---
title: "Fundamental physics · Simulations · Simulation Hypothesis"
url: https://simulation-hypothesis.com/simulations/fundamental-physics
description: "Quarks, nuclei, plasmas and quantum matter: the smallest systems simulated, and among the most computationally expensive."
license: https://creativecommons.org/licenses/by/4.0/
credit: "Ross Allan Dahl, Simulation Hypothesis (simulation-hypothesis.com)"
---

[Simulations](https://simulation-hypothesis.com/simulations)domain 1 of 18

# Fundamental physics

Quarks, nuclei, plasmas and quantum matter: the smallest systems simulated, and among the most computationally expensive.

The foundation of the hierarchy. These simulations start from fundamental theory, the Standard Model and quantum mechanics, and compute its consequences. They come closest to generating physical phenomena from first principles. They also explain why the Sandbox's finest matter floors take so much computing.

## Particles and fields

### Lattice QCD

Quarks and gluons on a four-dimensional grid of spacetime points, used to compute the masses and properties of protons, neutrons and other hadrons from the strong force alone.

Question it answers: What is the mass of a proton, starting from nothing but the theory?

Leaves out: The grid spacing and box size are compromises. Results are extrapolated towards the continuum and infinite volume, but never reach them.

Runs on: about 10^17 FLOPS rough a national supercomputer allocation, weeks of a large partition. Since: 1979 Creutz’s Monte Carlo study of pure SU(2) lattice gauge theory, without quarks; quarks entered later [source](https://doi.org/10.1103/PhysRevLett.43.553) In the simulations tree: [Lattice gauge Monte Carlo](https://simulation-hypothesis.com/trees/simulations?n=mat-lqcd)

[Lattice field theory](https://simulation-hypothesis.com/simulations/methods#m-lattice)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Collider event generation

Each proton–proton collision in an accelerator, from the hard scatter through parton showers to the spray of hadrons that reaches the detector.

Question it answers: What would the data look like if a proposed new particle were real?

Leaves out: Approximates the quantum interference between all contributing processes by retaining only the dominant ones, with parameters tuned to match past data.

Runs on: about 10^15 FLOPS rough a grid-computing cluster, processing billions of simulated collisions. Since: 1982 early computerised parton-shower event generators for collider physics.

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Detector response

Every particle leaving a collision, stepped through layers of silicon, calorimeter and magnet, depositing energy as it goes.

Question it answers: Which real signals will the detector miss, and which will it fake?

Leaves out: Assumes the detector's geometry and calibration are exactly as designed, whereas ageing cables and radiation damage progressively degrade them.

Runs on: about 10^15 FLOPS rough a university or grid-computing cluster, millions of CPU-hours a year. Since: 1974 CERN's first general particle-transport code for detector design.

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Cosmic-ray air showers

One very energetic particle from space hitting the upper atmosphere and cascading into billions of secondaries on the way down.

Question it answers: What kind of particle, from how far away, made the pattern our ground detectors saw?

Leaves out: Relies on collision models extrapolated far beyond any energy an accelerator has tested.

Runs on: about 10^14 FLOPS rough a small cluster or powerful workstation, hours per shower set. Since: 1961 early Monte Carlo models of cosmic-ray particle cascades.

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Accelerator beam dynamics

Bunches of charged particles circling through magnets for millions of turns, pushed by the fields and by each other.

Question it answers: Does the beam remain tightly focused, or does it gradually diverge and strike the walls?

Leaves out: Idealises the magnets as built to specification, when real ones have small manufacturing errors that matter over millions of turns.

Runs on: about 10^13 FLOPS rough a desktop workstation or small cluster, minutes per lattice design. Since: 1959 early computer tracking studies for the first strong-focusing synchrotrons.

[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Subatomic

### Neutrino detector simulation

Light or charge from a neutrino interacting deep in a tank of water, ice or liquid, tracked through the detector to work out what a real event looks like.

Question it answers: What signal would this kind of neutrino leave, and can we tell it apart from background?

