How To Combine Quantum Computing And Machine Learning

Quantum Machine Learning is the field of research that combines principles from quantum computing with traditional machine learning 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.

Quantum Machine Learning: Is It Engineering Or Research?

The Tension Between Working Code And Deeper Meaning Of Learning

August 26, 2025•5 min

Quantum Machine Learning promises results that seem otherwise impossible. But what does that really mean for you? Is it about building pipelines that work today? Or is it about asking the questions that shape tomorrow? The answer may decide not just how you work, but where you'll stand when the field breaks through.

On an abstract level, the idea sounds simple: take the raw power of Quantum Computing,Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics.
Learn more about Quantum Computing add the flexibility of Machine LearningMachine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning, and expect breakthroughs.

However, as soon as you get down to specifics, difficulties arise.

And this is where the real obstacle lies. Quantum ComputingQuantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics.
Learn more about Quantum Computing and Machine LearningMachine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning approach problems in fundamentally different ways.

On one side is Machine LearningMachine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning. It works through Probabilistic Pattern RecognitionProbabilistic Pattern Recognition is the classification of patterns based on probability models, where decisions are made by estimating class-conditional probabilities and applying Bayes' rule.
Learn more about Probabilistic Pattern Recognition, where ModelA **model** in machine learning is a mathematical representation of patterns learned from data. It takes **inputs** (features) and produces **outputs** (predictions or classifications) based on relationships it has identified during training. Essentially, it’s a function that generalizes from examples to make decisions or predictions on new data.
Learn more about Models start as rough approximations, accept errors as inevitable, and rely on OptimizationOptimization is the process of finding the best possible solution to a problem within given constraints. It involves adjusting variables to minimize or maximize an objective function, such as cost, time, or efficiency. In simple terms, it’s about achieving the most effective outcome with the least waste or effort.
Learn more about Optimization to steadily reduce these errors until they generalizeGeneralization in machine learning is the model’s ability to perform well on new, unseen data, not just the data it was trained on. It measures how well the model captures the underlying patterns rather than memorizing the training examples. Poor generalization usually means overfitting—when a model learns noise or details specific to the training set instead of general rules.
Learn more about GeneralizationBishop, C., 2006, Information Science and Statistics, . However, after training, a Machine Learning ModelA **model** in machine learning is a mathematical representation of patterns learned from data. It takes **inputs** (features) and produces **outputs** (predictions or classifications) based on relationships it has identified during training. Essentially, it’s a function that generalizes from examples to make decisions or predictions on new data.
Learn more about Model provides a single, definitive answer to a specific questionBennett, K., 2006, The Journal of Machine Learning Research, Vol. 7, pp. 1265-1281.

Quantum ComputingQuantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics.
Learn more about Quantum Computing, on the other hand, works according to the principle of Unitary EvolutionUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution. This is the rule according to which one Quantum StateA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State transforms into another without losing or creating information.

You can think of it as a perfectly reversible rotation in a very high-dimensional (Hilbert) spaceA Hilbert space is a complete vector space equipped with an inner product, which allows for measuring angles and lengths between vectors. "Complete" means that every Cauchy sequence of vectors converges to a vector within the space. It generalizes the idea of Euclidean space to possibly infinite dimensions and forms the foundation for quantum mechanics and functional analysis.
Learn more about Hilbert Space. Just as turning a Rubik's cube shifts its stickers without tearing or duplicating them, a unitary transformationUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution rearranges the AmplitudesIn quantum computing an amplitude is a complex number that describes the weight of a basis state in a quantum superposition. The squared magnitude of an amplitude gives the probability of measuring that basis state. Amplitudes can interfere, this means adding or canceling, allowing quantum algorithms to bias outcomes toward correct solutions.
Learn more about Amplitude of a Quantum StateA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State while keeping the total probability sum exactly the same.

