With a universal error-corrected quantum computer still decades away, researchers hope to make current noisy intermediate-scale quantum (NISQ) devices useful in areas such as quantum chemistry and quantum machine learning. Two CQT PhD graduates have proposed a tool that could help.
CQT graduates Tobias Haug and Kishor Bharti and their collaborator show that a metric known as the ‘quantum Fisher information’ is useful to evaluate the power of parametrised quantum circuits, a building block of algorithms for quantum computers. This could pave the way for improved circuit design.
“NISQ devices are very poor in terms of quantum resources,” says Kishor. “Because you need to get your task done while spending little resources, you need to think about all the hacks you can do.” Better circuits could help extract better performance overall.
The researchers published their findings in PRX Quantum on 14 October. Tobias and Kishor started collaborating while they were PhD students at CQT. Tobias completed his PhD in March 2021 and is now at Imperial College London, working with their co-author Myungshik Kim. Kishor completed his PhD in July 2021 and will be moving to the Joint Center for Quantum Information and Computer Science at the University of Maryland.
Building quantum circuits
To get good performance from NISQ devices, researchers frequently implement algorithms using parametrised quantum circuits. A quantum circuit is a sequence of logic gates performed on quantum states. A parametrised quantum circuit has flexible settings: parameters with which their quantum gates can be adjusted.
The flexibility is used in NISQ devices to repeatedly test performance at different settings. The outcomes are analysed by a classical computer, which will then propose a new set of parameters.
In designing parametrised quantum circuits, it is ideal to have as few parameters as possible. This would mean performing fewer measurements, saving time and quantum resources. At the same time, the parametrised quantum circuits should be ‘expressible’, capable of representing a wide set of quantum states. This would give the NISQ device a better chance of solving the target problem well.
“Circuits are built by arranging gates in some order. Which arrangement is better or worse was not something really thought about. We want to use the quantum Fisher information to understand how powerful a particular circuit is, and whether we can remove parameters without sacrificing expressibility,” says Tobias, who is also the first author of the paper.
The quantum Fisher information is a metric that gives an indication of how the quantum states change when parameters are adjusted.
Quantum Fisher information
In their paper, the researchers showed that quantum Fisher information could characterise a circuit’s expressibility and identify which parameters of the circuit are redundant.
As a demonstration, the researchers investigated popular hardware-efficient circuits, composed of layered single-qubit rotations and two-qubit entangling gates in various arrangements. These circuits can be implemented efficiently on existing NISQ devices.
Tobias says, “We found that some circuit arrangements are highly expressible while others are not very expressible. For the first time, we have a diagnostic tool that we can use to analyse any quantum circuit and understand which circuit design is good.”
The researchers think there could be more applications of quantum Fisher information for parametrised quantum circuits and NISQ devices. Other possible extensions of the work include using quantum Fisher information within algorithms to improve optimisation performance.
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