fdmsim · quantum simulation program

Two Frontiers of Quantum Simulation

Two 2024 papers, reproduced & extended — the analog face (mimic the physics with a stand-in physical system) and the digital face (run it as a quantum circuit) of quantum simulation, both on one core engine: our differentiable spectral solver.

VACUA · vacuum decay in a cold-atom BEC

Jenkins et al., PRD 109, 023506 (2024)

The paper · mechanism

Analog · cold-atom experiment (their proposal)

What we did · our reproduction

Numerical simulation (classical spectral)

Two-component BEC

⁴¹K condensate of two atomic states; relative phase φ is the field.

Differentiable spectral split-step solver

Same FFT engine as our FDM code.

Modulated coupling (λ) → false-vacuum well

An rf drive sculpts the double-well potential.

Seed the correct quantum jitter

Bogoliubov-correlated fluctuations — not plain random noise.

Fluctuations → bubble

Nucleates and expands relativistically.

Evolve the two-field GPE

Bubble nucleates & expands at 45° (relativistic).

Image the condensate

Read out the relative phase to watch the decay.

Fit the decay rate Γ(n̄)

Matches the paper's theory.

⚙

Runs on — a cold-atom BEC (analog)

Proposed platform, not built yet. The paper's own figures are classical numerics.

⚙

Runs on — an ordinary classical computer

Our spectral solver; no quantum hardware.

QVLASOV · quantum algorithm for neutrino structure

Miyamoto et al., PRR 6, 013200 (2024)

The paper · algorithm

Digital quantum algorithm

What we did · our reproduction

Numerical simReal IonQ hardware

Linearize Vlasov

Drop neutrino self-gravity → the equation becomes linear.

Classical Vlasov reference

scipy matrix-exp — the ground truth.

Recast as Schrödinger (H = iA)

i∂ₜ|f⟩ = H|f⟩, with A antisymmetric.

Trotterize + exact statevector emulation

4–6 qubits, noiseless.

Qubits + Trotter

Load f into amplitudes; split e^(−iHt) into gate steps.

Would require a fault-tolerant machine: a logarithmic number of error-corrected logical qubits + a QRAM (O(n_gr³) entries). A realistic 6-D cosmological run → thousands of physical qubits + QRAM that doesn't exist yet.FTQC · not today's hardware

Transpile → real IonQ Forte-1

4 physical NISQ qubits, 300 shots, no error correction — the core mechanism at toy scale (n_gr = 4), not the full algorithm.

Quantum hardware

Run the circuit → power spectrum

Measure, reconstruct the neutrino power spectrum.

Benchmark classical ↔ simulator ↔ hardware

And root-cause the noise.

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Runs on — fault-tolerant QC + QRAM (digital)

Proposed platform, not built yet. Paper's own figures are classical numerics.

⚙

Runs on — classical + real IonQ Forte-1 qubits

The one place real quantum hardware enters this program.

The gap: the paper's full algorithm needs a fault-tolerant machine (thousands of logical qubits + QRAM); we ran its core mechanism on 4 real NISQ qubits — a faithful toy, not the full speedup.

Deck · 20 Jul 2026 · use ← / → to navigate

Paper 1 · VACUA · the physics

False-vacuum decay, on a tabletop

Quantum nucleation of true-vacuum bubbles from a metastable "false vacuum" — the early-universe process behind eternal inflation, electroweak baryogenesis, Higgs metastability and gravitational-wave backgrounds — realized as an analog in a two-component ⁴¹K Bose–Einstein condensate.

The condensate's relative phase φ obeys a relativistic Klein–Gordon equation (a relativistic wave equation) in a double-well potential.
The "speed of light" is the sound speed c = √(gn/m) ≈ 6 mm/s — relativity, at walking pace.
A metastable well at φ = π appears only when the modulation λ > 1; below that it vanishes.

U(φ) = 4εφ₀² (m²c²/ℏ²) [ 1 − cos(φ/φ₀) + ½ λ² sin²(φ/φ₀) ] Jenkins+24, Eq. 10 — λ is the knob that carves the middle dip.

