By Aritra Sarkar

If you’ve not yet been impacted by Artificial Intelligence in today’s world, you’ve probably been living under a rock. But does it have any influence on Quantum Computing research? This post will explore the synergies between Artificial Intelligence (AI) and Quantum Computation (QC). In doing so, I will map out the landscape of research directions at the intersection of these two exciting fields.

Let’s start off by defining these two. QC, of course, needs no special introduction to the readers of the QuTech blog. My favorite one-liner is ‘using laws of quantum mechanics to a computational advantage.’ The deliberate vagueness encompasses the full spectrum of scientists between quantum information theorists and quantum computing engineers.

AI, however, is a term that is much harder to define. There are too many dimensions of intelligence – logic, rationality, adaptation, pattern recognition, generalization, efficiency, interaction, explainability, causality, etc. Moreover, it is difficult to distinguish between ‘intelligent behavior’ and ‘fancy computation’. For the sake of this blog post, let’s have a hand-wavy definition of AI as – an advanced form of automation that’s non-trivial to build, but once in place, it can stand in for tasks that take substantial human cognitive effort. The trick is in the subjectivity of ‘substantial effort.’ Pocket calculators and chess-playing bots can both be AI based on whom you are asking. We will dive into these subtleties soon, but let’s go forward with this definition for now.

AI and QC are both special cases of computation. The three steps of computation are input, processing, and output. These will be our compass in mapping out the landscape. In one direction, we will classify the type of input/output. This represents the data. Since quantum information can be represented on a classical storage medium and vice versa, what we really mean here is the native data source. For example, cat and dog images are classical, while a Hamiltonian representing a molecule is inherently quantum, even though both can well be stored as states on bits or qubits. The processing is in the other direction. This represents the nature of physical hardware and the algorithm. Again, QC can be classically simulated (albeit at a worst-case exponential cost); however, we are interested in formulating the algorithmic logic as classical/quantum information processing.

With these distinctions at hand, we get this map:

Figure 1: The 4 classifications of AI&QC: (i) Classical Artificial Intelligence (CAI), (ii) Quantum Computing for Artificial intelligence (QC4AI), (iii) Quantum Artificial Intelligence (QAI), (iv) Artificial Intelligence for Quantum Computing (AI4QC)

Now let’s navigate through this map and learn what wonders these territories have in store.

We will visit them in this order: CAI → QC4AI → QAI → AI4QC.

Classical Artificial Intelligence

The first area we will explore is ‘vanilla’ classical AI. We live in the era of AI systems that can play games better than world champions, diagnose diseases better than healthcare specialists, generate novel images from textual prompts, and whatnot! All these wonders are based on classical algorithms processing classical datasets to find insights with classical semantics.

The history of CAI and classical computing are intertwined. The pioneers of computation often extrapolated their geniuses to contemplate ways to bridge our biological cognitive capabilities with engineered computing machines. As the complexity of computation increases, it gradually extends beyond our limits of cognitively tracking and simulating the system’s internal states and transitions. At this level, we perceive the system’s behavior as imitating intelligence. With this argument, you find your cat to have a mind of its own, while the dynamics of a weakened bacteria as part of a vaccine are predictable and intelligible.

AI can be classified under different modalities. For example, whether semantic labels are associated with the data, whether a model is built before prediction, whether the learning stops after the training phase, or if it’s inspired by human brains and biological evolution. A common way is to differentiate if the logical formulations and intermediate representations are transparent to human reasoning (called symbolic AI) or if the focus is on replicating a behavior (called sub-symbolic AI, statistical AI, data-driven AI, or more commonly, machine learning (ML)).

While the field of AI originally started with symbolic AI (like knowledge graphs and theorem provers), it ran into phases of funding scarcity, called AI winters. This was relieved by low-cost, high-speed computing and the availability of digital data – into what we now experience as the success of ML. Typical ML data-driven problems include classification, clustering, regression, association, dimensionality reduction, optimization, etc.; while learning methods can be supervised (learning associations of given labels and data), unsupervised (finding similarities between data to infer classes), reinforcement (interacting with the environment to gain information), etc. While these solutions were based initially on statistical methods, the spotlight has shifted towards architectures based on artificial neural networks and their more extended variants called deep learning. Apart from neural networks (inspired by models of biological neurons), other inspirations from biological and physical phenomena for heuristic algorithms in optimization include evolutionary computation like genetic algorithms, optimizations based on particle-swarm, thermal annealing, ant colony, flocking bird, etc.