Two key features make a unitary transformationUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution special:
• Reversibility: Every unitary transformationUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
  Learn more about Unitary Evolution has an InverseIn math, an *inverse* undoes the effect of an operation or function. For a number, the inverse under addition is its opposite (e.g., the inverse of 5 is −5), and under multiplication it’s its reciprocal (e.g., the inverse of 5 is 1/5). For a function ( f(x) ), the inverse ( f^(x) ) reverses its action so that ( f(f^(x)) = x ).
  Learn more about Inverse. Applying the transformation and then its InverseIn math, an *inverse* undoes the effect of an operation or function. For a number, the inverse under addition is its opposite (e.g., the inverse of 5 is −5), and under multiplication it’s its reciprocal (e.g., the inverse of 5 is 1/5). For a function ( f(x) ), the inverse ( f^(x) ) reverses its action so that ( f(f^(x)) = x ).
  Learn more about Inverse returns you to the original Quantum StateA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
  Learn more about Quantum State.
• Probability-preserving: Since the transformationUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
  Learn more about Unitary Evolution preserves length (technically, it preserves Inner ProductsAn inner product is a mathematical operation that takes two vectors and returns a single number measuring how similar or aligned they are. In Euclidean space, it’s the sum of the products of corresponding components (e.g., ). It generalizes the dot product and defines geometric concepts likelength and angle in vector spaces.
  Learn more about Inner Product), the total probability of all possible outcomes remains at .

So when we talk about the Unitary EvolutionUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution, we mean that we transform the Quantum StateA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State in a structured, reversible way. Nothing is lost during this process. Randomness and irreversibility only occur when you finally measureIn quantum computing, measurement is the process of extracting classical information from a quantum state. It collapses a qubit’s superposition into one of its basis states (usually or ), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition.
Learn more about Measurement the Quantum StateA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State.

Essentially, Machine LearningMachine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning treats information as error-prone but correctable through OptimizationOptimization is the process of finding the best possible solution to a problem within given constraints. It involves adjusting variables to minimize or maximize an objective function, such as cost, time, or efficiency. In simple terms, it’s about achieving the most effective outcome with the least waste or effort.
Learn more about Optimization. Quantum ComputingQuantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics.
Learn more about Quantum Computing, by contrast, strictly preserves information, so much so that every computation can be reversedIn math, an *inverse* undoes the effect of an operation or function. For a number, the inverse under addition is its opposite (e.g., the inverse of 5 is −5), and under multiplication it’s its reciprocal (e.g., the inverse of 5 is 1/5). For a function ( f(x) ), the inverse ( f^(x) ) reverses its action so that ( f(f^(x)) = x ).
Learn more about 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 LearningQuantum Machine Learning is the field of research that combines principles from quantum computing with traditional machine learning to solve complex problems more efficiently than classical approaches.
Learn more about Quantum Machine Learning positions itself. It finds itself in a challenging area where two conflicting philosophies come together.

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 dynamicsUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution without being thrown off course by their differences.

So, the evolutionUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution of a Quantum SystemA quantum system is any physical system that is subject to the laws of quantum mechanics, whereby quantities such as energy or spin can only assume discrete (quantized) values. Its behavior is described by a wave function that encodes the probabilities of possible measurement results.
Learn more about Quantum System is described by a unitary transformationUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution acting on an initial Quantum StateA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State that we know in advance. In practice, this Unitary OperatorA **unitary operator** is a linear operator ( U ) on a complex vector space that satisfies ( U^\dagger U = UU^\dagger = I ), meaning it preserves inner products. In simpler terms, it preserves the **length** and **angle** between vectors—so it represents a **reversible, norm-preserving transformation**. In quantum mechanics, unitary operators describe the evolution of isolated systems because they conserve probability.
Learn more about Unitary Operator is built from a finite set of Quantum GatesA quantum gate is a basic operation that changes the state of one or more qubits, similar to how a logic gate operates on bits in classical computing. It uses unitary transformations, meaning it preserves the total probability (the state’s length in complex space). Quantum gates enable superposition and entanglement, allowing quantum computers to perform computations that classical ones cannot efficiently replicate.
Learn more about Quantum Gate within the circuit modelA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit. Each Quantum GateA quantum gate is a basic operation that changes the state of one or more qubits, similar to how a logic gate operates on bits in classical computing. It uses unitary transformations, meaning it preserves the total probability (the state’s length in complex space). Quantum gates enable superposition and entanglement, allowing quantum computers to perform computations that classical ones cannot efficiently replicate.
Learn more about Quantum Gate is itself a Unitary OperatorA **unitary operator** is a linear operator ( U ) on a complex vector space that satisfies ( U^\dagger U = UU^\dagger = I ), meaning it preserves inner products. In simpler terms, it preserves the **length** and **angle** between vectors—so it represents a **reversible, norm-preserving transformation**. In quantum mechanics, unitary operators describe the evolution of isolated systems because they conserve probability.
Learn more about Unitary Operator. By combining them in sequence, we obtain the overall transformationUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolutionthat defines how the Quantum CircuitA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about 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 operationsA logical operator is a symbol or word used to combine or modify Boolean (true/false) values in logic or programming. The main ones are **AND (&&)**, **OR (||)**, and **NOT (!)**. They determine the truth of a compound statement — for example, “A AND B” is true only if both A and B are true.
Learn more about Logical Operator The distinction is that in the Quantum CircuitA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit case the operators are unitary and not logical.

