Reduced space-time and time costs Ising dislocation codes and arbitrary ancillas

@article{Hastings2015ReducedSA,
  title={Reduced space-time and time costs Ising dislocation codes and arbitrary ancillas},
  author={Matthew B. Hastings and Alan Geller},
  journal={Quantum Inf. Comput.},
  year={2015},
  volume={15},
  pages={962-986}
}
We propose two distinct methods of improving quantum computing protocols based on surface codes. First, we analyze the use of dislocations instead of holes to produce logical qubits, potentially reducing spacetime volume required. Dislocations[8, 9] induce defects which, in many respects, behave like Majorana quasi-particles. We construct circuits to implement these codes and present fault-tolerant measurement methods for these and other defects which may reduce spatial overhead. One advantage… Expand
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References

SHOWING 1-10 OF 25 REFERENCES
Simulating chemistry efficiently on fault-tolerant quantum computers
Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. Here we consider methods to make proposedExpand
Fault-tolerant renormalization group decoder for abelian topological codes
TLDR
The 3D generalization of a renormalization group decoding algorithm for topological codes with Abelian anyonic excitations inherits many properties of the 2D algorithm, including a complexity linear in the space-time volume of the memory, which can be parallelized to logarithmic time. Expand
Surface codes: Towards practical large-scale quantum computation
This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer,Expand
Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
We describe two implementations of the optimal error correction algorithm known as the maximum likelihood decoder (MLD) for the 2D surface code with a noiseless syndrome extraction. First, we showExpand
A State Distillation Protocol to Implement Arbitrary Single-qubit Rotations
TLDR
An efficient protocol for distilling other nonstabilizer states that requires only Clifford operations, measurement, and magic states is proposed, efficiently and fault-tolerantly implementing arbitrary, non-Clifford, single-qubit rotations in, on average, constant online circuit depth and polylogarithmic offline resource cost. Expand
Universal quantum computation with ideal Clifford gates and noisy ancillas (14 pages)
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis.Expand
Measurement-only topological quantum computation without forced measurements
We investigate themeasurement-only topological quantum computation (MOTQC) approach proposed by Bonderson et al (2008 Phys. Rev. Lett. 101 010501)where the braiding operation is shown to beExpand
Improving quantum algorithms for quantum chemistry
TLDR
Improvements to the standard Trotter-Suzuki based algorithms used in the simulation of quantum chemistry on a quantum computer by modifying how Jordan-Wigner transformations are implemented to reduce their cost from linear or logarithmic in the number of orbitals to a constant. Expand
Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
TLDR
The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits. Expand
Repeat-until-success: non-deterministic decomposition of single-qubit unitaries
TLDR
An algorithm based on RUS circuits is constructed that approximates an arbitrary single-qubit Z-axis rotation to within distance e, where the number of T gates scales as 1:26 log2(1/e) - 3:53, an improvement of roughly three-fold over state-of-the-art techniques. Expand
...
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3
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