Leaves out: A real detector's cables, bubbles and rock overburden add noise no simulation fully anticipates.

Runs on: about 10^15 FLOPS rough a university or collaboration cluster, weeks per detector design. Since: 1987 detector simulations built to interpret the 1987 supernova neutrino burst.

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Generative calorimeter shower models

A neural network trained on full particle-transport runs that produces the energy deposits of a shower in a detector at a tiny fraction of the cost.

Question it answers: Can a trained generator stand in for the slowest part of a detector simulation?

Leaves out: It reproduces the statistics of the training runs, not new physics, and drifts outside the energies it has seen.

Runs on: about 10^16 FLOPS rough Training on millions of full shower events, then cheap sampling Since: 2017 CaloGAN, a generative adversarial network for 3D electromagnetic showers (2017) [source](https://arxiv.org/abs/1705.02355)

[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Subatomic

### Flow-based sampling for lattice field theory

A trained normalising flow proposes whole field configurations on a lattice, which are then corrected by an exact accept-or-reject step so the answer stays unbiased.

Question it answers: Can learned samplers beat the critical slowing down of ordinary lattice Monte Carlo?

Leaves out: Demonstrated mostly in low-dimensional toy theories; training cost grows quickly with lattice volume.

Runs on: about 10^17 FLOPS rough Training plus large lattice ensembles Since: 2019 Flow-based generative models for Markov chain Monte Carlo in lattice field theory (2019) [source](https://arxiv.org/abs/1904.12072)

[Lattice field theory](https://simulation-hypothesis.com/simulations/methods#m-lattice)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Subatomic

## Nuclei and radiation

### Nuclear structure

Protons and neutrons bound in a nucleus, computed from the forces between them.

Question it answers: Which isotopes can exist at all, and what shapes do they take?

Leaves out: The force between nucleons is still not known exactly, so every nucleus is computed from an approximation to it.

Runs on: about 10^15 FLOPS rough a university cluster, days for one heavy nucleus. Since: 1965 early shell-model diagonalisation calculations on a mainframe.

[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Reactor core physics

Neutrons born, scattered, absorbed and splitting nuclei inside a power reactor, coupled to heat and coolant flow.

Question it answers: Does the chain reaction stay steady as the fuel burns down?

Leaves out: Cannot fully capture every crack, weld and flow path in an ageing real reactor.

Runs on: about 10^15 FLOPS rough a university or industry cluster, hours per core cycle. Since: 1948 Ulam, von Neumann and Metropolis's first Monte Carlo neutron runs on ENIAC.

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Subatomic

### Radiation transport

Particles passing through matter, one interaction at a time: radiotherapy beams in a patient, cosmic rays in a spacecraft hull.

Question it answers: How much dose lands in the tumour, and how much in everything around it?

Leaves out: Treats the body or hull as a fixed geometry, omitting its motion during exposure, such as respiration.

Runs on: about 10^13 FLOPS rough a hospital physics workstation or small cluster, minutes per plan. Since: 1968 first Monte Carlo dose calculations proposed for radiotherapy planning.

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Nuclear criticality safety

Monte Carlo neutron transport through stored or handled fissile material, checking that no accidental chain reaction can start.

Question it answers: Could this arrangement of fissile material go critical by accident?

Leaves out: Assumes the geometry and material recorded on the declaration match what is actually present, so the result is only as reliable as the documentation.

Runs on: about 10^13 FLOPS rough a desktop workstation; minutes to hours per configuration. Since: 1957 early computerised criticality calculations after wartime accidents prompted formal safety rules.

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Radioactivation and decay chains

Materials exposed to neutrons or radiation building up new radioactive isotopes, then decaying through chains towards stability.

Question it answers: How radioactive will this material be, and for how long, after it is irradiated?

Leaves out: Nuclear data for rare, short-lived isotopes is patchier than for common ones, so minor pathways carry more guesswork.

Runs on: about 10^12 FLOPS rough a laptop; a full decay-chain calculation takes seconds. Since: 1962 early computer codes for activation and decay in reactor materials.

