What Does The CNOT Operator Do?

From a simple swap of amplitudes to real effects you can measure

The CNOT operator does not create a cause-effect relationship. It does not even have a directed effect. It's only a simple swap of amplitudes. But one that produces Boolean logic, phase kickback, or entanglement, depending on how you look at it.

by Frank Zickert

October 7, 2025

The Controlled Not GateA controlled-NOT (CNOT) gate is a two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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. where the first QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (control) determines whether the second QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (target) is flipped on the -axis. If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in state is a basis state., the target Qubit'sA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. is inverted . If the control is is a basis state., the target is unchanged. It’s essential for creating entanglement, since applying aCNOT to a superposed control qubit links the states of both qubits. is the workhorse of Quantum Computing.Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. Every textbook, every course, every quantum toolkit leans on it. It's the 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. that somehow flips QubitsA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states., supports Phase KickbackPhase kickback is a quantum phenomenon where a phase shift applied to a *target* qubit in a controlled operation gets "kicked back" onto the *control* qubit instead. It happens because the control qubit’s superposition interacts with the target’s phase, effectively transferring that phase information to the control. This mechanism is fundamental in algorithms like phase estimation and the quantum Fourier transform., and creates EntanglementEntanglement is a quantum phenomenon where two or more particles become correlated so that measuring one instantly determines the state of the other, no matter how far apart they are. This correlation arises because their quantum states are linked as a single system, not as independent parts. It doesn’t allow faster-than-light communication but shows that quantum systems can share information in ways classical physics can’t explain..

And yet, when you look at what it actually does, it's almost disappointingly simple. All the Controlled Not GateA controlled-NOT (CNOT) gate is a two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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. where the first QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (control) determines whether the second QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (target) is flipped on the -axis. If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in state is a basis state., the target Qubit'sA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. is inverted . If the control is is a basis state., the target is unchanged. It’s essential for creating entanglement, since applying aCNOT to a superposed control qubit links the states of both qubits. does is swap two 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..

That's it.

If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is is a basis state., it flips the target QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states.. A bare-bones reshuffling of numbers.

So, a question opens a small crack in the story we've been told: If the Controlled Not GateA controlled-NOT (CNOT) gate is a two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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. where the first QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (control) determines whether the second QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (target) is flipped on the -axis. If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in state is a basis state., the target Qubit'sA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. is inverted . If the control is is a basis state., the target is unchanged. It’s essential for creating entanglement, since applying aCNOT to a superposed control qubit links the states of both qubits. is really only swapping Amplitudes,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. where on earth does the Quantum 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. come from?

This post is accompanied by a PDF file summarizing the key points.

Let’s strip the Controlled Not GateA controlled-NOT (CNOT) gate is a two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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. where the first QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (control) determines whether the second QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (target) is flipped on the -axis. If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in state is a basis state., the target Qubit'sA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. is inverted . If the control is is a basis state., the target is unchanged. It’s essential for creating entanglement, since applying aCNOT to a superposed control qubit links the states of both qubits. down to its essentials. Behind all the talk of control and target, there's just one rule:

Swap the amplitudes of the two states where the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is is a basis state..

That's all it ever does.

Figure 1 denotes how the Controlled Not GateA controlled-NOT (CNOT) gate is a two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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. where the first QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (control) determines whether the second QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (target) is flipped on the -axis. If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in state is a basis state., the target Qubit'sA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. is inverted . If the control is is a basis state., the target is unchanged. It’s essential for creating entanglement, since applying aCNOT to a superposed control qubit links the states of both qubits. touches only the last two terms. These are the ones where the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is is a basis state..

No new terms appear, and none vanish. No probabilities are created or destroyed. Nothing travels from the control to the target or back. There is no directed information flow. The Controlled Not GateA controlled-NOT (CNOT) gate is a two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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. where the first QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (control) determines whether the second QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (target) is flipped on the -axis. If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in state is a basis state., the target Qubit'sA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. is inverted . If the control is is a basis state., the target is unchanged. It’s essential for creating entanglement, since applying aCNOT to a superposed control qubit links the states of both qubits. is symmetric, unitaryA **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., and lossless. It is just a reshuffling of the Quantum State Vector.A quantum state vector is a mathematical object (usually denoted |ψ⟩) that fully describes the state of a quantum system. Its components give the probability amplitudes for finding the system in each possible basis state. The squared magnitude of each component gives the probability of measuring that corresponding outcome.

Yet this modest reshuffle behaves completely differently depending on the basis in which we look at it.

In one context, it feels like a logical operation.

In another, it acts like a mirror that sends Quantum PhaseA **quantum phase** is the angle component of a particle’s wavefunction that determines how its probability amplitude interferes with others. It doesn’t affect observable probabilities directly but becomes crucial when comparing two or more states, as phase differences lead to interference effects. Essentially, it encodes the relative timing or “alignment” of quantum waves. information backward.

And in most others, it ties the QubitsA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. together so tightly that neither can be described alone.

So if you think of the Controlled Not GateA controlled-NOT (CNOT) gate is a two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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. where the first QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (control) determines whether the second QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (target) is flipped on the -axis. If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in state is a basis state., the target Qubit'sA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. is inverted . If the control is is a basis state., the target is unchanged. It’s essential for creating entanglement, since applying aCNOT to a superposed control qubit links the states of both qubits. as a little arrow shooting information from the control to the target, you'll miss the point. It's more like a geometric twist in the two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. state 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.. It is a reversible turn that changes how 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. align or interfereInterference in quantum computing refers to the way probability amplitudes of quantum states combine—sometimes reinforcing each other (constructive interference) or canceling out (destructive interference). Quantum algorithms exploit this to amplify the probability of correct answers while suppressing incorrect ones. It’s a key mechanism that gives quantum computers their computational advantage..