φ — the field: the relative phase between the two BEC species (the ball's position on the landscape).
φ₀ — the yardstick: a fixed scale (√(ℏ²n/2m)); we plot φ/φ₀, so vacua land at 0, π, 2π…
λ — the knob: the modulation strength that shapes the landscape; λ>1 creates the false-vacuum dip.

Fig. 2 — the false-vacuum landscape: metastable minimum at φ=π for λ>1.

Paper 1 · VACUA · simulation approach

Spectral split-step + the correct quantum vacuum

We evolve the condensate with our own spectral split-step solver (the same engine as our FDM code — no new machinery). The hard part isn't evolving the field; it's how you start it.

You must seed the correct quantum jitter. Even a "resting" vacuum trembles; the simulation must start from that exact tremor pattern — strong at large scales, flat at tiny scales.
The lazy shortcut fails. Seeding plain random noise makes the vacuum decay too fast (it's secretly an excited state) — a fake, inflated result. The paper flags this as the easy-to-botch step.
This chart is the receipt. It checks our starting jitter is right — and it is.

THE PAPER — Jenkins+24, Fig. 3. Right panel: the fluctuation spectrum — Klein–Gordon at big scales, flat "white noise" (¼) at tiny scales.

OURS — the same spectrum (right panel), reproduced.

The point: our sampled starting conditions (circles) land on the correct theory curve — matched to 0.1% — reproducing the paper's right panel. It is not flat: it bends at the healing scale, so naïve "white noise" would be visibly wrong. This quality gate makes the bubble & decay-rate results trustworthy.

Paper 1 · VACUA · results in the paper

Bubbles nucleate; the rate obeys the theory

Jenkins et al. demonstrate quantum-regime false-vacuum decay in a two-component ⁴¹K condensate — an Editors' Suggestion in Phys. Rev. D. The headline: the decay rate is set by the fluctuation amplitude, exactly as the instanton theory predicts.

Editors' Suggestion PRD 109, 023506 (2024) T ≲ 10.9 nK charges ~ppb

The paper — Jenkins+24, Fig. 6

Sweeps amplitude n̄ = 10–50, 1024 simulations per point.
Left: survival P(t) ~ exp(−Γt). Right: decay rate Γ/V falls steeply as n̄ grows.
Vacuum (blue) decays slower than white-noise (red) — white noise is an excited state that over-nucleates.
The rate is set by the fluctuation amplitude, exactly as instanton theory predicts (Eq. 22).

our reproduction: decay rate vs amplitude

Ours — reproduced on our engine

The same measurement: Γ vs n̄, vacuum (blue) vs white-noise (orange).
Both trends reproduced: Γ falls with n̄, and white-noise decays faster.
Honest differences: n̄ = 3–8 (a cheaper laptop slice), fewer samples, different normalization — trends match, not an exact overlay.
The full n̄ = 10–50 GPU reproduction is queued.

Paper 1 · VACUA · what we reproduced

A bubble nucleating, on our own engine

Blind, check-by-check reproduction (G0–G4) on our differentiable spectral solver — the money shot: a true-vacuum bubble whose wall expands at 45°, i.e. at the phonon "speed of light."

The paper — Jenkins+24, Fig. 1

A space-time diagram: time runs up, position across, colour = which vacuum each point sits in.
A true-vacuum bubble (red) nucleates out of the fluctuating false vacuum (blue).
Its walls expand at 45° — the phonon "speed of light" — exactly as vacuum-decay theory predicts.
Run on their cold-atom analog model (2048-site lattice).

our space-time diagram of bubble nucleation

Ours — reproduced on our engine

Blind, check-by-check (G0–G4) on our differentiable spectral solver.
A bubble nucleates (~ct 450) and its wall races out at the identical 45°.
Engine checks: conserved quantities hold to 3×10⁻¹²; the correct quantum-jitter start to 0.1%.
Honest: reduced-statistics laptop run (N=1024) — same phenomenon, our own run beside the paper's.

Paper 2 · QVLASOV · the physics

Massive neutrinos as hot dark matter

Neutrinos have tiny mass but huge velocities — hot dark matter that shapes cosmic large-scale structure differently from cold dark matter. Observing that structure constrains the neutrino mass.