[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Fusion breeding blanket neutronics

Neutrons from a fusion reaction slowing down in the surrounding blanket, breeding the tritium fuel and depositing the heat that would drive a turbine.

Question it answers: Does the blanket breed enough tritium to keep the reactor fuelled?

Leaves out: Modelled on a design that does not exist yet at full scale, so key material behaviour is extrapolated.

Runs on: about 10^14 FLOPS rough a workstation or small cluster, hours per design variant. Since: 1980 early neutronics studies for proposed fusion reactor blankets.

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Nuclear lattice effective field theory

Protons and neutrons placed on a spacetime lattice and interacting through a chiral effective theory, solved by Monte Carlo to give nuclear structure.

Question it answers: Can the excited states of light nuclei, such as the Hoyle state of carbon-12, be computed from nucleon forces?

Leaves out: Limited to light and medium nuclei; sign problems restrict which systems can be reached.

Runs on: about 10^18 FLOPS rough Large Monte Carlo runs on leadership machines Since: 2011 Ab initio calculation of the Hoyle state (2011) [source](https://doi.org/10.1103/PhysRevLett.106.192501)

[Lattice field theory](https://simulation-hypothesis.com/simulations/methods#m-lattice)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Time-dependent nuclear mean-field dynamics

Colliding and fissioning nuclei followed in real time, each nucleon moving in the average field of all the others as it evolves.

Question it answers: What happens to two nuclei as they touch, fuse or bounce apart?

Leaves out: A mean field cannot describe quantum tunnelling between different outcomes or the fluctuations that split fission yields.

Runs on: about 10^15 FLOPS rough three-dimensional Skyrme-type time-dependent runs on a cluster. Since: 1976 Bonche, Koonin and Negele's one-dimensional time-dependent Hartree-Fock calculation of nuclear collisions. [source](https://doi.org/10.1103/physrevc.13.1226)

[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Subatomic

### Neutron-star crust pasta dynamics

The deepest layer of a neutron star crust, where neutrons and protons form rods and sheets, followed with molecular dynamics to find its stiffness and how it scatters neutrinos.

Question it answers: What shapes does matter take at the base of a neutron star crust?

Leaves out: The nucleon interaction is a simple fitted potential and the box is far smaller than a real crust.

Runs on: about 10^15 FLOPS rough molecular dynamics of tens of thousands of nucleons, repeated across densities. Since: 2004 Horowitz, Perez-Garcia and Piekarewicz's molecular dynamics of nonuniform neutron-rich matter and its neutrino opacity. [source](https://doi.org/10.1103/physrevc.69.045804)

[Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Subatomic

## Plasma

### Fusion plasma turbulence

A hydrogen plasma hotter than the Sun’s core, confined by a magnetic field, together with the turbulent transport that drives heat loss.

Question it answers: How big does the machine need to be before it makes more energy than it takes?

Leaves out: Full turbulence at reactor scale is still too expensive, so most runs simulate a slice and extrapolate.

Runs on: about 10^17 FLOPS rough a national supercomputer, a large allocation for weeks. Since: 1983 early gyrokinetic turbulence codes for tokamak plasmas.

[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Fields

### Particle-in-cell plasma

Millions of charged macro-particles moving through electric and magnetic fields stored on a grid, used for lasers hitting plasma and wakefield acceleration.

Question it answers: Can a plasma wave accelerate electrons in centimetres instead of kilometres?

Leaves out: Each simulated particle stands for many real ones, which blurs the fine graininess of an actual plasma.

Runs on: about 10^16 FLOPS rough a large GPU cluster, days for a full wakefield run. Since: 1959 Buneman and Dawson's first electrostatic particle-in-cell plasma runs.

[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Bodies

### Plasma equilibrium and stability

The whole shape of a magnetically confined plasma, checked against the pressure and current it can support before it kinks, tears or disrupts.

Question it answers: Will this plasma configuration hold its shape, or collapse?

Leaves out: Real disruptions often start from small imperfections and impurities that an idealised equilibrium does not include.

