What is Quantum Computing?

2025-08-27 • quantum, primer, education

TL;DR

Quantum computers use qubits that can exist in combinations of 0 and 1 (superposition), be correlated at a distance (entanglement), and interfere to amplify right answers and cancel wrong ones. They’re powerful for certain problems (like simulating quantum chemistry or searching unstructured data) but not a drop-in replacement for classical computers yet.

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Classical bits vs. qubits

- Bit (classical): either 0 or 1. - Qubit (quantum): a state vector α|0⟩ + β|1⟩ with complex amplitudes α, β where |α|² + |β|² = 1. When you measure, you get 0 with probability |α|² or 1 with probability |β|².

Multiple qubits live in a state space that doubles with each qubit (2, 4, 8, …, 2ⁿ basis states). This exponential space is what makes some quantum algorithms interesting.

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The three “superpowers”

1. Superposition – a qubit can be in a mixture of 0 and 1. 2. Entanglement – measurement outcomes of qubits can be correlated in ways impossible classically. 3. Interference – amplitudes add or cancel; algorithms are designed so “good” paths interfere constructively and “bad” paths destructively.

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How a quantum program runs

1. Initialize qubits (usually to |0⟩). 2. Apply gates (unitary operations) such as: - H (Hadamard) to create superposition - X, Y, Z (Pauli rotations) - CNOT, CZ (two-qubit entangling gates) - parameterized rotations Rx(θ), Ry(θ), Rz(θ) for variational circuits 3. Measure some or all qubits to get classical bits.

Because measurement collapses the state, we often repeat the circuit many times (shots) to estimate probabilities.

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What can quantum computers do well?

- Quantum simulation & chemistry Molecules are quantum systems; simulating them classically is hard. Algorithms like VQE (Variational Quantum Eigensolver) and QPE (Quantum Phase Estimation) target ground-state energies and reaction pathways.

- Speedups for search & optimization Grover’s algorithm gives a quadratic speedup for unstructured search. Variational methods (e.g., QAOA) explore combinatorial optimization instances, though real-world advantage is still an open question.

- Cryptography impact Shor’s algorithm can factor large integers and compute discrete logs, threatening RSA/ECC if large, error-corrected machines become available. That’s why post-quantum cryptography (PQC) is being standardized.

What quantum computers don’t do: run your existing apps faster or replace CPUs/GPUs for general workloads.

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Hardware in the wild

- Superconducting circuits (transmons): fast gates, mature toolchains; challenges with coherence and scaling interconnects. - Trapped ions: long coherence and high-fidelity gates; slower operations but excellent control. - Neutral atoms: flexible qubit layouts using optical tweezers; active research on gate fidelities. - Photonic qubits: room-temperature, great for networking; deterministic gates are challenging. - Spin qubits (silicon/diamond): chip-fabrication compatibility; still maturing for large-scale systems.

Each platform trades off coherence time, gate fidelity, connectivity, and manufacturability.

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Errors and error correction

Physical qubits are noisy (decoherence, gate errors, crosstalk). To compute reliably, we need quantum error correction (QEC):

- Logical qubits are encoded across many physical qubits (e.g., the surface code). - Overhead is large (hundreds to thousands of physical qubits per logical qubit), but roadmaps show steady improvements in fidelities and layout.

Today’s devices are mostly NISQ (Noisy Intermediate-Scale Quantum): tens–thousands of qubits without full error correction.

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Where we are (and aren’t)

- Real hardware is accessible via clouds and SDKs. - Demonstrations in chemistry, materials, and small optimization problems exist. - Clear, sustained quantum advantage for production workloads is still rare; expect hybrid workflows where classical and quantum parts cooperate.

Be skeptical of hype, but don’t sit out: the stack (algorithms, compilers, controls, hardware) is advancing quickly.

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How to get hands-on

- Math & CS: linear algebra (vectors, matrices, eigenvalues), complex numbers, probability. - SDKs: Qiskit (IBM), Cirq (Google), Braket SDK (AWS), PennyLane (Xanadu), PyQuil/Forest. - Workflows: start on simulators, then try small hardware backends; use noise models to reason about errors. - Domains: chemistry simulation, optimization, secure comms (QKD), random number generation (QRNG), and PQC migration strategies.

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Glossary (quick)

- Qubit – quantum bit (α|0⟩ + β|1⟩). - Gate – unitary operation on qubits. - Circuit – sequence of gates and measurements. - Entanglement – nonclassical correlations between qubits. - Decoherence – loss of quantum information due to the environment. - Error correction – encoding logical info in many physical qubits to suppress errors.

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