Because they fly freely (free-streaming), they wash out structure below a characteristic size.
To predict that, you must track their full spread over both position and velocity — the 6-D distribution f(x, v).
The neutrino mass is one of the last unmeasured Standard-Model numbers — cosmology is the sharpest probe.

THE PAPER — Miyamoto+24, Fig. 2. Phase space f(x,v) at three times — the calm band shears as gravity acts.

Miyamoto Fig 2 phase space (three panels in a row)

OURS — the same phase-space evolution, reproduced.

Reading both: position across, velocity up, colour = how many neutrinos at each position-and-speed. The distribution starts as a flat band and shears under gravity — this whole object is what the simulation evolves. Our run reproduces the paper's.

Paper 2 · QVLASOV · simulation approach

From Vlasov to a quantum circuit

The Vlasov equation isn't quantum — but a few honest approximations turn it into exactly the kind of problem a quantum computer is built to solve. Follow the chain:

Linearize the physics

Neutrinos are <1% of all matter, so ignore their own gravity and treat the dark-matter pull as a fixed external force. With that, the Vlasov equation becomes linear.

∂f/∂t + v·∂f/∂x + F_CDM·∂f/∂v = 0 (Eq. 4)

Rewrite it as a Schrödinger equation

Put the distribution f on a grid and the equation becomes df/dt = A·f with A antisymmetric. Multiply by i and it is literally a Schrödinger equation — a cosmology equation in disguise as quantum mechanics.

i ∂_t|f⟩ = H|f⟩, H = iA (Hermitian)

Load f into qubits

Store the grid of numbers in the amplitudes of qubits. n qubits hold 2ⁿ grid points — so the 6-D phase-space explosion becomes "a few more qubits," not exponentially more memory. This is where the quantum advantage comes from.

n qubits → 2ⁿ grid points

Evolve with Hamiltonian simulationthe missing bridge

The answer is |f(T)⟩ = e^−iHt|f(0)⟩. A quantum computer can't apply that giant operator in one shot — so split it into tiny alternating steps: a little streaming, a little gravity, repeated. That's Trotterization, and each tiny step is just a small set of standard quantum gates.

|f(T)⟩ = e^−iHt|f(0)⟩ ≈ ( e^−iH_xτ · e^−iH_vτ )^N

Run & measure

Those gates form a circuit. Run it, measure the qubits many times, and the measurement statistics reconstruct f(T) → the neutrino power spectrum P(k).

circuit → shots → f(T) → P(k)

Net: a 6-D cosmology PDE → a Schrödinger equation → a gate circuit a quantum computer runs natively. In our QVLASOV lane we actually ran this on IonQ hardware — see slide 10.

Paper 2 · QVLASOV · results in the paper

A quantum algorithm, plus a small demo

This is a quantum-algorithm paper — designed for a future fault-tolerant machine — accompanied by a small classical demonstration of the physics.

Small classical demo (Sec. IV): one dimension in position and velocity, a 64-point grid, a single gravity ripple F = A·sin(Kx).
That one gravity ripple (wavenumber K) drives only the matching neutrino ripple (k=K) — nothing else (Figs. 3–4).
The quantum algorithm scales as Õ(n_gr+n_t) vs classical O(n_gr⁶) — the potential speedup.
Reading out the power spectrum (structure vs. size) needs quantum amplitude estimation and a quantum memory (QRAM).

THE PAPER — Miyamoto+24, Figs. 3–4. Left: the neutrino density ripple. Right: its spectrum — a single spike at k=K.

Miyamoto Figs 3-4 density and Fourier mode

OURS — the same single-mode response, reproduced.

our density perturbation, only k=K mode driven

Reading both: feed in one gravity ripple (wavenumber K) and exactly one matching neutrino ripple responds — everything else stays zero. The clean single-mode result the demo is meant to show; ours reproduces the paper's.

Paper 2 · QVLASOV · what we reproduced — and extended

We ran it on real quantum hardware

Beyond reproducing the paper, we did what the authors never did: ran the core step on a real quantum computer — IonQ's trapped-ion Forte-1.