Standing today, there are a couple of directions that researchers think will be most relevant in the years to follow. (i) Specialized hardware for the type of computation tasks inherent to AI is one trajectory that will enable the proliferation of AI. For example, this includes tensor processing units that accelerate ML based on neural networks. (ii) Most AI in the past has focused on pattern recognition, spatial or temporal. However, on a more creative side, we are now witnessing increasing interest in pattern generation – which requires identifying patterns in data and thereby creating novel data that preserve some aspect of the pattern, e.g., your portrait in the style of some specific painter like Vincent van Gogh. (iii) Another essential focus is on explainable AI, which generates logically interpretable outputs, at least by domain experts. This is of paramount importance as we increasingly rely on automation in critical infrastructure and insights in domains like medical diagnostics, transportation, etc. These techniques, like neuro-symbolic AI, bridge the gap between data-driven input/output behavior and logical reasoning/processing-driven semantic intent. (iv) At the societal scale, it is vital that AI remains understandable and employed for the general good, and we don’t end up being enslaved like in sci-fi movie plots. This direction, called AI alignment, becomes crucial in ensuring fairness, for example, by overcoming the limitations of biases in training data. (v) The shiny centerpiece among AI goals is, however, Artificial General Intelligence (AGI) – famously quoted as ‘the last invention that mankind will ever have to make.’ AGI distinguishes itself from most modern narrow/specialized AI systems by allowing itself to generalize over multiple domains, e.g., playing chess as well as detecting fractured bones in X-ray plates. The so-called AI singularity is to AGI what quantum supremacy is to universal QC. At this point, the AGI will surpass humans in most modalities of what we consider intelligent behavior and, after that, self-improve itself beyond our current imagination. While this sounds all sci-fi, there are concrete directions that research teams are pursuing that we can already witness as fragments of such systems.

Quantum Computing for Artificial Intelligence

The next area on our map is QC4AI, where we will acquaint ourselves with the quantum versions of the techniques in the last section. Our goal is to solve the same problems, but better, using a QC. If you’re working in the quantum technology field, you’re pushing the boundaries of what’s computable and what’s not via quantum computing endeavors. Naturally, better computing hardware will also aid information processing involved in AI. Or not? Well, there are arguments on either side.

From a rigorous theoretical perspective, QC is a realizable violation of the complexity-theoretical Church-Turing thesis. This means some procedures in quantum logic cannot be simulated on classical Turing universal automata within the usual polynomial-time overhead. Instead, the time required to calculate the solution using the best possible algorithm grows exponentially with respect to the time on a QC as the problem size grows. Problems in computer science are classified into complexity classes based on the resources needed to solve them, like time, memory, precision, and accuracy. The problems that would benefit the most from speedup on a QC come under the complexity of BQP\BPP. A bounded-error solution to these problems can be reached within a polynomial time (scaling with respect to the problem instance size) on a QC while not being solvable by a probabilistic classical computer using the same resource. There are some algorithms in this region of the complexity zoo that are crucial for AI. These include, for example, solving linear equations, using the larger dimension of Hilbert space via kernels to identify patterns, and generalizing from fewer training data.

The proponents of the other camp are the pragmatists. They interpret the equivalence of computing models in the light of no-free-lunch-theorems. These allow a specific universal computing model to be (polynomially) better for a particular set of tasks than another, similar to how some programming languages are better for some applications while bad for others. In most industrial pipelines, even a constant factor improvement over the previous state-of-the-art algorithms/heuristics can be capitalized for both quality and profit. These are typically quantization of classical statistical learning and ML techniques. Some names of techniques that quantum algorithm designers are focusing on include k-means clustering, recommendation systems, support vector machines, variational auto-encoders, generative adversarial networks, convolutional neural networks, Boltzmann machines, etc.

Many pragmatic problems, however, involve NP-hard optimization, and thus we expect only a Grover search-type quadratic speedup on quantum. In the era of noisy intermediate-scale quantum (NISQ) computing, hybrid algorithms, primarily based on parametric quantum circuits with classical variational optimization are the central focus. Since the state-of-the-art classical algorithms already incorporate heuristics to boost the quantum formulations, various heuristics are also employed in their corresponding quantum formulations, like QAOA and quantum annealing for QUBOs. Despite pitfalls and challenges (like barren plateaus in optimization), many researchers believe this is the most promising direction for quantum advantage in the near term. The diversity of the various application domains of these techniques is impressive – from industrial automation to computational biology, from satellite image processing to financial portfolio management. It is the most active territory on our landscape.

Somewhere between these two levels of rigor and pragmatism lies quantum computation for symbolic AI. Here, the focus is on finding domains that can be cast into and benefit from the formalism of quantum mechanics. This is a much younger field, with initial results now being realized in applications like natural language processing and reinforcement learning.

The way forward under this heading is simple. Keep applying these quantum heuristic algorithms to broader application domains. Keep quantizing more such classical AI techniques. Keep proving complexity benefits for such formalism where possible And most importantly, strive to demonstrate quantum advantage. This involves clever co-design approaches that trade-off between the capabilities of current quantum hardware and the problem formulations.

Quantum Artificial Intelligence

If the world is eventually quantum at finer scales, can we elude the classical middle-man and directly formulate a quantum version of intelligent systems? This is the aim of QAI, the next area on our map.

