Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque and unwieldy. We show how to transform the process matrix of a gate into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generators, classify them, and show how to represent the error generator of any gate as a mixture of elementary error generators with various rates. Finally, we show how to build a large variety of reduced models for gate errors by combining elementary error generators and/or entire subsectors of generator space. We conclude with a few examples of reduced models, including one with just 9N2 parameters that describes almost all commonly predicted errors on an N-qubit processor.
Nuclear spins were among the first physical platforms to be considered for quantum information processing1,2, because of their exceptional quantum coherence3 and atomic-scale footprint. However, their full potential for quantum computing has not yet been realized, owing to the lack of methods with which to link nuclear qubits within a scalable device combined with multi-qubit operations with sufficient fidelity to sustain fault-tolerant quantum computation. Here we demonstrate universal quantum logic operations using a pair of ion-implanted 31P donor nuclei in a silicon nanoelectronic device. A nuclear two-qubit controlled-Z gate is obtained by imparting a geometric phase to a shared electron spin4, and used to prepare entangled Bell states with fidelities up to 94.2(2.7)%. The quantum operations are precisely characterized using gate set tomography (GST)5, yielding one-qubit average gate fidelities up to 99.95(2)%, two-qubit average gate fidelity of 99.37(11)% and two-qubit preparation/measurement fidelities of 98.95(4)%. These three metrics indicate that nuclear spins in silicon are approaching the performance demanded in fault-tolerant quantum processors6. We then demonstrate entanglement between the two nuclei and the shared electron by producing a Greenberger–Horne–Zeilinger three-qubit state with 92.5(1.0)% fidelity. Because electron spin qubits in semiconductors can be further coupled to other electrons7–9 or physically shuttled across different locations10,11, these results establish a viable route for scalable quantum information processing using donor nuclear and electron spins.
As noise limits the performance of quantum processors, the ability to characterize this noise and develop methods to overcome it is essential for the future of quantum computing. In this report, we develop a complete set of tools for improving quantum processor performance at the application level, including low-level physical models of quantum gates, a numerically efficient method of producing process matrices that span a wide range of model parameters, and full-channel quantum simulations. We then provide a few examples of how to use these tools to study the effects of noise on quantum circuits.
After decades of R&D, quantum computers comprising more than 2 qubits are appearing. If this progress is to continue, the research community requires a capability for precise characterization (“tomography”) of these enlarged devices, which will enable benchmarking, improvement, and finally certification as mission-ready. As world leaders in characterization -- our gate set tomography (GST) method is the current state of the art – the project team is keenly aware that every existing protocol is either (1) catastrophically inefficient for more than 2 qubits, or (2) not rich enough to predict device behavior. GST scales poorly, while the popular randomized benchmarking technique only measures a single aggregated error probability. This project explored a new insight: that the combinatorial explosion plaguing standard GST could be avoided by using an ansatz of few-qubit interactions to build a complete, efficient model for multi-qubit errors. We developed this approach, prototyped it, and tested it on a cutting-edge quantum processor developed by Rigetti Quantum Computing (RQC), a US-based startup. We implemented our new models within Sandia’s PyGSTi open-source code, and tested them experimentally on the RQC device by probing crosstalk. We found two major results: first, our schema worked and is viable for further development; second, while the Rigetti device is indeed a “real” 8-qubit quantum processor, its behavior fluctuated significantly over time while we were experimenting with it and this drift made it difficult to fit our models of crosstalk to the data.