Reproduced the classical demo (one gravity ripple drives one neutrino ripple; total probability held to 1e-15).
The step-by-step (Trotter) version, run on an exact simulator (4–6 qubits), converges to the true answer (top figure).
Our extension: ran it on IonQ Forte-1 — 4 real qubits, circuits of 40/78/116 two-qubit gates, 300 runs each.
Checked classical → cloud simulator (0.996 match) → real machine; when well-calibrated it reproduces the answer to ~90–95%.

Honest ceiling. The full future-hardware algorithm (needs an error-corrected / fault-tolerant machine, a quantum memory / QRAM, 6-D, amplitude estimation) won't run on today's noisy quantum computers — we ran the toy-scale core step, not the asymptotic speedup.

Top — the point: the step-by-step (Trotter) error shrinks toward zero as you add more steps, on an exact simulator. The method itself is sound, before any hardware noise.

Bottom — the point: on real IonQ hardware — how closely the output matches truth (fidelity) and how much probability leaks to wrong states (leakage), across circuit depths. Calibrated circuits reach ~90–95%.

Paper 2 · QVLASOV · questions & our RCA

Why was the shallowest circuit the worst?

Counterintuitively, the fewest-gate circuit was reproducibly the worst (fidelity ~0.6). A root-cause analysis cleanly separated two error regimes.

We varied the number of steps n_t at the same total evolution time and compared to a random-noise model — that separates the two error types.
Random gate noise alone would make the fewest-gate circuit best (model: 0.84) — but on hardware it's the worst.
⇒ the culprit is a systematic (coherent) error in the shallow, large-rotation-angle case — not random depth noise.
From n_t ≥ 2 the results follow the random-noise trend; the sweet spot is n_t=2.

Next: prove the coherent-error mechanism (randomized compiling / error mitigation), push larger n_gr on simulator, and find where the quantum speedup actually pays off.

RCA: hardware vs depolarizing noise model

The point of this chart (RCA): real hardware (points) vs a pure random-noise model (line). They disagree exactly where the circuit is shallowest — proof of a systematic error there, not random noise. Two error regimes, cleanly separated.

The big picture · how × what

The Quantum-Simulation Map

Two axes — the method (how) and the phenomenon (what). Most phenomena can be done several ways; each method spans several phenomena. Our two papers sit here ↓; the next slide is the full catalog.

Cold-atom / BECAnalog

Rydberg / lattice arraysAnalog

Superconducting / ionDigital

Fault-tolerant algorithmFTQC · future

Classical numericalClassical

Vacuum decay & the early universe

✓ oursJenkins · VACUAEckelViermann

Black holes & Hawking radiation

Steinhauer '16Steinhauer '19

Benhemou

Shi

Cosmic structure: dark matter & neutrinos

✓ oursMiyamoto · QVLASOV

SchiveMocz

Quantum matter & magnetism

BernienEbadiSemeghiniMazurenko

Arute · FHAndersen · braiding

Lattice gauge theories

Yang

MartinezKokail

Time crystals & non-equilibrium order

Quantum chemistry & molecules

Kandala · VQEArute · HF

Particle physics & quantum field theory

Klco · SchwingerBauer · partonHall · neutrinos

Jordan–Lee–Preskill

Nuclear physics

Dumitrescu · deuteron

Quantum information: scrambling & holography

Landsman · scrambling

Glowing cells = runs on (or algorithms for) a real programmable quantum computer — Rydberg / optical-lattice arrays, superconducting & trapped-ion processors, and fault-tolerant algorithms. Un-glowed cells are analog-gravity mimicry (cold-atom BEC) or classical numerics. Most are small proof-of-principle demos today.

Analog is the physics; digital & algorithmic compute it; classical is the yardstick — but all reduce to Hamiltonian evolution on a grid.

The wider field · 29 papers

The Quantum Simulation Landscape

Where our two papers sit in the quantum-simulation landscape — 29 papers, analog and digital, from cosmology-in-the-lab to Rydberg arrays, and digital quantum processors running chemistry, high-energy, nuclear & scrambling problems. Our two reproductions are highlighted. Click any chart to enlarge.