Once we have internalized the idea that a Quantum CircuitA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit generates a unitary transformationUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution from simple building blocks, known as Quantum Gates,A quantum gate is a basic operation that changes the state of one or more qubits, similar to how a logic gate operates on bits in classical computing. It uses unitary transformations, meaning it preserves the total probability (the state’s length in complex space). Quantum gates enable superposition and entanglement, allowing quantum computers to perform computations that classical ones cannot efficiently replicate.
Learn more about Quantum Gate a new question arises: How can we design circuitsA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit that generate unitary transformationsUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution that are not fixed but adaptable? The analogy to a classical computer program proves helpful once again.

Let's consider a function. In PythonPython is a high-level, interpreted programming language known for its simple syntax and readability. It supports multiple programming paradigms, including procedural, object-oriented, and functional programming. Its extensive standard library and large ecosystem make it useful for tasks ranging from web development to data science and automation.
Learn more about 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.

In a similar way, we can create Quantum CircuitsA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit. Just as Logical OperatorsA logical operator is a symbol or word used to combine or modify Boolean (true/false) values in logic or programming. The main ones are **AND (&&)**, **OR (||)**, and **NOT (!)**. They determine the truth of a compound statement — for example, “A AND B” is true only if both A and B are true.
Learn more about Logical Operator use parameter values, Quantum GatesA quantum gate is a basic operation that changes the state of one or more qubits, similar to how a logic gate operates on bits in classical computing. It uses unitary transformations, meaning it preserves the total probability (the state’s length in complex space). Quantum gates enable superposition and entanglement, allowing quantum computers to perform computations that classical ones cannot efficiently replicate.
Learn more about Quantum Gate transformUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution Quantum StatesA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State based on parameters. For example, rotations use the rotation angle as a parameter.

When we do not fix these parameters within the Quantum CircuitA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit and expose them externally, we create a Parameterized Quantum CircuitA **Parameterized Quantum Circuit (PQC)** is a quantum circuit where certain gate operations depend on adjustable parameters—typically real numbers representing rotation angles. These parameters are tuned (often by classical optimization) to perform a specific task, such as minimizing a cost function. PQCs are central to **variational quantum algorithms**, where quantum computation provides state preparation and measurement, and a classical computer optimizes the parameters.
Learn more about Parameterized Quantum Circuit. This circuit acts as a template that represents different Unitary EvolutionsUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution depending on the parameter values.

