Hierarchical memories: Simulating quantum LDPC codes with local gates
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1.
California Institute of Technology
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2.
Stanford University
Abstract
Constant-rate low-density parity-check (LDPC) codes are promising candidates for constructing efficient fault-tolerant quantum memories. However, if physical gates are subject to geometric-locality constraints, it becomes challenging to realize these codes. In this paper, we construct a new family of [[N,K,D]] codes, referred to as hierarchical codes, that encode a number of logical qubits K=Ω(N/log(N)²). The Nth element of this code family is obtained by concatenating a constant-rate quantum LDPC code with a surface code; nearest-neighbor gates in two dimensions are sufficient to implement the corresponding syndrome-extraction circuit and achieve a threshold. Below threshold the logical failure rate vanishes superpolynomially as a function of the distance D(N). We present a bilayer architecture for implementing the syndrome-extraction circuit, and estimate the logical failure rate for this architecture. Under conservative assumptions, we find that the hierarchical code outperforms the basic encoding where all logical qubits are encoded in the surface code.
Copyright and License
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
Acknowledgement
AK is supported by the Bloch Postdoctoral Fellowship from Stanford University. AK acknowledges funding from NSF award CCF-1844628. CAP acknowledges funding from the Air Force Office of Scientific Research (AFOSR), FA9550-19-1-0360. JP acknowledges funding from the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, (DE-NA0003525, DE-SC0020290), the U.S. Department of Energy QuantISED program (DESC0018407), the U.S. Department of Energy Quantum Systems Accelerator, the Air Force Office of Scientific Research (FA9550-19-1-0360), and the National Science Foundation (PHY-1733907). The Institute for Quantum Information and Matter is an NSF Physics Frontiers Center. We thank Nicolas Delfosse, Mary Wootters, Anthony Leverrier, Nouédyn Baspin, Bailey Gu, Alex Kubica, David Schuster, Manuel Endres, Michael Vasmer, and Pavel Panteleev for helpful conversations.
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Additional details
Related works
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- Discussion Paper: arXiv:2303.04798 (arXiv)
Funding
- Stanford University
- Bloch Postdoctoral Fellowship -
- National Science Foundation
- CCF-1844628
- Air Force Office of Scientific Research
- FA9550-19-1-0360
- Department of Energy
- DE-NA0003525
- Department of Energy
- DE-SC0020290
- Department of Energy
- DE- SC0018407
- Air Force Office of Scientific Research
- FA9550-19-1-0360
- National Science Foundation
- PHY-1733907