Paper

Physics · Approach · Result

Hero chart

Cosmology & curved spacetime, in the lab · analog

Jenkins et al. 2024 — Analog vacuum decay from vacuum initial conditions ✓ reproduced · this deck arXiv 2307.02549 · PRD 109, 023506

PhysicsFalse-vacuum decay / bubble nucleation

ApproachCold-atom BEC, 2-field GPE (analog)

ResultDecay rate Γ set by the correlated-vacuum amplitude; naïve white noise over-nucleates

Eckel et al. 2018 — A rapidly expanding BEC: an expanding universe in the lab arXiv 1710.05800

PhysicsExpanding-universe cosmology

ApproachCold-atom BEC, expanding ring (analog)

ResultPhonon redshift + Hubble friction + preheating-like turbulent cascade

Viermann et al. 2022 — Quantum field simulator for dynamics in curved spacetime arXiv 2202.10399

PhysicsScalar QFT in curved / expanding spacetime

ApproachCold-atom BEC, tunable 2D metric (analog)

ResultCosmological particle production & Sakharov oscillations in a programmable metric

Steinhauer 2016 — Observation of quantum Hawking radiation & its entanglement in an analogue black hole arXiv 1510.00621 · Nat. Phys.

PhysicsHawking radiation (spontaneous, quantum)

ApproachCold-atom BEC sonic horizon (analog)

ResultObserved entangled Hawking–partner phonon pairs across the horizon

Steinhauer 2019 — Observation of thermal Hawking radiation & its temperature in an analogue black hole arXiv 1809.00913 · Nature

PhysicsHawking radiation thermality & temperature

ApproachCold-atom BEC sonic horizon (analog)

ResultMeasured the Hawking temperature; confirmed a thermal spectrum

Shi et al. 2023 — Hawking radiation & curved spacetime with a superconducting on-chip black hole arXiv 2111.11092

PhysicsHawking radiation / curved spacetime

ApproachSuperconducting qubit chain, on-chip (analog)

ResultStimulated Hawking-like emission & wave propagation in a curved metric on chip

Benhemou et al. 2023 — Probing black holes with a Floquet-driven optical-lattice simulator arXiv 2312.14058

PhysicsAnalog black hole (Hawking, scrambling)

ApproachOptical lattice, Floquet-driven (analog · proposal)

ResultPosition-dependent tunnelling encodes the curved metric; Hawking T from site populations

Nixon et al. 2023 — Individually tunable tunnelling in optical lattices via local periodic driving arXiv 2309.12124

PhysicsEngineered lattice Hamiltonians (enabling toolkit)

ApproachOptical lattice, local Floquet driving (analog · theory)

ResultFull local control of tunnelling → SSH / topological & curved-space lattices

Fuzzy dark matter & neutrino cosmology · numerical / quantum-algorithm

Schive et al. 2014 — Cosmic structure as the quantum interference of a coherent dark wave arXiv 1406.6586 · Nat. Phys.

PhysicsFuzzy dark matter cosmic structure

ApproachClassical spectral Schrödinger–Poisson

ResultSolitonic core in every halo; boson mass m_B ≈ 8×10⁻²³ eV

Mocz et al. 2019 — First star-forming structures in fuzzy cosmic filaments arXiv 1910.01653

PhysicsFDM structure formation in filaments

ApproachClassical spectral Schrödinger–Poisson

ResultSolitons, caustics & interference along filaments; first-star formation delayed

Miyamoto et al. 2024 — Quantum algorithm for the Vlasov simulation of LSS with massive neutrinos ✓ reproduced · this deck arXiv 2310.01832 · PRR 6, 013200

PhysicsMassive-neutrino hot dark matter / large-scale structure

ApproachQuantum algorithm, Vlasov→Schrödinger (digital)

ResultÕ(n_gr+n_t) vs classical O(n_gr⁶); one CDM force mode drives one density mode

Neutral-atom & optical-lattice quantum simulators · analog

Bernien et al. 2017 — Probing many-body dynamics on a 51-atom quantum simulator arXiv 1707.04344 · Nature

