**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

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Joshua Skanes-Norman| Applied Mathematics, University of Waterloo

On Realistic Errors in Quantum Computers

In this thesis, we are concerned with the problem of characterizing noise associated with implementations of quantum circuits. We first explore the notion of error rates of quantum circuits and argue that the semantic distinction between process fidelity as “average error rate” and diamond distance as “worst-case error rate” is wrong. To this end, we analyze their worst-case and average analogies, and show they are proportional to their original measures. We show that the non-unital contributions to the diamond distance are negligible and the discrepancy between the process fidelity and diamond distance is primarily due to unitary errors.

We then turn to a new analysis of cycle benchmarking, a randomized benchmarking-like protocol to estimate the process fidelity of a cycle as engineered by randomized compiling. Using this approach, we prove that gate-dependent noise on the randomized gates is de- scribed by a single perturbation term that decays rapidly as long as the implementation is close to a representation. We also comment on how the protocol can be extended to qudits, what the cycle benchmarking decay actually measures, and how our analysis is amenable to the Fourier analysis of randomized benchmarking. We end with a discussion of how the gate-dependent cycle benchmarking process fidelity relates to gate-dependent randomized compiling.

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.