Parameterized Quantum CircuitsA **Parameterized Quantum Circuit (PQC)** is a quantum circuit where certain gate operations depend on adjustable parameters—typically real numbers representing rotation angles. These parameters are tuned (often by classical optimization) to perform a specific task, such as minimizing a cost function. PQCs are central to **variational quantum algorithms**, where quantum computation provides state preparation and measurement, and a classical computer optimizes the parameters.
Learn more about Parameterized Quantum Circuit enable the integration of Quantum ComputingQuantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics.
Learn more about Quantum Computing and Machine LearningMachine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning into Quantum Machine LearningQuantum Machine Learning is the field of research that combines principles from quantum computing with traditional machine learning to solve complex problems more efficiently than classical approaches.
Learn more about Quantum Machine Learning. In Quantum Machine LearningQuantum Machine Learning is the field of research that combines principles from quantum computing with traditional machine learning to solve complex problems more efficiently than classical approaches.
Learn more about Quantum Machine Learning, the Parameterized Quantum CircuitA **Parameterized Quantum Circuit (PQC)** is a quantum circuit where certain gate operations depend on adjustable parameters—typically real numbers representing rotation angles. These parameters are tuned (often by classical optimization) to perform a specific task, such as minimizing a cost function. PQCs are central to **variational quantum algorithms**, where quantum computation provides state preparation and measurement, and a classical computer optimizes the parameters.
Learn more about Parameterized Quantum Circuit acts as a ModelA **model** in machine learning is a mathematical representation of patterns learned from data. It takes **inputs** (features) and produces **outputs** (predictions or classifications) based on relationships it has identified during training. Essentially, it’s a function that generalizes from examples to make decisions or predictions on new data.
Learn more about Model within the standard Machine LearningMachine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning Training LoopA **training loop** in quantum computing is the iterative process used to optimize parameters in a hybrid quantum-classical algorithm, such as a variational quantum circuit. The quantum computer evaluates a cost function by running the circuit and measuring outputs, while a classical optimizer updates the circuit parameters to minimize (or maximize) that cost. This loop repeats until the model converges to an optimal or near-optimal solution.
Learn more about Training Loop. It thus functions like aNeural NetworkAn artificial neural network is a computational model of interconnected nodes inspired by biological neurons, used to approximate functions and recognize patterns.
Learn more about Neural Network in classical Machine LearningMachine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning and serves as a tunable mapping of input data to predictions.

Even though Quantum StatesA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State preserve all information during theirtransformationsUnitary evolution is the rule that describes how a closed quantum system changes over time according to the Schrödinger equation. The system’s state vector is transformed by a *unitary operator*, meaning probabilities (the total norm) are exactly preserved. This ensures quantum evolution is reversible and information is never lost.
Learn more about Unitary Evolution we cannot directly access this information. The complete Quantum StateA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State generated by a Quantum CircuitA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit exists only as a mathematical object.

To extract information, we must apply a measurement operatorIn quantum computing, measurement is the process of extracting classical information from a quantum state. It collapses a qubit’s superposition into one of its basis states (usually or ), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition.
Learn more about Measurement that collapses the complex Quantum StateA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State into a defined and accessibleBasis StateA basis state in quantum computing is one of the fundamental states that form the building blocks of a quantum system’s state space. For a single qubit, the basis states are and ; any other qubit state is a superposition of these. In systems with multiple qubits, basis states are all possible combinations of s and s (e.g., , , , and ), forming an orthonormal basis for the system’s Hilbert space.
Learn more about Basis State.

Unfortunately, this MeasurementIn quantum computing, measurement is the process of extracting classical information from a quantum state. It collapses a qubit’s superposition into one of its basis states (usually or ), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition.
Learn more about Measurement is irreversible and the accessibleBasis StateA basis state in quantum computing is one of the fundamental states that form the building blocks of a quantum system’s state space. For a single qubit, the basis states are and ; any other qubit state is a superposition of these. In systems with multiple qubits, basis states are all possible combinations of s and s (e.g., , , , and ), forming an orthonormal basis for the system’s Hilbert space.
Learn more about Basis State reveals only part of the information. In Quantum Computing,Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics.
Learn more about Quantum Computing MeasurementIn quantum computing, measurement is the process of extracting classical information from a quantum state. It collapses a qubit’s superposition into one of its basis states (usually or ), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition.
Learn more about Measurement results are inherently probabilistic. Running the same Quantum CircuitA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit multiple times with identical input states results in different MeasurementsIn quantum computing, measurement is the process of extracting classical information from a quantum state. It collapses a qubit’s superposition into one of its basis states (usually or ), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition.
Learn more about Measurement that originate from a Probability DistributionA probability distribution describes how the probabilities of different possible outcomes of a random variable are spread out. It shows which values are more or less likely to occur, either as a list (for discrete variables) or a curve (for continuous ones). Essentially, it’s a complete mathematical summary of a random variable’s behavior.
Learn more about Probability Distribution defined by the Quantum StateA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State.

