# Introduction to Quantum Gate Set Tomography

@article{Greenbaum2015IntroductionTQ, title={Introduction to Quantum Gate Set Tomography}, author={Daniel Greenbaum}, journal={arXiv: Quantum Physics}, year={2015} }

Quantum gate set tomography (GST) has emerged as a promising method for the full characterization of quantum logic gates. In contrast to quantum process tomography (QPT), GST self-consistently and correctly accounts for state preparation and measurement (SPAM) errors. It therefore provides significantly more accurate estimates than QPT as gate fidelities increase into the fault-tolerant regime. We give a detailed review of GST and provide a self-contained guide to its implementation. The method…

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## References

SHOWING 1-10 OF 35 REFERENCES

Robust, self-consistent, closed-form tomography of quantum logic gates on a trapped ion qubit

- Mathematics
- 2013

We introduce and demonstrate experimentally: (1) a framework called "gate set tomography" (GST) for self-consistently characterizing an entire set of quantum logic gates on a black-box quantum…

Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking.

- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2015

A systematic experimental estimate of quantum gate fidelities using randomized benchmarking of 1-qubit gates in the Clifford group is presented, finding evidence that the present limitation to the gate fidelity is mostly related to the external hardware and not the intrinsic behaviour of the qubit.

Robust error bars for quantum tomography

- Mathematics
- 2012

In quantum tomography, a quantum state or process is estimated from the results of measurements on many identically prepared systems. Tomography can never identify the state or process exactly. Any…

On single qubit quantum process tomography for trace-preserving and nontrace-preserving maps

- Mathematics
- 2015

We review single-qubit quantum process tomography for trace-preserving and nontrace-preserving processes, and derive explicit forms of the general constraints for fitting experimental data. These…

Characterizing universal gate sets via dihedral benchmarking

- Computer Science
- 2015

The dihedral benchmarking protocol is a generalization of randomized benchmarking that relaxes the usual unitary 2-design condition and enables direct benchmarking of the $T$ gate even for the gate-dependent error model that is expected in leading approaches to fault-tolerant quantum computation.

Estimating the Coherence of Noise

- Physics
- 2015

It is shown that the coherence of a noise source can be quantified by the unitarity, which relates to the average change in purity averaged over input pure states and provides a lower bound on the optimal achievable gate infidelity under a given noisy process.

Compressibility of Positive Semidefinite Factorizations and Quantum Models

- Computer ScienceIEEE Transactions on Information Theory
- 2016

Applications of compressibility of the dimension of positive semidefinite matrices range from the analysis of experimental data to bounding the one-way quantum communication complexity of Boolean functions.

"J."

- Philosophy
- 1890

however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)…

A Bibliography of Publications in Linear Algebra and its Applications: 1980{1989

- Physics
- 1997

(AB) = B− mrA − lr [WHG79]. (k) [Cha79]. (k, n) [MT79]. 0 [JGK79]. 0− 1 [HP78]. 2 [Sto79]. 2× 2 [Est79]. 3× 3 [AYP79]. A [Nic79]. AB +BA [Nic79]. AX − Y B = C [BK79a]. AX = B [PM79]. AXC = B [PM79].…

Phys

- Rev. Lett. 77, 4281
- 1996