Runs on: about 10^15 FLOPS rough a university cluster, hours per equilibrium scan. Since: 1958 early computed equilibria for the first magnetic confinement devices.

[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields

### Inertial confinement implosion

A small capsule of fuel driven inward by intense radiation until it is hot and dense enough to fuse, modelled as radiation, hydrodynamics and burning plasma together.

Question it answers: Will the fuel compress evenly enough to ignite before it blows itself apart?

Leaves out: Tiny asymmetries in the drive seed instabilities that break the spherical symmetry the simplest runs assume.

Runs on: about 10^16 FLOPS rough a large cluster or supercomputer partition, days per design. Since: 1972 early radiation-hydrodynamics simulations of laser-driven fuel capsules.

[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields

### Magnetic reconnection

Magnetic field lines in a plasma breaking and rejoining, converting stored field energy into heat and fast particles.

Question it answers: How fast can magnetic field lines actually break and reconnect?

Leaves out: The real process spans scales from electron orbits to whole star systems that no single run covers at once.

Runs on: about 10^15 FLOPS rough a university cluster, days for one reconnection event. Since: 1963 early computed models of field-line reconnection following Sweet and Parker's theory.

[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields

### Industrial plasma processing

Ions and reactive species in a low-temperature plasma striking and etching a surface, used to shape materials at microscopic precision.

Question it answers: Will the plasma etch or coat the surface evenly?

Leaves out: Surface chemistry at the wall is still simplified far below the detail a real contaminated chamber has.

Runs on: about 10^13 FLOPS rough a workstation or small cluster, hours per process recipe. Since: 1985 early computer models of plasma etching for surface processing.

[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Molecules

### Laser wakefield acceleration

Particle-in-cell runs of an intense laser pulse driving a plasma wave that traps and accelerates electrons over millimetres.

Question it answers: How can a plasma wave accelerate electrons to high energy in a very short distance?

Leaves out: Ionisation, radiation reaction and laser-target imperfections are usually idealised.

Runs on: about 10^18 FLOPS rough 3D particle-in-cell, billions of particles over many wave periods Since: 2002 Highly non-linear broken-wave (bubble) regime simulations (2002) [source](https://doi.org/10.1007/s003400200795)

[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Atoms

### Stellarator configuration optimisation

The shape of a twisted magnetic bottle for fusion plasma, adjusted by computer until particle orbits stay confined and the equilibrium is stable without a driven current.

Question it answers: What three-dimensional magnetic shape traps a hot plasma best?

Leaves out: Optimised shapes are judged on idealised equilibria; turbulence and coil tolerances come later and often spoil the result.

Runs on: about 10^15 FLOPS rough thousands of equilibrium and orbit calculations inside an optimisation loop. Since: 1988 Nuhrenberg and Zille's computed quasi-helically symmetric stellarators. [source](https://doi.org/10.1016/0375-9601%2888%2990080-1)

[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Evolutionary](https://simulation-hypothesis.com/simulations/methods#m-evolutionary)floor: Fields

### Tokamak edge pedestal and ELM modelling

The steep-edged layer at the rim of a tokamak plasma and the periodic bursts that throw heat onto the wall, computed from magnetohydrodynamic stability of the edge.

Question it answers: How high can the edge pressure climb before the plasma erupts?

Leaves out: Stability thresholds are well predicted but the full nonlinear burst, with its kinetic and wall physics, is still beyond routine forecasting.

Runs on: about 10^16 FLOPS rough nonlinear extended-MHD runs of one burst on a large allocation. Since: 2002 Snyder and colleagues' peeling-ballooning model of edge localised modes and the pedestal. [source](https://doi.org/10.1063/1.1449463)

[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields

### Tokamak whole-device modelling

Heating, transport, equilibrium, edge and wall models for a whole fusion device coupled into one integrated workflow that predicts a full discharge.

Question it answers: Can a complete plasma discharge be predicted before the machine is built?

Leaves out: Most modules are reduced models tuned to past machines, so predictions for a new regime carry wide uncertainty.

