng, D. Bluvstein, J. P. B. Ataides, M. D. Lukin, and L. Jiang, Fast and parallelizable logical computation with homological product codes, Physical Review X 15
2025
Closest in time.
A. J. Malcolm, A. N. Glaudell, P. Fuentes, D. Chandra, A. Schotte, C. DeLisle, R. Haenel, A. Ebrahimi, J. Roffe, A. O. Quintavalle, S. J. Beale, N. R. Lee-Hone, and S. Simmons, Computing efficiently in qldpc codes (2025), arXiv:2502.07150 [quant-ph]
Original
2025
Closest in time.
T. J. Yoder, E. Schoute, P. Rall, E. Pritchett, J. M. Gambetta, A. W. Cross, M. Carroll, and M. E. Beverland, Tour de gross: A modular quantum computer based on bivariate bicycle codes, arXiv preprint arXiv:2506.03094 (2025)
Original
2025
Closest in time.
G. Zhang, Y. Zhu, X. Yuan, and Y. Li, Constant-overhead magic state injection into qldpc codes with error independence guarantees, arXiv preprint arXiv:2505.06981 (2025)
Original
2025
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

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2023

Cited alongside, same era.

D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kalinowski, D. Hangleiter, J. P. B. Ataides, N. Maskara, I. Cong, X. Gao, P. S. Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuletić, and M. D. Lukin, Logical quantum processor based on reconfigurable atom arrays, Nature 2023 , 1 (2023)

2023

Cited alongside, same era.

S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, High-threshold and low-overhead fault-tolerant quantum memory, Nature 627

2024

Cited alongside, same era.

Q. Xu, J. P. Bonilla Ataides, C. A. Pattison, N. Raveendran, D. Bluvstein, J. Wurtz, B. Vasić, M. D. Lukin, L. Jiang, and H. Zhou, Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays, Nature Physics 20

2024

Cited alongside, same era.

A. Cross, Z. He, P. Rall, and T. Yoder, Improved qldpc surgery: Logical measurements and bridging codes, arXiv preprint arXiv:2407.18393 (2024)

Original

2024

Cited alongside, same era.

T.-C. Lin, Transversal non-clifford gates for quantum ldpc codes on sheaves, arXiv preprint arXiv:2410.14631 (2024)

Original

2024

Cited alongside, same era.

S. Heußen and J. Hilder, Efficient fault-tolerant code switching via one-way transversal cnot gates, arXiv preprint arXiv:2409.13465 (2024)

Original

2024

Cited alongside, same era.

H.-K. Lin and L. P. Pryadko, Quantum two-block group algebra codes, Physical Review A 109

2024

Cited alongside, same era.

L. Golowich and V. Guruswami, Asymptotically good quantum codes with transversal non-clifford gates, in Proceedings of the 57th Annual ACM Symposium on Theory of Computing (2025) pp. 707–717

2025

Closest in time.

G. Zhu, A topological theory for qldpc: non-clifford gates and magic state fountain on homological product codes with constant rate and beyond the n 1 / 3 n^{1/3} distance barrier (2025), arXiv:2501.19375 [quant-ph]

Original

2025

Closest in time.

Z. He, V. Vaikuntanathan, A. Wills, and R. Y. Zhang, Quantum codes with addressable and transversal non-clifford gates, arXiv preprint arXiv:2502.01864 (2025)

Original

2025

Closest in time.

X. Fu, H. Zheng, Z. Li, and Z.-W. Liu, No-go theorems for logical gates on product quantum codes, arXiv preprint arXiv:2507.16797 (2025)

Original

2025

Closest in time.

L. Daguerre and I. H. Kim, Code switching revisited: Low-overhead magic state preparation using color codes, Physical Review Research 7

2025

Closest in time.

L. Golowich and T.-C. Lin, Quantum ldpc codes with transversal non-clifford gates via products of algebraic codes, in Proceedings of the 57th Annual ACM Symposium on Theory of Computing (2025) pp. 689–696

2025

Closest in time.

N. Berthusen, M. J. Gullans, Y. Hong, M. Mudassar, and S. J. S. Tan, Automorphism gadgets in homological product codes, arXiv preprint arXiv:2508.04794 (2025)

Original

2025

Closest in time.

A. Jacob, C. McLauchlan, and D. E. Browne, Single-shot decoding and fault-tolerant gates with trivariate tricycle codes, arXiv preprint arXiv:2508.08191 (2025)

Original

2025

Closest in time.

V. Menon, J. P. Bonilla-Ataides, R. Mehta, D. B. Tan, and M. D. Lukin, Magic tricycles: efficient magic state generation with finite block-length quantum ldpc codes, arXiv preprint arXiv:2508.10714 (2025)

Original