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 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.
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 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.. This is the rule according to which one A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. transforms into another without losing or creating information.
You can think of it as a perfectly reversible rotation in a very high-dimensional A 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.. Just as turning a Rubik's cube shifts its stickers without tearing or duplicating them, a Unitary 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. rearranges the In 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. of a A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. while keeping the total probability sum exactly the same.
Figure 2 The Rubik's cube
Two key features make a Unitary 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. special:
Reversibility: Every Unitary 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. has an In 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 ).. Applying the transformation and then its In 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 ). returns you to the original A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin..
Probability-preserving: Since the Unitary 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. preserves length (technically, it preserves An **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., (a \cdot b = a_1b_1 + a_2b_2 + \dots + a_nb_n)). It generalizes the dot product and defines geometric concepts like **length** and **angle** in vector spaces.), the total probability of all possible outcomes remains at .
So when we talk about the Unitary 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., we mean that we transform the A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. in a structured, reversible way. Nothing is lost during this process. Randomness and irreversibility only occur when you finally In 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 |0⟩ or |1⟩), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition. the A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin..
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 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.. 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 In 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 )..
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 with traditional machine learning 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 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. without being thrown off course by their differences.
So, the Unitary 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. of a A quantum system is any physical system governed by the rules of quantum mechanics, where quantities like energy or spin are quantized (can take only specific values). Its behavior is described by a wavefunction that encodes probabilities of measurement outcomes rather than definite values. Unlike classical systems, it exhibits superposition and entanglement, meaning components can exist in multiple states simultaneously and be correlated across distance. is described by a Unitary 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. acting on an initial A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. that we know in advance. In practice, this A **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. is built from a finite set of 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. within the A 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.. Each 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. is itself a A **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.. By combining them in sequence, we obtain the overall Unitary 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.that defines how the A 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. acts on its input. This is not so different from a classical computer program, which can be understood as a composition of A 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. The distinction is that in the A 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. case the operators are unitary and not logical.
Once we have internalized the idea that a A 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. generates a Unitary 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. from simple building blocks, known as 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. a new question arises: How can we design A 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. that generate Unitary 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. that are not fixed but adaptable? The analogy to a classical computer program proves helpful once again.
Let's consider a function. In Python 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., 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 A 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.. Just as A 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. use parameter values, 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.Unitary 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.A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. based on parameters. For example, rotations use the rotation angle as a parameter.
When we do not fix these parameters within the A 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. and expose them externally, we create a A **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.. This circuit acts as a template that represents different Unitary 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. depending on the parameter values.
Figure 4 Parameterized Quantum Circuit
A **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. 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 with traditional machine learning to solve complex problems more efficiently than classical approaches.. In 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., the A **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. acts as a A **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. within the standard Machine Learning is an approach on solving problems by deriving the rules from data instead of explicitly programming.A **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.. 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 A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. preserve all information during theirUnitary 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. we cannot directly access this information. The complete A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. generated by a A 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. exists only as a mathematical object.
To extract information, we must apply a In 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 |0⟩ or |1⟩), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition. that collapses the complex A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. into a defined and accessibleA **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 (|0⟩) and (|1⟩); any other qubit state is a superposition of these. In systems with multiple qubits, basis states are all possible combinations of 0s and 1s (e.g., (|00⟩, |01⟩, |10⟩, |11⟩)), forming an orthonormal basis for the system’s Hilbert space..
Unfortunately, this In 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 |0⟩ or |1⟩), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition. is irreversible and the accessibleA **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 (|0⟩) and (|1⟩); any other qubit state is a superposition of these. In systems with multiple qubits, basis states are all possible combinations of 0s and 1s (e.g., (|00⟩, |01⟩, |10⟩, |11⟩)), forming an orthonormal basis for the system’s Hilbert space. reveals only part of the information. In Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics.In 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 |0⟩ or |1⟩), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition. results are inherently probabilistic. Running the same A 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. multiple times with identical input states results in different In 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 |0⟩ or |1⟩), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition. that originate from a A 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. defined by the A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin..
The Probabilistic Perspective
This contrasts with the deterministic results expected in classical computing.
Consequently, when applying A 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. 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 A **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. train on datasets with clear target labels, such as class indices or real output values. In contrast, a single evaluation of a A 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. provides only a random sample from its output A 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. 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 A **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. must therefore be built around extracting useful information from these A 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. since they are the only channel through which the quantum A **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. communicates with the classical world.
A typical way to cope with the probabilistic In 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 |0⟩ or |1⟩), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition., is to work with the computation of The 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. that further reduce the statistical quantities toward classical prediction targets. In this way, the A 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. of In 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 |0⟩ or |1⟩), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition. 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.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.
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. is still a long way from reaching its full potential.
A **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. 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 A 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. are deliberately short-lived to withstand Decoherence 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., 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 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.A **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**. become available. With reliable Quantum 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., new integration patterns will open up. Instead of squeezing Quantum information is the study of how information is represented, processed, and transmitted using quantum systems—where data is stored in quantum bits (qubits) that can exist in superpositions of 0 and 1. This allows fundamentally different computation and communication methods than classical systems. Key effects like entanglement and measurement uncertainty enable applications such as quantum computing and quantum cryptography. into short-lived A 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. and letting them collapse prematurely, we could design architectures that make more direct use of the rich internal structure of A **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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin.. Even before we reach that stage, there is untapped potential: in current practice, In 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 |0⟩ or |1⟩), with probabilities determined by the amplitudes of those states. After measurement, the qubit’s state becomes definite, destroying the original superposition. results are often reduced to a single The 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., but A 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.contain more information than a single number. Exploring 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. based on A 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. 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 A **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. framework. One of the most pressing problems is that of The **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.. These are areas of the parameter space where the training signal disappears as the depth of the A 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. increases. This is an active area of research: How can A **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. 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 with traditional machine learning to solve complex problems more efficiently than classical approaches. approach? Where is theQuantum 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. in 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. Why should a A quantum system is any physical system governed by the rules of quantum mechanics, where quantities like energy or spin are quantized (can take only specific values). Its behavior is described by a wavefunction that encodes probabilities of measurement outcomes rather than definite values. Unlike classical systems, it exhibits superposition and entanglement, meaning components can exist in multiple states simultaneously and be correlated across distance. be superior to other A **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.? This is the search for the essence of 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.
