Hardness of Braided Quantum Circuit Optimization in the Surface Code

@article{Wasa2023HardnessOB,
  title={Hardness of Braided Quantum Circuit Optimization in the Surface Code},
  author={Kunihiro Wasa and Shin Nishio and Koki Suetsugu and Michael Hanks and Ashley M. Stephens and Yukina Yokoi and Kae Nemoto},
  journal={IEEE Transactions on Quantum Engineering},
  year={2023},
  volume={4},
  pages={1-7}
}
Large-scale quantum information processing requires the use of quantum error-correcting codes to mitigate the effects of noise in quantum devices. Topological error-correcting codes, such as surface codes, are promising candidates, as they can be implemented using only local interactions in a 2-D array of physical qubits. Procedures, such as defect braiding and lattice surgery, can then be used to realize a fault-tolerant universal set of gates on the logical space of such topological codes… 
View on IEEE
ieeexplore.ieee.org
1 Citation
Background Citations
1

Figures from this paper

One Citation

A High Performance Compiler for Very Large Scale Surface Code Computations

The compiler offers an end to end error correction workflow implemented by a pluggable architecture centered around an intermediate representation of lattice surgery instructions, which supports customizable circuit layouts, can be used for quantum benchmarking and includes a quantum resource estimator.

32 References

Quantum circuit optimization by topological compaction in the surface code

This work examines the problem of minimizing computation time on a two-dimensional qubit lattice of arbitrary, but fixed dimension, and proposes two algorithms for doing so.

AutoBraid: A Framework for Enabling Efficient Surface Code Communication in Quantum Computing

This paper focuses on the compilation for fault-tolerant quantum hardware and provides a framework for efficiently scheduling braiding paths and discovers that for quantum programs with a local parallelism pattern, the framework guarantees an optimal solution, while the previous greedy-heuristic-based solution cannot.

Surface code quantum computing by lattice surgery

This paper introduces a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer, and shows how lattice surgery allows us to distribute encoded GHZ states in a more direct manner, and how a demonstration of an encoded CNOT between two distance-3 logical states is possible with 53 physical qubits.

Optimization of lattice surgery is NP-hard

This work introduces an optimality condition, which corresponds to a circuit with the lowest resource requirements in terms of physical qubits and computational time, and proves that the complexity of optimizing a quantum circuit in the lattice surgery model is NP-hard.

Surface codes: Towards practical large-scale quantum computation

The concept of the stabilizer, using two qubits, is introduced, and the single-qubit Hadamard, S and T operators are described, completing the set of required gates for a universal quantum computer.

Fault-tolerant, high-level quantum circuits: form, compilation and description

This work introduces a package that converts high-level quantum circuits consisting of commonly used gates into a form employing all decompositions and ancillary protocols needed for fault-tolerant error correction and outputs a standard circuit or a canonical geometric description, a necessity for operating current state-of-the-art hardware architectures using topological quantum codes.

A bridge to lower overhead quantum computation

This work addresses the second challenge of practical large-scale quantum computation, presenting a new technique, bridge compression, which enables remarkably low volume structures to be found that implement complex computations in the surface code.

Two-bit gates are universal for quantum computation.

  • DiVincenzo
  • Physics
    Physical review. A, Atomic, molecular, and optical physics
  • 1995
A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The…

Tradeoffs for reliable quantum information storage in 2D systems

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.

Stabilizer Codes and Quantum Error Correction

An overview of the field of quantum error correction and the formalism of stabilizer codes is given and a number of known codes are discussed, the capacity of a quantum channel, bounds on quantum codes, and fault-tolerant quantum computation are discussed.