Runs on: about 10^16 FLOPS rough coupled reduced and high-fidelity modules run for a full discharge. Since: 2015 Imbeaux and colleagues' integrated modelling and analysis suite for ITER, the first applications of a standard data model linking such modules. [source](https://doi.org/10.1088/0029-5515/55/12/123006)

[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)floor: Fields

### Collisionless shock simulation

Shock waves in space plasma where particles never collide, with ions followed individually and electrons as a fluid so the shock front forms from the fields alone.

Question it answers: How do ions get accelerated at a shock where nothing collides?

Leaves out: Electrons are treated as a fluid and the box is a tiny patch of a shock, so large-scale structure is missing.

Runs on: about 10^16 FLOPS rough large hybrid kinetic runs in two or three dimensions. Since: 1985 Quest's hybrid simulations of high-Mach-number collisionless perpendicular shocks. [source](https://doi.org/10.1103/physrevlett.54.1872)

[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields

### Dusty plasma and Yukawa-system simulation

Charged grains suspended in a plasma, modelled as particles repelling through a screened potential that freeze into crystals or melt into liquids.

Question it answers: At what coupling strength does a cloud of charged grains crystallise?

Leaves out: The screened-repulsion potential replaces the plasma and ignores wakes and grain charging that real dust clouds show.

Runs on: about 10^12 FLOPS rough molecular dynamics of up to a million grains for long times. Since: 1994 Hamaguchi and Farouki's thermodynamics of strongly coupled Yukawa systems from Monte Carlo and molecular dynamics. [source](https://doi.org/10.1063/1.467954)

[Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Molecules

### One-component plasma simulation

Charges immersed in a uniform neutralising background, simulated to find the equation of state and crystallisation of the dense matter inside white dwarfs and giant planets.

Question it answers: At what density does dense stellar matter freeze?

Leaves out: The uniform electron background stands in for the real, polarisable electrons.

Runs on: about 10^10 FLOPS rough Monte Carlo of tens of thousands of ions, modest by modern standards. Since: 1966 Brush, Sahlin and Teller's Monte Carlo study of a one-component plasma. [source](https://doi.org/10.1063/1.1727895)

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)floor: Subatomic

### Learned plasma control in simulation

A reinforcement-learning controller practises shaping and holding a tokamak plasma by commanding the magnet coils in a fast simulation of its equilibrium and evolution, then is run on the real device.

Question it answers: Can a controller learned entirely in simulation hold a hot plasma in a requested shape?

Leaves out: The training model leaves out turbulence and fast instabilities, so the controller is trusted only inside the conditions it captures.

Runs on: about 10^16 FLOPS rough days of training on a few hundred accelerators, running the plasma model millions of times. Since: 2022 Degrave and colleagues' deep reinforcement learning controller trained in simulation and run on a tokamak. [source](https://doi.org/10.1038/s41586-021-04301-9)

[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[Real time](https://simulation-hypothesis.com/simulations/methods#m-real-time)floor: Fields

## Quantum matter and computers

### Quantum many-body systems

Many interacting electrons or spins on a lattice, handled with tensor networks and quantum Monte Carlo because the exact state is far too big to store.

Question it answers: Why do some materials superconduct, and could one do it at room temperature?

Leaves out: Tensor networks and quantum Monte Carlo both fail on some of the most interesting frustrated or fermionic systems.

Runs on: about 10^16 FLOPS rough a large cluster or supercomputer partition, days per material. Since: 1980 Ceperley and Alder's first accurate quantum Monte Carlo of the electron gas.

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Subatomic

### Quantum computer emulation

A classical computer storing the full quantum state of a register of qubits and applying gates to it. Memory doubles with every qubit added.

Question it answers: Does this quantum algorithm work before anyone builds the hardware to run it?

Leaves out: The memory needed doubles with every extra qubit, so it can only ever emulate the small cases with no quantum advantage.

Runs on: about 10^15 FLOPS rough a memory-heavy cluster node; doubles in cost with each extra qubit. Since: 1996 early classical simulators of small quantum circuits.

