BBS code dimension equals the algebraic multiplicity of finite nonzero common roots of the defining bivariate polynomials, enabling a root-based prescription for arbitrary boundary shapes that avoids corner corrections when edge conditions hold.
Tradeoffs for reliable quantum information storage in 2D systems
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abstract
We ask whether there are fundamental limits on storing quantum information reliably in a bounded volume of space. To investigate this question, we study quantum error correcting codes specified by geometrically local commuting constraints on a 2D lattice of finite-dimensional quantum particles. For these 2D systems, we derive a tradeoff between the number of encoded qubits k, the distance of the code d, and the number of particles n. It is shown that kd^2=O(n) where the coefficient in O(n) depends only on the locality of the constraints and dimension of the Hilbert spaces describing individual particles. We show that the analogous tradeoff for the classical information storage is k\sqrt{d} =O(n).
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An exact positive-probability decomposition of thermal relaxation noise into Clifford gates and resets exists for T2 ≤ T1, with a negativity-free approximation that outperforms Pauli twirling for T2 > T1.
A programmable 2D toric oscillator network enables efficient routing for bivariate bicycle LDPC codes, reducing long-range couplers to O(sqrt(n)) and achieving 3.06% logical error rate per cycle in simulations for the [[18,4,4]] code.
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Algebra of Bivariate-Bicycle Surface Codes
BBS code dimension equals the algebraic multiplicity of finite nonzero common roots of the defining bivariate polynomials, enabling a root-based prescription for arbitrary boundary shapes that avoids corner corrections when edge conditions hold.
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Exact and Efficient Stabilizer Simulation of Thermal-Relaxation Noise for Quantum Error Correction
An exact positive-probability decomposition of thermal relaxation noise into Clifford gates and resets exists for T2 ≤ T1, with a negativity-free approximation that outperforms Pauli twirling for T2 > T1.
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Efficient Routing of Quantum LDPC Codes on Programmable 2D Toric Architectures
A programmable 2D toric oscillator network enables efficient routing for bivariate bicycle LDPC codes, reducing long-range couplers to O(sqrt(n)) and achieving 3.06% logical error rate per cycle in simulations for the [[18,4,4]] code.