One of the earliest insights that led to the development of quantum computers is that natural quantum systems can be modeled, simulated, and studied on a controllable quantum system with much less overload than on a classical computer. Such natural systems, specifically in many-body physics and chemistry, hold the key to better materials, a better understanding of physical and bio-molecules, and thereby better computers, medicines, fuels, etc. While a quantum computer or algorithms like VQE are general-purpose, the insights obtained by applying such techniques might lie beyond our otherwise cognitive and computing abilities.

We don’t clearly understand what quantum intelligence would entail. Theories linking quantum mechanics and consciousness, like Orch OR and Integrated Information Theory, are still highly debatable and poorly understood. However, quantum biology, i.e., the study of quantum effects in biological systems, is an active research field. Another foundation offshoot of QAI stems from the irreversible measurement of quantum superpositions. These lead to various interpretations of quantum mechanics. Interpretations like QBism, relational QM, and quantum Darwinism, offer alternate explanations to scenarios like the extended Wigner’s friend thought experiment, many Worlds, and time symmetry. Going forward, QAI research must address these with experimental verification and theoretical rigor.

In efforts to engineer QAI, we will hopefully uncover clues to two of the most profound unsettled conundrums of contemporary science, the measurement problem of quantum mechanics and the hard problem of consciousness.

Artificial Intelligence for Quantum Computing

With the field of AI having its dream run, it can undoubtedly aid in building this fancy gadget – a quantum computer. This is what our last part of the landscape will involve.

The idea looks very simple on paper. As a sloppy explanation, it involves building an artificial quantum computer researcher. Well, if AI has managed to play games like world champions and publish research like scientists, why not quantum research? Automation can be implemented either on the application/algorithms/programming level (which I am going to call AI4QIP, an acronym for quantum information processing) or at the various layers of the computing stack/firmware/processor (which I am going to call AI4QCE, an abbreviation for quantum computer engineering). These two are among the primary focus of the Quantum Machine Learning group of QuTech that I am currently involved in.

AI4QCE can manifest itself as classical AI techniques on data that involve the execution process along the quantum computing stack. These can be recurrent neural networks for error correction, mapping and routing quantum circuits using reinforcement learning, generative adversarial networks for QPU characterization using gate set tomography, etc.

The bridge between AI4QCE and AI4QIP involves various compiler optimizations (e.g., using diagrammatic reasoning, scheduling algorithms, distributed quantum algorithms) or circuit synthesis and computer-aided design for quantum software engineering (quantum circuit versions of techniques used in classical hardware logic synthesis). These tools of AI4QSE (for quantum software engineering) aid the development process of quantum algorithm designers.

Finally, AI4QIP falls under the purview of a somewhat benign form of AGI called automated science. This is my personal research niche, so excuse my enthusiasm. Doing science, so to say, involves a delicate mix of stringent formal proofs and creative selection of axioms. AI4QIP requires a careful selection of this exploration-exploitation trade-off. When we hear a music score composed by an algorithm or read a paragraph of coherent text generated by a large language model, we typically remark that the AI doesn’t inherently understand what it is doing. But in designing quantum algorithms, we are at par with AI, taking a mathematical formulation modeling the physical world for granted and innovating our way up from that base. We do not have added phenomenological advantage over AI systems. Instead, engineered systems are far more efficient in enumerating and evaluating mathematical models than our biological brains. Efforts in this direction have yielded fascinating results in designing new quantum experiments and gaining insights. My research [1] involves formalizing and designing such frameworks and applying them for modeling quantum phenomena and thereby generating novel quantum algorithms. How’s that going so far? Well, that’s a story for the next time.

Aritra started his career as a programmer for satellites. Having placed his code around the earth (across 10+ remote-sensing and space observatory satellites) and the moon (aboard ISRO’s Chandrayaan-2), he started wondering about the limits of information processing. That rabbit hole led him to quantum computation, and in this pursuit, to the Netherlands. During his master’s thesis at QuTech, he worked on developing quantum algorithms for applications in genomics. Thereafter, in his doctoral research, he extended these techniques for causal modeling and reinforcement learning. Currently, he is a postdoctoral researcher in the Quantum Machine Learning group within QuTech’s Quantum Computing Division.He loves creating mind maps of research fields, stemming from his passion for interdisciplinary exploration. His current research interests are in artificial general intelligence and quantum program synthesis. In his free time, Aritra likes building his website, reading about the philosophy of science, and playing Dota2.

Footnote

1. The cover banner is a collage of images depicting human intelligence (left), artificial intelligence (right), and a quantum mechanical system (center). The classical interfaces of the quantum system are controlled, sensed, and interpreted using artifacts of mathematical logic and corresponding semantics.

References

[1] A. Sarkar, “Applications of quantum computation and algorithmic information for causal modeling in genomics
and reinforcement learning,” Ph.D. dissertation, Delft University of Technology, Jul. 2022.