Quantum 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.
by Frank ZickertNovember 12, 2025
Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. Learn more about Quantum Computing sounds like magic. A computer doing everything at once.
Finally, a computer that tries all possibilities simultaneously and spits out the answer instantly.
It’s an appealing image. And completely wrong.
It is not least that misunderstanding why Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. Learn more about Quantum Computing feels so mysterious. But when people discover that A quantum computer is typically a large, highly controlled system kept at near-absolute-zero temperatures to preserve quantum behavior. It contains a processor with qubits—often made from superconducting circuits, trapped ions, or photons—manipulated by microwaves, lasers, or magnetic fields. Surrounding systems handle cooling, error correction, and control electronics to maintain quantum coherence and read out results. Learn more about Quantum Computer don’t instantly solve every problem, they assume the field is overhyped. Yet, the truth is subtler and far more interesting: A 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 don’t explore every path at once. They sculpt 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. Learn more about Interference patterns.
Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. Learn more about Quantum Computing isn’t about parallel universes guessing in sync. It’s about engineering how probability waves add or cancel. And Quantum Information is the foundation to build upon.
The one-qubit experiment that breaks the "both at once" myth
A single A qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. Learn more about Quantum Bit isn’t both and . But, it’s in 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 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 can 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. Learn more about Interference with itself. If you change the A **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. Learn more about Quantum Phase, that is the relative sign between the two possible states, you can flip the outcome completely, without touching any classical A bit (short for “binary digit”) is the smallest unit of data in computing, representing a value of either 0 or 1. It’s the fundamental building block of all digital information. Multiple bits combine to form larger units like bytes (8 bits) and encode more complex data such as numbers, text, or images. Learn more about Binary Digit Let’s make that concrete.
? depicts the The HZH routine means applying a Hadamard gate (H), then a Pauli-Z gate (Z), then another Hadamard (H). This sequence effectively turns the Z operation into a Not (X) operation because . In other words, it flips the qubit’s state from to by rotating the Z-axis operation into the X-axis basis. Learn more about HZH-Routine. It iconically shows how quantum computations differ from classical.
hzh.py
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from qiskit import QuantumCircuit
from qiskit.quantum_info import Statevector
defrun(include_z: bool):
qc = QuantumCircuit(1, 1)
# Step 1: create superposition
qc.h(0)
# Step 2: flip phase of |1>
if include_z:
qc.z(0)
# Step 3: interfere the two paths
qc.h(0)
# obtain the quantum state vector
psi = Statevector.from_instruction(qc)
# compute and return the measurement probabilities
counts = psi.probabilities_dict()
print("No Z:", run(False)) # Expect {'0': ~1000}
print("With Z:", run(True)) # Expect {'1': ~1000}
Listing 1 The HZH-subroutine.
More specifically, Listing 1 creates and returns two 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. Learn more about Quantum Circuit The first is a version of the The HZH routine means applying a Hadamard gate (H), then a Pauli-Z gate (Z), then another Hadamard (H). This sequence effectively turns the Z operation into a Not (X) operation because . In other words, it flips the qubit’s state from to by rotating the Z-axis operation into the X-axis basis. Learn more about HZH-Routine but the The Z-gate changes the phase of the state by (or radians) while leaving the state unchanged. This means the amplitude of gains a negative sign, effectively flipping its phase. It's a phase-flip operation that rotates the quantum state vector a half turn around the Z-axis of the Bloch sphere. Learn more about Z-Gate. Essentially, it consists of two subsequent The Hadamard operator, often denoted H, is a single-qubit quantum gate that creates an equal superposition of and . In other words, It turns the states of the computational basis and into the states of the Fourier basis and . Learn more about Hadamard Operator The second is the full The HZH routine means applying a Hadamard gate (H), then a Pauli-Z gate (Z), then another Hadamard (H). This sequence effectively turns the Z operation into a Not (X) operation because . In other words, it flips the qubit’s state from to by rotating the Z-axis operation into the X-axis basis. Learn more about HZH-Routine the center The Z-gate changes the phase of the state by (or radians) while leaving the state unchanged. This means the amplitude of gains a negative sign, effectively flipping its phase. It's a phase-flip operation that rotates the quantum state vector a half turn around the Z-axis of the Bloch sphere. Learn more about Z-Gate.
