How To Combine Quantum Computing And Machine Learning
Between Fireworks And Rockets
Quantum Machine Learning promises breakthroughs by merging two very different worlds: probabilistic pattern recognition of machine learning and the unitary dynamics of quantum computing. Can we turn short-lived fireworks into rockets—systems powerful and stable enough to achieve real quantum advantage?
by Frank ZickertAugust 29, 2025
Quantum Machine Learning is the field of research that combines principles from Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. with traditional Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. to solve complex problems more efficiently than classical approaches.
That is the promise. And if you want to become a Quantum Machine Learning Researcher, it is your duty to fulfill that promise.
On an abstract level, the idea sounds simple: take the raw power of Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. add the flexibility of Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. , and expect breakthroughs.
However, as soon as you get down to specifics, difficulties arise.
Figure 1. What are you building?
It is all too easy to build fireworks. Things that light up impressively but burn out without direction. It is difficult, on the other hand, to build a real rocket. An engine that converts explosions into controlled thrust that is powerful enough to escape the force of gravity.
And this is where the real obstacle lies. Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. and Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. approach problems in fundamentally different ways.
Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. , on the other hand, works according to the principle of Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator.. This is the rule according to which one Quantum State is... transforms into another without losing or creating information.
You can think of it as a perfectly reversible rotation in a very high-dimensional Hilbert Space. Just as turning a Rubik's cube shifts its stickers without tearing or duplicating them, a Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. rearranges the Amplitude of a Quantum State is... while keeping the total probability sum exactly the same.
Figure 2. The Rubik's cube
Two key features make a Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. special:
Reversibility: Every Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. has an Inverse. Applying the transformation and then its Inverse returns you to the original Quantum State is....
Probability-preserving: Since the Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. preserves length (technically, it preserves Inner Product), the total probability of all possible outcomes remains at .
So when we talk about the Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator., we mean that we transform the Quantum State is... in a structured, reversible way. Nothing is lost during this process. Randomness and irreversibility only occur when you finally Measurement the Quantum State is....
Essentially, Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. treats information as error-prone but correctable through Optimization is.... Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. , by contrast, strictly preserves information, so much so that every computation can be Inverse.
At first glance, these two concepts don't fit. They don't even seem to belong in the same workshop. But this is precisely where Quantum Machine Learning is the field of research that combines principles from Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. with traditional Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. to solve complex problems more efficiently than classical approaches. positions itself. It finds itself in a challenging area where two conflicting philosophies come together.
Figure 3. Quantum Computing and Machine Learning do not live side by side in Quantum Machine Learning
The task is not simply to place them side by side. It is about developing a hybrid engine in which probabilistic training loops work together with Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. without being thrown off course by their differences.
So, the Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. of a Quantum System is described by a Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. acting on an initial Quantum State is... that we know in advance. In practice, this An Unitary operator is built from a finite set of Quantum Gate within the Quantum Circuit. Each Quantum Gate is itself a An Unitary operator. By combining them in sequence, we obtain the overall Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator.that defines how the Quantum Circuit acts on its input. This is not so different from a classical computer program, which can be understood as a composition of Logical Operator The distinction is that in the Quantum Circuit case the operators are unitary and not logical.
Once we have internalized the idea that a Quantum Circuit generates a Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. from simple building blocks, known as Quantum Gate a new question arises: How can we design Quantum Circuit that generate Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. that are not fixed but adaptable? The analogy to a classical computer program proves helpful once again.
Let's consider a function. In Python, we define functions with the keyword def, followed by the name of the function and a list of arguments in parentheses. The function body contains a series of statements that depend on and manipulate these parameters.
function.py
1
2
defadd(a, b):
return a+b
In a similar way, we can create Quantum Circuit. Just as Logical Operator use parameter values, Quantum GateUnitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator.Quantum State is... based on parameters. For example, rotations use the rotation angle as a parameter.
When we do not fix these parameters within the Quantum Circuit and expose them externally, we create a Parameterized Quantum Circuit. This circuit acts as a template that represents different Unitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. depending on the parameter values.
