Quantum computing characterization and benchmarking.

Megan Dahlhauser, Travis S. Humble

Megan Lilly, Travis S. Humble

Jonas Helsen

Quantum computers promise to be a revolutionary new technology. However, in order to realise this promise many hurdles must first be overcome. In this thesis we investigate two such hurdles: the presence of noise in quantum computers and limitations on the connectivity and control in large scale quantum computing architectures.In order to combat noise in quantum devices we must first characterize this noise. To do this several diagnostic tools have been developed over the last two decades. The current industry standard for such a diagnostic tool is called randomized benchmarking. Randomized benchmarking doesn't give a full characterization of the noise afflicting the quantum device but rather attempts to give some indication of of the device's average behavior, captured in a quantity called the average fidelity. Because it does not endeavor to characterize every small detail of the noise it can be efficiently applied even to very large quantum devices. However, with this power also comes increased complexity. Randomized benchmarking has a lot of moving parts, and some fairly strong assumptions must be made in order to guarantee its correctness. In this thesis we attempt to justify these assumptions and if possible remove or weaken them, making randomized benchmarking a more robust and general tool. In chapter 6 of this thesis we investigate the finite statistics of randomized benchmarking. We prove strong bounds on the number of samples needed to perform rigorous randomized benchmarking. To do this we make use tools from representation theory. In particular we use a characterization of certain representations of the Clifford group, which we develop in chapter 5. In chapter 7 we re-use these tools to also bound the number of samples needed to perform rigorous unitarity randomized benchmarking, a newer variant of randomized benchmarking quickly gaining in popularity. These results retroactively justify the use of randomized benchmarking in an experimental setting and also provide guidance on optimal statistical practices in the context of randomized benchmarking. In chapter 8 we expand upon the standard randomized benchmarking protocol and formulate a new class of protocols which we call character randomized benchmarking. This new class of protocols removes a critical assumption made in standard randomized benchmarking, making character randomized benchmarking vastly more generally applicable. To show the advantages of character randomized benchmarking we implement it in an experiment characterizing the noise in a Si/SiGe quantum dot device. This experiment is detailed in chapter 9. Finally we deal with the second main topic of this thesis in chapter 10. Large scale quantum computer will, like classical computers, face limitations in the connectivity between different parts of the computer. This is due to a fundamental law in computer design called Rent's rule, which states that the number of wires connecting a (quantum) computer chip to the outside world is much smaller than the number of components in that chip. This means the individual components of the chip can not be controlled individually in parallel. Given that parallelism is absolutely critical for the functioning of quantum computers this is a serious problem for the development of large scale quantum computers. Luckily it is possible to organize quantum computing devices in such a way that they can be controlled using a relatively small amount of input wires. One example of such an organization is called a crossbar architecture. Recently a proposal was made for a crossbar architecture quantum computer in quantum dots, and in chapter 10 of this thesis we investigate in detail the advantages and disadvantages of such an architecture. We focus in particular on its effect on standard quantum error correction procedures, a key part of a functioning quantum computer, and one where parallel control of all parts of the quantum device is essential.

Robson Giles

Akel Hashim, Long B. Nguyen, Noah Goss +16 more

Rapid progress in quantum technology has transformed quantum computing and quantum information science from theoretical possibilities into tangible engineering challenges. Breakthroughs in quantum algorithms, quantum simulations, and quantum error correction are bringing useful quantum computation closer to fruition. These remarkable achievements have been facilitated by advances in quantum characterization, verification, and validation (QCVV). QCVV methods and protocols enable scientists and engineers to scrutinize, understand, and enhance the performance of quantum information-processing devices. In this tutorial, we review the fundamental principles underpinning QCVV, and introduce a diverse array of QCVV tools used by quantum researchers. We define and explain QCVV’s core models and concepts—quantum states, measurements, and processes—and illustrate how these building blocks are leveraged to examine a target system or operation. We survey and introduce protocols ranging from simple qubit characterization to advanced benchmarking methods. Along the way, we provide illustrated examples and detailed descriptions of the protocols, highlight the advantages and disadvantages of each, and discuss their potential scalability to future large-scale quantum computers. This tutorial serves as a guidebook for researchers unfamiliar with the benchmarking and characterization of quantum computers, and also as a detailed reference for experienced practitioners.

Rafael N. Alexander, Peter S. Turner, Stephen D. Bartlett

Randomized benchmarking is routinely used as an efficient method for characterizing the performance of sets of elementary logic gates in small quantum devices. In the measurement-based model of quantum computation, logic gates are implemented via single-site measurements on a fixed universal resource state. Here we adapt the randomized benchmarking protocol for a single qubit to a linear cluster state computation, which provides partial, yet efficient characterization of the noise associated with the target gate set. Applying randomized benchmarking to measurement-based quantum computation exhibits an interesting interplay between the inherent randomness associated with logic gates in the measurement-based model and the random gate sequences used in benchmarking. We consider two different approaches: the first makes use of the standard single-qubit Clifford group, while the second uses recently introduced (non-Clifford) measurement-based 2-designs, which harness inherent randomness to implement gate sequences.