[Rules and states](https://simulation-hypothesis.com/simulations/methods#m-rules)floor: Subatomic

### Analogue quantum simulation

One controllable quantum system, such as ultracold atoms in a lattice of laser light, tuned to behave like another that is too hard to compute.

Question it answers: If a classical computer cannot solve the model, can a controllable physical system be made to do it instead?

Leaves out: Informs only on the one model it was built to emulate, not necessarily on the real material that motivated it.

Runs on: no computer. the atoms themselves compute; a control computer only records results. Since: 2002 Greiner and colleagues’ superfluid-to-Mott-insulator transition of ultracold atoms in an optical lattice, later read as an early analogue quantum simulation [source](https://www.nature.com/articles/415039a) In the simulations tree: [Cold-atom quantum simulator](https://simulation-hypothesis.com/trees/simulations?n=mat-qanalog)

[Physical analogue](https://simulation-hypothesis.com/simulations/methods#m-analogue)floor: Atoms

### Quantum error correction

A quantum computer's qubits and the noise that corrupts them, checked against a code designed to detect and fix errors before they spread.

Question it answers: Does this error-correcting code actually protect the computation, given realistic noise?

Leaves out: Real noise is correlated and drifts over time in ways that idealised models rarely capture.

Runs on: about 10^15 FLOPS rough a memory-heavy cluster node; larger codes cost far more. Since: 1996 early simulations testing the first proposed error-correcting codes.

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Rules and states](https://simulation-hypothesis.com/simulations/methods#m-rules)floor: Subatomic

### Topological quantum matter

Electrons on a lattice arranged so that their collective state depends on its overall shape rather than local details, computed to find quantum Hall states and other topological phases.

Question it answers: Does this material host a phase of matter protected by its topology rather than its symmetry?

Leaves out: Telling a genuinely topological state from a very similar ordinary one can hinge on numerical precision most runs cannot quite reach.

Runs on: about 10^16 FLOPS rough a large cluster or supercomputer partition, days per candidate system. Since: 1988 early numerical studies following the theoretical discovery of topological order.

[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Ultracold atomic gas dynamics

A cloud of atoms cooled until they share one quantum wavefunction, evolved with the mean-field equation that describes a Bose-Einstein condensate.

Question it answers: How does the condensate oscillate, split or form vortices when perturbed?

Leaves out: The mean-field equation misses the individual atom correlations that matter close to a phase transition.

Runs on: about 10^13 FLOPS rough a workstation; minutes to hours per trapped cloud. Since: 1995 modelling built around the first laboratory Bose-Einstein condensates.

[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Atoms

### Digital quantum simulation on hardware

A quantum computer built from controllable qubits runs a sequence of gates that imitates the evolution of another such system.

Question it answers: Can a programmable quantum device reproduce the dynamics of a model too large for classical memory?

Leaves out: Noise limits depth, and the Trotter approximation introduces its own error.

Runs on: no computer. Quantum hardware, not classical FLOPS; verification on conventional machines only at small size Since: 2011 Universal digital quantum simulation with trapped ions (2011) [source](https://doi.org/10.1126/science.1208001)

[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Subatomic

### Lattice gauge theory on quantum hardware

A few-qubit quantum computer evolves a lattice gauge theory in real time, a task that is hard for classical Monte Carlo because of the sign problem.

Question it answers: Can real-time dynamics of a gauge theory be run on a quantum computer?

Leaves out: Only one spatial dimension and a handful of sites so far.

Runs on: no computer. Small qubit counts; classical cost of cross-checking grows exponentially Since: 2016 Real-time dynamics of lattice gauge theories with a few-qubit quantum computer (2016) [source](https://arxiv.org/abs/1605.04570)

[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)[Lattice field theory](https://simulation-hypothesis.com/simulations/methods#m-lattice)floor: Subatomic

### Neural-network quantum states

A neural network represents the wavefunction of a many-body system, and its parameters are tuned by variational Monte Carlo to find ground states and dynamics.