There are three distinct worlds this single twist can create:
• Classical logic when the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in the Computational Basis,The **computational basis** is the standard set of basis states used to describe qubits in quantum computing—typically (|0⟩) and (|1⟩) for a single qubit, or all possible combinations like (|00⟩, |01⟩, |10⟩, |11⟩) for multiple qubits. These states correspond to classical bit strings and form an orthonormal basis for the system’s Hilbert space. Any quantum state can be expressed as a superposition of these computational basis states.
• Phase KickbackPhase kickback is a quantum phenomenon where a phase shift applied to a *target* qubit in a controlled operation gets "kicked back" onto the *control* qubit instead. It happens because the control qubit’s superposition interacts with the target’s phase, effectively transferring that phase information to the control. This mechanism is fundamental in algorithms like phase estimation and the quantum Fourier transform. when the target QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in the Fourier Basis,The Fourier basis is a set of sine and cosine functions that can represent any periodic signal as a weighted sum of these functions. Each basis function corresponds to a specific frequency, capturing how much of that frequency is present in the signal. In essence, it’s the coordinate system for expressing signals in terms of their frequency components instead of time. and
• EntanglementEntanglement is a quantum phenomenon where two or more particles become correlated so that measuring one instantly determines the state of the other, no matter how far apart they are. This correlation arises because their quantum states are linked as a single system, not as independent parts. It doesn’t allow faster-than-light communication but shows that quantum systems can share information in ways classical physics can’t explain. when neither fits those special cases.

Let's start with the simplest and most deceptive case.

Suppose the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in one of the Computational BasisThe **computational basis** is the standard set of basis states used to describe qubits in quantum computing—typically (|0⟩) and (|1⟩) for a single qubit, or all possible combinations like (|00⟩, |01⟩, |10⟩, |11⟩) for multiple qubits. These states correspond to classical bit strings and form an orthonormal basis for the system’s Hilbert space. Any quantum state can be expressed as a superposition of these computational basis states. Basis States:A **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.: is a basis state. or is a basis state.. In that case, the effect Controlled Not GateA controlled-NOT (CNOT) gate is a two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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. where the first QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (control) determines whether the second QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (target) is flipped on the -axis. If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in state is a basis state., the target Qubit'sA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. is inverted . If the control is is a basis state., the target is unchanged. It’s essential for creating entanglement, since applying aCNOT to a superposed control qubit links the states of both qubits. is a simple, uni-directed Boolean logical operator as depicted in ?. If the control is is a basis state., it flips 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. of the target Qubit.A qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states.. if it's is a basis state., it does nothing.

However, this seemingly directed effect of the control on the target QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is nothing more than a swap of the Amplitudes,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. as shown in ?.

In both situations, the full 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. can be factorized. We can write it as a clean product of a control (QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states.) and a target (QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states.) 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin.. No Entanglement,Entanglement is a quantum phenomenon where two or more particles become correlated so that measuring one instantly determines the state of the other, no matter how far apart they are. This correlation arises because their quantum states are linked as a single system, not as independent parts. It doesn’t allow faster-than-light communication but shows that quantum systems can share information in ways classical physics can’t explain. no subtle Interference,Interference in quantum computing refers to the way probability amplitudes of quantum states combine—sometimes reinforcing each other (constructive interference) or canceling out (destructive interference). Quantum algorithms exploit this to amplify the probability of correct answers while suppressing incorrect ones. It’s a key mechanism that gives quantum computers their computational advantage. just a conditional bit-flip. The control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. emerges completely untouched, faithfully carrying the information that determined what happened to the target.

That's why, in this restricted basis, the Controlled Not GateA controlled-NOT (CNOT) gate is a two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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. where the first QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (control) determines whether the second QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (target) is flipped on the -axis. If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in state is a basis state., the target Qubit'sA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. is inverted . If the control is is a basis state., the target is unchanged. It’s essential for creating entanglement, since applying aCNOT to a superposed control qubit links the states of both qubits. feels so familiar. It mimics a classical logic gate, like a two-input where the control acts as the switch.

But as soon as we let the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. drift away from the Computational BasisThe **computational basis** is the standard set of basis states used to describe qubits in quantum computing—typically (|0⟩) and (|1⟩) for a single qubit, or all possible combinations like (|00⟩, |01⟩, |10⟩, |11⟩) for multiple qubits. These states correspond to classical bit strings and form an orthonormal basis for the system’s Hilbert space. Any quantum state can be expressed as a superposition of these computational basis states. ( is a basis state., is a basis state.), the picture changes dramatically. Then, the simple directed control-target effect dissolves, and the swap of amplitudes begins to look like something entirely different.

Now let's look at the same Controlled Not GateA controlled-NOT (CNOT) gate is a two-QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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. where the first QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (control) determines whether the second QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. (target) is flipped on the -axis. If the control QubitA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. is in state is a basis state., the target Qubit'sA qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. 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** (ψ) or a **state vector** (|ψ⟩) in a Hilbert space. The state defines probabilities—not certainties—for observable quantities like position, momentum, or spin. is inverted . If the control is is a basis state., the target is unchanged. It’s essential for creating entanglement, since applying aCNOT to a superposed control qubit links the states of both qubits. from a different angle. Literally, a different basis.