Quantum Computing in the NISQ era and beyond
John Preskill (2018)
The essay that named the NISQ era. Almost no equations, and it frames what near-term hardware can and cannot do more honestly than anything else you will read.
Beginner · 7 resources
Noise & decoherence
Qubits leak their quantum information into the environment within microseconds to milliseconds, and every gate applied to them is slightly wrong. That is why building a useful quantum computer is hard.
Learn first:Qubits
Why it matters
Noise explains the entire shape of the industry: why machines have hundreds rather than millions of qubits, why error correction is the central research problem, and why "NISQ" is a word you keep seeing.
After this you will be able to
- Explain decoherence and gate error in plain language
- Say what T1 and T2 times mean
- Explain what the NISQ era is and why it is called that
Read it here first
The plain-language version
Qubits must be isolated well enough that nothing measures them by accident, yet accessible enough that you can control them precisely. Those requirements pull in opposite directions. Today a qubit stays coherent for microseconds to milliseconds and every gate is slightly wrong.
Analogy
Balancing a pencil on its tip in a room where the air itself keeps nudging it — and you must also perform a thousand precise operations on the pencil before it falls.
Common misconception
We just need to keep adding more qubits.
What is actually true
Adding noisy qubits without improving fidelity makes things worse, not better. The 2024 below-threshold results mattered precisely because they showed scaling up finally helping rather than hurting.
The thing to remember
Error correction is the answer, but it costs roughly a thousand physical qubits per reliable logical qubit. That ratio is why useful machines are still years away.
Start here
2 best places to start
Hand-picked and ordered. If you only have time for one, take the first.
QuTech Academy video lectures
QuTech, TU Delft
Free lecture videos from the Delft MOOCs, organised by topic. Uniquely strong on the hardware side — how you actually build and control a qubit — and on quantum internet.
Also covering this
5 more resources
A Quantum Engineer's Guide to Superconducting Qubits
Krantz, Kjaergaard, Yan, Oliver, Orlando & Gustavsson (2019)
How transmons actually work, from Josephson junctions through control electronics to readout. The reference for anyone whose algorithms run on IBM, Google or Rigetti hardware.
Black Opal
Q-CTRL
A polished, heavily visual self-paced program aimed squarely at newcomers without a physics background. The interactive Bloch sphere and noise demos are the standouts.
Mitiq — error mitigation toolkit
Unitary Fund
Zero-noise extrapolation, probabilistic error cancellation and more, wrapping whichever SDK you already use. The docs are the best practical tutorial on mitigation anywhere.
Quantum Error Mitigation
Cai, Babbush, Benjamin, Endo, Huggins, Li, McClean & O’Brien (2022)
The comprehensive review of mitigation techniques and, crucially, their sampling overheads — the honest accounting of what mitigation costs you in shots.
QuTiP — Quantum Toolbox in Python
QuTiP developers
The standard Python library for simulating open quantum systems: density matrices, Lindblad master equations, noise models. Where you go when pure-state circuit simulators stop being enough.
Next
This unlocks
Topics that list Noise & decoherence as a prerequisite.
Error mitigation
Post-processing techniques — zero-noise extrapolation, probabilistic error cancellation, readout correction — that recover accurate expectation values from noisy hardware without full error correction, at the cost of extra shots.
AdvancedHardware modalities
The competing physical platforms — superconducting transmons, trapped ions, neutral atoms, photonics, spin qubits — each with different gate speeds, fidelities, connectivity and scaling problems.
Advanced