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.
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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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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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.