The Probabilistic Perspective

Coming soon...

This contrasts with the deterministic results expected in classical computing.

Consequently, when applying Quantum CircuitsA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit to Machine Learning,Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning this probabilistic nature poses a challenge. Classical ModelsA **model** in machine learning is a mathematical representation of patterns learned from data. It takes **inputs** (features) and produces **outputs** (predictions or classifications) based on relationships it has identified during training. Essentially, it’s a function that generalizes from examples to make decisions or predictions on new data.
Learn more about Model train on datasets with clear target labels, such as class indices or real output values. In contrast, a single evaluation of a Quantum CircuitA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit provides only a random sample from its output distributionA probability distribution describes how the probabilities of different possible outcomes of a random variable are spread out. It shows which values are more or less likely to occur, either as a list (for discrete variables) or a curve (for continuous ones). Essentially, it’s a complete mathematical summary of a random variable’s behavior.
Learn more about Probability Distribution and no definitive prediction that can be directly compared to a label.

This has important implications for combining Quantum ComputingQuantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics.
Learn more about Quantum Computing with Machine LearningMachine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning.

The learning processA **training loop** in quantum computing is the iterative process used to optimize parameters in a hybrid quantum-classical algorithm, such as a variational quantum circuit. The quantum computer evaluates a cost function by running the circuit and measuring outputs, while a classical optimizer updates the circuit parameters to minimize (or maximize) that cost. This loop repeats until the model converges to an optimal or near-optimal solution.
Learn more about Training Loop must therefore be built around extracting useful information from these distributionsA probability distribution describes how the probabilities of different possible outcomes of a random variable are spread out. It shows which values are more or less likely to occur, either as a list (for discrete variables) or a curve (for continuous ones). Essentially, it’s a complete mathematical summary of a random variable’s behavior.
Learn more about Probability Distribution since they are the only channel through which the quantum ModelA **model** in machine learning is a mathematical representation of patterns learned from data. It takes **inputs** (features) and produces **outputs** (predictions or classifications) based on relationships it has identified during training. Essentially, it’s a function that generalizes from examples to make decisions or predictions on new data.
Learn more about Model communicates with the classical world.

A typical way to cope with the probabilistic MeasurementsIn quantum computing, measurement is the process of extracting classical information from a quantum state. It collapses a qubit’s superposition into one of its basis states (usually or ), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition.
Learn more about Measurement, is to work with the computation of Expectation ValuesThe expectation value is the average result you'd get if you repeated a measurement of a quantity many times under identical conditions. Mathematically, it’s the weighted average of all possible outcomes, where each outcome is weighted by its probability. In quantum mechanics, it represents the average value of an observable calculated from the wavefunction.
Learn more about Expectation Value that further reduce the statistical quantities toward classical prediction targets. In this way, the distributionA probability distribution describes how the probabilities of different possible outcomes of a random variable are spread out. It shows which values are more or less likely to occur, either as a list (for discrete variables) or a curve (for continuous ones). Essentially, it’s a complete mathematical summary of a random variable’s behavior.
Learn more about Probability Distribution of MeasurementIn quantum computing, measurement is the process of extracting classical information from a quantum state. It collapses a qubit’s superposition into one of its basis states (usually or ), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition.
Learn more about Measurement outcomes is reduced to averaged values that are compatible with Machine LearningMachine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning Loss Functions.A loss function measures how far a model’s predictions are from the actual target values. It assigns a numerical value to this difference—lower values mean better performance. During training, the model adjusts its parameters to minimize this loss.
Learn more about Loss Function

Quantum Machine LearningQuantum Machine Learning is the field of research that combines principles from quantum computing with traditional machine learning to solve complex problems more efficiently than classical approaches.
Learn more about Quantum Machine Learning is still a long way from reaching its full potential.