Figure 4. Parameterized Quantum Circuit
Parameterized Quantum Circuit enable the integration of Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. and Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. into Quantum Machine Learning is the field of research that combines principles from Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. with traditional Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. to solve complex problems more efficiently than classical approaches. . In Quantum Machine Learning is the field of research that combines principles from Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. with traditional Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. to solve complex problems more efficiently than classical approaches. , the Parameterized Quantum Circuit acts as a Model is... within the standard Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. Training Loop. It thus functions like aAn artificial neural network is a computational model of interconnected nodes inspired by biological neurons, used to approximate functions and recognize patterns. in classical Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. and serves as a tunable mapping of input data to predictions.
Even though Quantum State is... preserve all information during theirUnitary evolution is the reversible, deterministic time evolution of a quantum system governed by a unitary operator. we cannot directly access this information. The complete Quantum State is... generated by a Quantum Circuit exists only as a mathematical object.
To extract information, we must apply a Measurement that collapses the complex Quantum State is... into a defined and accessibleBasis State.
Unfortunately, this Measurement is irreversible and the accessibleBasis State reveals only part of the information. In Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. Measurement results are inherently probabilistic. Running the same Quantum Circuit multiple times with identical input states results in different Measurement that originate from a Probability Distribution defined by the Quantum State is....
The Probabilistic Perspective
This contrasts with the deterministic results expected in classical computing.
Consequently, when applying Quantum Circuit to Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. this probabilistic nature poses a challenge. Classical Model is... train on datasets with clear target labels, such as class indices or real output values. In contrast, a single evaluation of a Quantum Circuit provides only a random sample from its output Probability Distribution and no definitive prediction that can be directly compared to a label.
This has important implications for combining Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. with Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. .
The Training Loop must therefore be built around extracting useful information from these Probability Distribution since they are the only channel through which the quantum Model is... communicates with the classical world.
A typical way to cope with the probabilistic Measurement, is to work with the computation of Expectation Value that further reduce the statistical quantities toward classical prediction targets. In this way, the Probability Distribution of Measurement outcomes is reduced to averaged values that are compatible with Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. Loss Function
Quantum Machine Learning is the field of research that combines principles from Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. with traditional Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. to solve complex problems more efficiently than classical approaches. is still a long way from reaching its full potential.
Parameterized Quantum Circuit represent just one specific way of combining Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. with Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. This is a way that caters to today's Noisy Intermediate-Scale Quantum refers to the current generation of quantum devices that have enough qubits to run non-trivial algorithms but are still small and error-prone, limiting their reliability and scalability. The Quantum Circuit are deliberately short-lived to withstand Decoherence, while long-term information is stored and processed classically. This hybrid pattern works for now, but it is not the last word.
In just a few years, the landscape will change once Error CorrectionLogical Qubit become available. With reliable Quantum Random Access Memory, new integration patterns will open up. Instead of squeezing Quantum Information into short-lived Quantum Circuit and letting them collapse prematurely, we could design architectures that make more direct use of the rich internal structure of Quantum State is.... Even before we reach that stage, there is untapped potential: in current practice, Measurement results are often reduced to a single Expectation Value, but Probability Distributioncontain more information than a single number. Exploring Loss Function based on Probability Distribution rather than averages could offer better training signals and faster convergence.
At the same time, we must not ignore the already apparent limitations of the current Parameterized Quantum Circuit framework. One of the most pressing problems is that of Barren Plateau. These are areas of the parameter space where the training signal disappears as the depth of the Quantum Circuit increases. This is an active area of research: How can Parameterized Quantum Circuit be designed so that they are expressive enough to represent meaningful patterns, yet structured enough to remain trainable?
This brings us to the most important question we have not yet addressed: Why?. Why should we pursue a Quantum Machine Learning is the field of research that combines principles from Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. with traditional Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. to solve complex problems more efficiently than classical approaches. approach? Where is theQuantum Advantage in Quantum Machine Learning is the field of research that combines principles from Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. with traditional Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. to solve complex problems more efficiently than classical approaches. Why should a Quantum System be superior to other Model is...? This is the search for the essence of Quantum Machine Learning is the field of research that combines principles from Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. with traditional Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming. to solve complex problems more efficiently than classical approaches.
In Search Of The Essence Of Quantum Machine Learning