So, the only difference is the The Z-gate changes the phase of the state by (or radians) while leaving the state unchanged. This means the amplitude of gains a negative sign, effectively flipping its phase. It's a phase-flip operation that rotates the quantum state vector a half turn around the Z-axis of the Bloch sphere. Learn more about Z-Gate or not. But the The Z-gate changes the phase of the state by (or radians) while leaving the state unchanged. This means the amplitude of gains a negative sign, effectively flipping its phase. It's a phase-flip operation that rotates the quantum state vector a half turn around the Z-axis of the Bloch sphere. Learn more about Z-Gate does not affect the measurement probabilities directly. It only changes the relative phase between the two 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 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 of the A qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. Learn more about Quantum BitSuperposition in quantum computing means a quantum bit (qubit) can exist in multiple states (0 and 1) at the same time, rather than being limited to one like a classical bit. Mathematically, it’s a linear combination of basis states with complex probability amplitudes. This allows quantum computers to process many possible inputs simultaneously, enabling exponential speedups for certain problems. Learn more about Superposition
However, look at ? that depicts the output when we run the code of Listing 1.
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No Z: {np.str_('0'): np.float64(0.9999999999999996)}
With Z: {np.str_('1'): np.float64(0.9999999999999996)}
Listing 2 Output of running two circuits.
When you run this, you’ll see about zeros if you skip the Z gate. And you'll see about ones if you include it.
There is no randomness; there are no signs that multiple states are being processed simultaneously.
Here: is the input state, is a basis state. Learn more about in our case. is the 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. Learn more about Unitary Operator describing the whole circuit. gives 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. Learn more about Amplitude for measuring result . The probability is the square of the magnitude of that 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. Learn more about Amplitude
A single-A qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. Learn more about Quantum Bit system has two possible 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 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. and . Each of our two circuits produces results in one of them.
Without Z: , giving .
With Z: , giving .
By adding a A **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. Learn more about Quantum Phase flip in the middle, we changed the outcome from a guaranteed into a guaranteed .
That’s not parallelism. That’s 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. Learn more about Interference.
The A qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. Learn more about Quantum Bit never held both answers. It carried 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. Learn more about Amplitude that, depending on how they were combined, determined which outcomes would strengthen and which would vanish. A quantum algorithm is a step-by-step computational procedure designed to run on a quantum computer, exploiting quantum phenomena such as superposition, entanglement, and interference to solve certain problems more efficiently than classical algorithms. Learn more about Quantum Algorithm are built on this trick. They choreograph a sequence 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. Learn more about Quantum Gate so that wrong answers cancel out, and right ones survive 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 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
First formalized by Richard FeynmanFeynman, R.P., 1982, International Journal of Theoretical Physics, Vol. 21, pp. 467-488, this principle was later refined by David Deutsch (1985)Deurtsch, D., 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, Vol. 400, pp. 97-117, who both realized that A 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 could simulate physics far more efficiently than classical computers. Modern treatments, such as the textbook by Nielsen & Chuang (2010)Nielsen, M.A., 2010, Cambridge university press, , define Quantum 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 precisely in these terms: information represented and manipulated through 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. Learn more about Interference
We’ve been using the wrong metaphor
Our intuition about uncertainty is classical. If we flip a coin and cover it, we think, It’s either heads or tails; I just don’t know which But a A qubit is the basic unit of quantum information, representing a superposition of 0 and 1 states. Learn more about Quantum Bit isn’t hiding a value. It’s in a Superposition in quantum computing means a quantum bit (qubit) can exist in multiple states (0 and 1) at the same time, rather than being limited to one like a classical bit. Mathematically, it’s a linear combination of basis states with complex probability amplitudes. This allows quantum computers to process many possible inputs simultaneously, enabling exponential speedups for certain problems. Learn more about Superposition that doesn’t have a definite outcome until 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 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. It is undecided. And the confusion comes from treating unknown like undecided.
And that is precisely what makes us uncomfortable. It does not correspond to our intuition that something is in a clearly defined state, but at the same time we cannot say with certainty what we will see when we look at it. So we arrive at the wrong idea that it was in two states at the same time.
Once you stop picturing Quantum Computing is a different kind of computation that builds upon the phenomena of Quantum Mechanics. Learn more about Quantum Computing as magic parallelism, it becomes understandable, even practical. It’s not mystical. It’s precision engineering of A **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. Learn more about Quantum Phase and 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. Learn more about Interference
Quantum 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 science is the study of how to represent, control, and protect 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. Learn more about Interference. It is not a quest for mystical parallel worlds.