Parameterized Quantum CircuitsA **Parameterized Quantum Circuit (PQC)** is a quantum circuit where certain gate operations depend on adjustable parameters—typically real numbers representing rotation angles. These parameters are tuned (often by classical optimization) to perform a specific task, such as minimizing a cost function. PQCs are central to **variational quantum algorithms**, where quantum computation provides state preparation and measurement, and a classical computer optimizes the parameters.
Learn more about Parameterized Quantum Circuit represent just one specific way of combining Quantum ComputingQuantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics.
Learn more about Quantum Computing with Machine Learning.Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.
Learn more about Machine Learning This is a way that caters to today's noisy devicesNoisy 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.
Learn more about Noisy Intermediate-Scale Quantum The Quantum CircuitsA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit are deliberately short-lived to withstand DecoherenceDecoherence is the process by which a quantum system loses its quantum behavior—like superposition—because it interacts with its surrounding environment. These interactions cause the system’s quantum states to become entangled with the environment, effectively destroying the system’s coherent phase relationships. As a result, the system starts to behave classically rather than quantum mechanically.
Learn more about 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-correctedError correction in quantum computing protects fragile quantum information from noise and decoherence by encoding one logical qubit into multiple physical qubits. It uses specially designed quantum codes that can detect and correct certain types of errors (like bit-flips or phase-flips) without directly measuring and collapsing the quantum state. This allows reliable computation even on imperfect hardware.
Learn more about Error Correction Logical QubitsA **logical qubit** is a qubit made from many **physical qubits** working together to protect quantum information from errors. Instead of storing data in a single unstable qubit, error-correcting codes distribute it across several, allowing detection and correction of mistakes. It’s the fundamental unit of computation in a **fault-tolerant quantum computer**.
Learn more about Logical Qubit become available. With reliable Quantum Random Access MemoryQuantum Random Access Memory (QRAM) is a theoretical type of memory that allows a quantum computer to access multiple memory locations simultaneously in superposition. Instead of retrieving one data element at a time, QRAM can query all relevant addresses in parallel, with the amplitudes encoding probabilities. It’s crucial for algorithms needing fast data lookup in quantum superposition, but no scalable physical implementation yet exists.
Learn more about Quantum Random Access Memory, new integration patterns will open up. Instead of squeezing Quantum InformationQuantum information is the study of how information is represented, processed, and transmitted using quantum systems. Essentially, data is stored in quantum bits (qubits) that exist in superpositions of its basis states and . This allows to create fundamentally different algorithms than classical systems support.
Learn more about Quantum Information into short-lived Quantum CircuitsA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit and letting them collapse prematurely, we could design architectures that make more direct use of the rich internal structure of Quantum StatesA quantum state is the complete mathematical description of a quantum system, containing all the information needed to predict measurement outcomes. It’s usually represented by a wavefunction or a state vector in a Hilbert space. The state defines probabilities, not certainties, for observable quantities like position, momentum, or spin.
Learn more about Quantum State. Even before we reach that stage, there is untapped potential: in current practice, MeasurementIn quantum computing, measurement is the process of extracting classical information from a quantum state. It collapses a qubit’s superposition into one of its basis states (usually or ), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition.
Learn more about Measurement results are often reduced to a single Expectation ValueThe expectation value is the average result you'd get if you repeated a measurement of a quantity many times under identical conditions. Mathematically, it’s the weighted average of all possible outcomes, where each outcome is weighted by its probability. In quantum mechanics, it represents the average value of an observable calculated from the wavefunction.
Learn more about Expectation Value, but Probability DistributionsA probability distribution describes how the probabilities of different possible outcomes of a random variable are spread out. It shows which values are more or less likely to occur, either as a list (for discrete variables) or a curve (for continuous ones). Essentially, it’s a complete mathematical summary of a random variable’s behavior.
