# Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes

@article{Lavasani2018LowOC, title={Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes}, author={Ali Lavasani and Maissam Barkeshli}, journal={Physical Review A}, year={2018} }

One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the $\mathbb{Z}_2$ surface code. Logical qubits can be encoded in a variety of ways in the surface code, based on either boundary defects, holes, or bulk twist defects. However proposed fault-tolerant implementations of the Clifford group in these schemes are limited and often require unnecessary overhead. For example, the Clifford phase gate in certain planar…

## Figures and Tables from this paper

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## 9 Citations

The boundaries and twist defects of the color code and their applications to topological quantum computation

- Physics, Computer ScienceQuantum
- 2018

This work builds upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes and provides lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects.

Universal logical gates with constant overhead: instantaneous Dehn twists for hyperbolic quantum codes

- Physics, MathematicsQuantum
- 2019

The results suggest the possibility of universal fault tolerant quantum computation with constant space overhead and time overhead of $\mathcal{O}(d/\log d)$ for quantum circuits that allow parallel gate operations, this yields the optimal scaling of space-time overhead known to date.

A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery

- Physics, Computer ScienceQuantum
- 2019

No knowledge of quantum error correction is necessary to understand the schemes in this paper, but only the concepts of qubits and measurements, which are based on surface-code patches.

Logical Majorana fermions for fault-tolerant quantum simulation

- Physics
- 2021

We show how to absorb fermionic quantum simulation’s expensive fermion-to-qubit mapping overhead into the overhead already incurred by surface-code-based fault-tolerant quantum computing. The key…

Low-overhead fault-tolerant quantum computing using long-range connectivity

- Physics
- 2021

Vast numbers of qubits will be needed for large-scale quantum computing using today’s faulttolerant architectures due to the overheads associated with quantum error correction. We present a scheme…

Instantaneous braids and Dehn twists in topologically ordered states

- Mathematics, Physics
- 2020

A defining feature of topologically ordered states of matter is the existence of locally indistinguishable states on spaces with non-trivial topology. These degenerate states form a representation of…

Surface code dislocations have code distance L+O(1)

- Physics
- 2019

In [Hastings et al 2014] it is stated that the code distance of a logical qubit stored using dislocations is 2L + O(1), where L is the separation between the dislocation twists. This code distance…

Fault-Tolerant Gates on Hypergraph Product Codes

- Computer Science, Physics
- 2019

This work demonstrates how to perform Clifford gates on this class of codes using code deformation and generalizes punctures and wormhole defects to perform a universal set of gates within a single block of the class of hypergraph product codes.

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