Machine learning methods have replaced traditional instruction-driven computer algorithms in many areas affecting our daily lives, such as facial recognition and self-driving cars. Most commonly, ‘artificial neural networks’ are trained with lots of data, either real or synthetic, to learn patterns in data and to estimate the functional relationship between the input and output variables. Depending on the complexity of the problem, a neural network can have complicated connections between the input and output variables through one or multiple ‘hidden layers’. Prof. Roger Melko is leading a group of researchers at the University of Waterloo and PIQuIL to understand the complex physics of many-particle systems, such as exotic states of matter and phase transitions using machine learning techniques.

A quantum information processor harnesses the power of quantum superposition and quantum entanglement for increased computational capability. In his laboratory for Quantum Information with Trapped Ions (QITI) at the Institute for Quantum Computing at the University of Waterloo, Prof. Rajibul Islam and colleagues are developing a quantum information processor made of laser-cooled atomic ytterbium ions. At sub-milliKelvin temperature, the motion of each ion is nearly frozen as they are trapped and levitated inside an ion-trapping apparatus in an ultra-high vacuum environment. Each ion can be made to behave like a qubit – a quantum register of states labeled 0 and 1 and their infinitely many superpositions – that can be manipulated by shining with laser beams. By appropriately controlling the intensity and frequency of the laser beams, ion-qubits can be made to interact with each other in a programmable way. A remarkable feature of the trapped ion system is the presence of long-range interactions with, in principle, the interaction between any pair of qubits being controllable. The possibility to tune the qubit-qubit interactions creates enormous opportunity to use the ion system as a simulator for many-particle quantum phenomena.

Examples include studying quantum magnetism and quantum phase transitions, computing molecular energies in quantum chemistry with potential applications in drug-discovery as well as simulating fundamental forces in nature to answer open questions like “why do we have more matter than anti-matter?

Following a number of informal discussions, Melko and Islam realized that a neural network could be trained to program a target set of interaction patterns between ion-qubits in a quantum simulator. This is an example of a so-called inverse problem, where calculating the output variable from a set of input variables is trivial but predicting the input variables from a target set of output variable-values is highly non-trivial; sometimes the problem can even be ill-posed. In this case, if the intensities and frequencies of laser beams shining on individual ion-qubits are known, the interactions between qubits can be calculated easily. However, to program the interaction parameters between qubits to simulate a specific quantum system, a non-linear optimization is necessary to determine the laser parameters. For a large system of even a few dozen ions, the optimization can take several hours on a powerful (classical) computer. Worse, if a slightly different interaction parameters are required, the optimizer needs to be rerun again “from scratch” with no “learned” or acquired benefits from the previous computation. Melko and Islam adopted a machine learning approach to solve this problem. Together with their students, Marina Drygala and Yi Hong Teoh, the team generated tens of thousands of synthetic data of qubit-qubit interactions from randomly chosen laser parameters and, using those, trained a neural network to learn the pattern in the data. This initial training of the network involved non-linear optimization and, depending on the number of ion qubits considered, typically took many hours of computation. However, and this is where the formidable payback arises: once the network had been trained, predicting the laser parameters to engineer an arbitrary set of qubit-qubit interactions took less than a millisecond! These exciting results illustrating the confluence of the usage of artificial intelligence to guide new research efforts were published in Quantum Science and Technology, 5 024001 (2020).

The group is now investigating several other problems where machine learning can significantly impact the design of a quantum processor. An example is to accurately predict the quantum state of ions from noisy data. Despite the best engineering efforts, signals from individual ion-qubits, in the form of emitted photons, are typically significantly corrupted by noise arising from unwanted stray photons and noise in the detectors themselves. Further, signals from neighbouring ion-qubits can interfere with each other. A neural network, trained to discern between the various noise origins and the sought signal would boost the efficiency of a quantum processor.