Question it answers: Can a neural network compactly encode a quantum state that is too large to store exactly?

Leaves out: The accuracy depends on network design, and the optimisation can stall in poor minima.

Runs on: about 10^16 FLOPS rough Training with variational Monte Carlo on accelerators Since: 2016 Solving the quantum many-body problem with artificial neural networks (2016) [source](https://arxiv.org/abs/1606.02318)

[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Subatomic

### Superconducting vortex dynamics

The tubes of magnetic flux that thread a type-II superconductor, followed as they move, pin on defects and dissipate energy, using a time-dependent field theory for the superconducting state.

Question it answers: How do magnetic vortices move and get stuck inside a superconductor?

Leaves out: The phenomenological field theory ignores microscopic electron behaviour and is valid only near the transition temperature.

Runs on: about 10^14 FLOPS rough three-dimensional time-dependent Ginzburg-Landau runs on a cluster. Since: 1996 Gropp and colleagues' numerical simulation of vortex dynamics in type-II superconductors. [source](https://doi.org/10.1006/jcph.1996.0022)

[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields

### Path-integral Monte Carlo of quantum fluids

Each quantum particle is represented as a ring of linked copies, sampled at finite temperature to compute superfluid helium and other bosonic liquids from the interaction alone.

Question it answers: Why does liquid helium flow without friction below two kelvin?

Leaves out: Fermions suffer the sign problem, so electrons and helium-3 need approximations that introduce uncontrolled error.

Runs on: about 10^14 FLOPS rough billions of path samples for a bulk liquid. Since: 1984 Pollock and Ceperley's path-integral simulation of quantum many-body systems and superfluid helium. [source](https://doi.org/10.1103/physrevb.30.2555)

[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms

### Stabilizer circuit simulation

A classical computer tracks a quantum circuit built only from Clifford gates by following how a small table of Pauli operators changes, instead of storing the full state. This lets error-correction circuits with thousands of qubits be run.

Question it answers: How often does an error-correcting code fail when every gate, measurement and idle step is noisy?

Leaves out: Only circuits made of Clifford operations and Pauli measurements can be tracked this way, so universal quantum computation is out of reach.

Runs on: about 10^12 FLOPS rough millions of noisy shots of a large code patch on a workstation cluster. Since: 2004 Aaronson and Gottesman's improved algorithm for simulating stabilizer circuits in polynomial time. [source](https://doi.org/10.1103/physreva.70.052328)

[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Rules and states](https://simulation-hypothesis.com/simulations/methods#m-rules)floor: Rules

### Learned error-correction decoders

A neural network is trained on simulated error patterns from a quantum code to read the measured syndromes and infer which correction to apply.

Question it answers: Can a learned decoder fix errors in a quantum memory faster or more accurately than a hand-designed algorithm?

Leaves out: The decoder only knows the noise model it was trained on, and real hardware drifts and has correlated errors the simulation did not include.

Runs on: about 10^15 FLOPS rough training on billions of simulated syndromes on GPU nodes. Since: 2016 Torlai and Melko's neural decoder for topological codes (arXiv 2016, published 2017). [source](https://arxiv.org/abs/1610.04238)

[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Rules

### Quantum network simulation

Nodes holding qubits, entangled links and noisy photon channels modelled as discrete events in time, so that protocols for sharing entanglement across a network can be tested.

Question it answers: How fast and how faithfully could two distant nodes share entanglement through repeaters and lossy fibre?

Leaves out: Hardware noise is reduced to a few parametrised models, and no network at scale exists to check the predicted rates against.

Runs on: about 10^11 FLOPS rough many long runs of a network protocol on a single server. Since: 2021 Coopmans and colleagues' NetSquid, a discrete-event simulator for quantum networks. [source](https://doi.org/10.1038/s42005-021-00647-8)

[Discrete event](https://simulation-hypothesis.com/simulations/methods#m-discrete-event)[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)[Network models](https://simulation-hypothesis.com/simulations/methods#m-network)floor: Rules

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