Learn more about Probability Distributioncontain more information than a single number. Exploring Loss FunctionsA loss function measures how far a model’s predictions are from the actual target values. It assigns a numerical value to this difference—lower values mean better performance. During training, the model adjusts its parameters to minimize this loss.
Learn more about Loss Function based on distributionsA probability distribution describes how the probabilities of different possible outcomes of a random variable are spread out. It shows which values are more or less likely to occur, either as a list (for discrete variables) or a curve (for continuous ones). Essentially, it’s a complete mathematical summary of a random variable’s behavior.
Learn more about 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-basedA **Parameterized Quantum Circuit (PQC)** is a quantum circuit where certain gate operations depend on adjustable parameters—typically real numbers representing rotation angles. These parameters are tuned (often by classical optimization) to perform a specific task, such as minimizing a cost function. PQCs are central to **variational quantum algorithms**, where quantum computation provides state preparation and measurement, and a classical computer optimizes the parameters.
Learn more about Parameterized Quantum Circuit framework. One of the most pressing problems is that of Barren PlateausThe barren plateau problem in quantum computing refers to regions in a quantum circuit’s parameter space where the **gradient of the cost function becomes exponentially small** as the number of qubits increases. This makes training variational quantum algorithms (like VQEs or QNNs) extremely difficult because optimization algorithms receive almost no useful signal to guide updates. It’s primarily caused by random circuit initialization and high circuit depth, leading to near-random output states.
Learn more about Barren Plateau. These are areas of the parameter space where the training signal disappears as the depth of the Quantum CircuitA quantum circuit is a sequence of quantum gates applied to qubits, representing the operations in a quantum computation. Each gate changes the qubits’ state using quantum mechanics principles like superposition and entanglement. The final qubit states, when measured, yield the circuit’s computational result probabilistically.
Learn more about Quantum Circuit increases. This is an active area of research: How can Parameterized Quantum CircuitsA **Parameterized Quantum Circuit (PQC)** is a quantum circuit where certain gate operations depend on adjustable parameters—typically real numbers representing rotation angles. These parameters are tuned (often by classical optimization) to perform a specific task, such as minimizing a cost function. PQCs are central to **variational quantum algorithms**, where quantum computation provides state preparation and measurement, and a classical computer optimizes the parameters.
Learn more about 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 LearningQuantum Machine Learning is the field of research that combines principles from quantum computing with traditional machine learning to solve complex problems more efficiently than classical approaches.
Learn more about Quantum Machine Learning approach? Where is theQuantum AdvantageQuantum advantage is the point where a quantum computer performs a specific task faster or more efficiently than the best possible classical computer. It doesn’t mean quantum computers are universally better—just that they outperform classical ones for that task. The first demonstrations (e.g., Google’s 2019 Sycamore experiment) showed speedups for highly specialized problems, not yet for practical applications.
Learn more about Quantum Advantage in Quantum Machine Learning?Quantum Machine Learning is the field of research that combines principles from quantum computing with traditional machine learning to solve complex problems more efficiently than classical approaches.
Learn more about Quantum Machine Learning Why should a Quantum SystemA quantum system is any physical system that is subject to the laws of quantum mechanics, whereby quantities such as energy or spin can only assume discrete (quantized) values. Its behavior is described by a wave function that encodes the probabilities of possible measurement results.
Learn more about Quantum System be superior to other ModelsA **model** in machine learning is a mathematical representation of patterns learned from data. It takes **inputs** (features) and produces **outputs** (predictions or classifications) based on relationships it has identified during training. Essentially, it’s a function that generalizes from examples to make decisions or predictions on new data.
Learn more about Model? This is the search for the essence of Quantum Machine LearningQuantum Machine Learning is the field of research that combines principles from quantum computing with traditional machine learning to solve complex problems more efficiently than classical approaches.
Learn more about Quantum Machine Learning

In Search Of The Essence Of Quantum Machine Learning

How parameterized quantum circuits turn exponential Hilbert spaces into learning models

September 2, 2025•5 min

Classic machine learning already provides universal approximators and massive models. So why resort to quantum circuits? This is the search for the real challenge, namely to design problem-specific circuits that translate theoretical capacities into practical learning.