# Optimal two-qubit circuits for universal fault-tolerant quantum computation

@article{Glaudell2020OptimalTC, title={Optimal two-qubit circuits for universal fault-tolerant quantum computation}, author={Andrew N. Glaudell and Neil J. Ross and Jacob M. Taylor}, journal={npj Quantum Information}, year={2020}, volume={7}, pages={1-11} }

We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS = diag(1, 1, 1, i ). The Clifford+CS gate set is universal for quantum computation and its elements can be implemented fault-tolerantly in most error-correcting schemes through magic state distillation. Since non-Clifford gates are typically more expensive to perform in a fault-tolerant manner, it is often desirable to construct circuits that use few CS…

## 11 Citations

Fixed-Depth Two-Qubit Circuits and the Monodromy Polytope

- Mathematics
- 2019

For a native gate set which includes all single-qubit gates, we apply results from symplectic geometry to analyze the spaces of two-qubit programs accessible within a fixed number of gates. These…

Two-Qubit Circuit Depth and the Monodromy Polytope

- MathematicsQuantum
- 2020

Results from symplectic geometry are applied to analyze the spaces of two-qubit programs accessible within a fixed number of gates to yield an explicit description of this subspace as a convex polytope, presented by a family of linear inequalities themselves accessible via a finite calculation.

On the Structure of the CNOT-Dihedral Group

- Mathematics
- 2020

In this note we present explicit canonical forms for all the elements in the $2$-qubit CNOT-Dihedral group, with minimal numbers of controlled-$S$ ($CS$) and controlled-$X$ ($CX$) gates, using the…

Quantum Theory from Principles, Quantum Software from Diagrams

- Mathematics
- 2021

This thesis consists of two parts. The first part is about how quantum theory can be recovered from first principles, while the second part is about the application of diagrammatic reasoning,…

T-count and T-depth of any multi-qubit unitary

- Mathematics
- 2021

While implementing a quantum algorithm it is crucial to reduce the quantum resources, in order to obtain the desired computational advantage. For most fault-tolerant quantum errorcorrecting codes the…

J un 2 02 1 Generators and Relations for the Group O n ( Z [ 1 2 ] )

- Mathematics
- 2021

We give a finite presentation by generators and relations for the group On(Z[1/2]) of ndimensional orthogonal matrices with entries in Z[1/2]. We then obtain a similar presentation for the group of…

A polynomial time and space heuristic algorithm for T-count

- Computer ScienceQuantum Science and Technology
- 2021

This work focuses on reducing the physical cost of implementing quantum algorithms when using the state-of-the-art fault-tolerant quantum error correcting codes, in particular, those for which implementing the T gate consumes vastly more resources than the other gates in the gate set.

Generators and Relations for the Group On(Z[1/2])

- MathematicsQPL
- 2021

A finite presentation by generators and relations is given for the group On(Z[ 1/2]) of ndimensional orthogonal matrices with entries in Z[1/2] and for thegroup of n-dimensional orthosomatic matrices of the form M/ √ 2, where k is a nonnegative integer and M is an integer matrix.

Optimized fermionic SWAP networks with equivalent circuit averaging for QAOA

- Physics
- 2021

Akel Hashim, 2, 3, ∗ Rich Rines, ∗ Victory Omole, Ravi K. Naik, 3 John Mark Kreikebaum, 5, † David I. Santiago, Frederic T. Chong, 6 Irfan Siddiqi, 3, 5 and Pranav Gokhale ‡ Quantum Nanoelectronics…

Experimental implementation of non-Clifford interleaved randomized benchmarking with a controlled-
S
gate

- Physics, Computer Science
- 2020

Calibration of a low error non-Clifford Controlled-\frac{\pi}{2}$ phase (CS) gate on a cloud based IBM Quantum computing using the Qiskit Pulse framework is demonstrated.

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