Research led by Dr Shuxiang Cao, Schmidt AI Fellow at the Department of Physics at the University of Oxford, introduces an innovative approach to gate set tomography (GST) that could simplify the characterisation of qudit-based quantum systems. The new methodology has been demonstrated to enhance the efficiency of characterising quantum systems which could greatly impact the ability to scale quantum systems in terms of quantum computing. A paper exploring the novel approach has been published in Physical Review Letters today.
In the context of quantum computing, characterisation refers to the process of accurately determining the properties, performance, and errors of quantum components, particularly quantum gates, states, and measurements. It is a key step in the development and deployment of quantum systems as it enables the understanding and mitigation of errors, ensuring that quantum systems can operate reliably at scale. The ultimate goal of characterisation is to bring quantum components as close to their ideal performance as possible, paving the way for practical and error-tolerant quantum computing.
Qudits vs qubits
The group’s GST methodology is a predictive characterisation method of logic operations (gates) on quantum computing processors and extends not only to qubit-based systems but qudit-based systems as well. While qubits are two-level systems that can be in state 0 or 1, or a superposition of both, qudits are systems with more than two levels. Qudits could be advantageous because they increase information capacity; they also open the way for quantum algorithms to be more efficiently implemented because qudits can perform more complex operations with fewer gates. This can lead to shorter circuit depths and potentially lower error rates. However, characterising qudits has traditionally been very costly in terms of computational resources.
In traditional methods, each two-level system, or subspace, within a qudit is parameterised separately, which results in a method that is parameter-heavy and computationally expensive. The traditional method of characterisation doesn't assume virtual Z gates are special in any way, and so the method has to consider the possibility of errors in every part of the system – this takes a lot of time and computing power. The new methodology however assumes that the virtual Z gates are perfect and error-free. By making this assumption, the number of measurements and calculations needed is drastically reduced, making the whole process faster and easier without sacrificing accuracy.
A simplified model
‘In our methodology, we focussed on reducing the number of parameters,’ comments Dr Cao. ‘We proposed and demonstrated an innovative configuration that requires only the Hadamard gate "H" to be parametrised; by focusing on this gate alone, we have been able to simplify the model significantly.’
To test the new method, the group led by Dr Peter Leek, performed experiments using a special type of quantum system called a ‘qutrit’. A qutrit is a qudit with three levels instead of two, making it more complex but also more powerful for certain quantum computations. The group’s new method produced almost identical results to the traditional method yet required much less effort.
‘Our results give a strong indication that our assumption about the virtual Z gates being error-free was accurate,’ concludes Dr Cao. ‘This means that we can use our method to accurately characterise more complex quantum systems, like those with multiple qubits or qutrits, without getting bogged down by too many calculations. We have developed a promising tool for characterising qudit-based quantum processors, making it easier to develop and scale quantum computing technologies. Our approach could also be particularly useful as quantum processors become more complex.’
Efficient characterisation of qudit logical gates with gate set tomography using an error-free virtual Z gate model, S Cao et al, Physical Review Letters, 17 September 2024