PhysicsMany-body dynamics / quantum scars

ApproachRydberg atom array, 51 qubits (analog)

ResultZ₂-ordered phases; persistent oscillations (scars) after a rapid quench

Ebadi et al. 2021 — Quantum phases of matter on a 256-atom programmable quantum simulator arXiv 2012.12281 · Nature

PhysicsQuantum phases of matter & criticality

ApproachRydberg atom array, 256 qubits (analog)

ResultMapped checkerboard / striped / star phases; quantum Kibble–Zurek scaling

Semeghini et al. 2021 — Probing topological spin liquids on a programmable quantum simulator arXiv 2104.04119 · Science

PhysicsTopological order / quantum spin liquid

ApproachRydberg array on kagome links, 219 atoms (analog)

ResultToric-code-type spin liquid detected via topological string operators

Yang et al. 2020 — Observation of gauge invariance in a 71-site Bose–Hubbard quantum simulator arXiv 2003.08945 · Nature

PhysicsU(1) lattice gauge theory / Gauss's law

ApproachOptical lattice, Bose–Hubbard, 71 sites (analog)

ResultObserved emergent gauge invariance (Gauss's law) in cold atoms

Mazurenko et al. 2017 — A cold-atom Fermi–Hubbard antiferromagnet arXiv 1612.08436 · Nature

PhysicsFermi–Hubbard antiferromagnetism (high-T_c)

ApproachOptical lattice + quantum-gas microscope (analog)

ResultLong-range antiferromagnetic order (staggered magnetization) reached

Digital quantum processors · superconducting & trapped-ion

Mi et al. 2021 — Time-crystalline eigenstate order on a quantum processor arXiv 2107.13571 · Nature

PhysicsDiscrete time crystal (non-equilibrium phase)

ApproachSuperconducting qubits (Google Sycamore) (digital)

ResultObserved stable eigenstate-ordered DTC across generic initial states

Martinez et al. 2016 — Real-time dynamics of lattice gauge theories with a few-qubit quantum computer arXiv 1605.04570 · Nature

PhysicsLattice gauge theory (Schwinger model) dynamics

ApproachTrapped-ion quantum computer (digital)

ResultFirst digital simulation of Schwinger pair-creation; gauge invariance preserved

Kokail et al. 2019 — Self-verifying variational quantum simulation of lattice models arXiv 1810.03421 · Nature

PhysicsLattice gauge theory (Schwinger model) ground states

ApproachTrapped-ion variational, 20 qubits (hybrid digital)

ResultVariational ground states + energies/gaps with built-in self-verification

Quantum computing · chemistry & materials

Kandala et al. 2017 — Hardware-efficient VQE for small molecules & quantum magnets arXiv 1704.05018 · Nature 549, 242

PhysicsMolecular ground-state energies (H₂, LiH, BeH₂)

ApproachSuperconducting qubits, hardware-efficient VQE (digital)

ResultBeH₂ energy on 6 qubits — largest molecule on a QC then; proof-of-principle

Arute et al. (Google) 2020 — Hartree–Fock on a superconducting qubit quantum computer arXiv 2004.04174 · Science 369, 1084

PhysicsElectronic structure — Hartree–Fock, diazene isomerization

ApproachSuperconducting qubits (Sycamore), up to 12 qubits, VQE (digital)

ResultLargest chemistry VQE at the time; error mitigation → chemically-relevant energies

Arute et al. (Google) 2020 — Separated dynamics of charge & spin in the Fermi–Hubbard model arXiv 2010.07965

PhysicsFermi–Hubbard dynamics — spin–charge separation

ApproachSuperconducting qubits (Sycamore), 16 qubits, Trotterized (digital)

ResultCharge & spin spread at different speeds in 1D chains — proof-of-principle

Arute Fermi-Hubbard charge-spin dynamics

Quantum computing · high-energy, nuclear & information

Jordan, Lee & Preskill 2012 — Quantum algorithms for quantum field theories arXiv 1111.3633 · Science 336, 1130

PhysicsRelativistic scattering in φ⁴ scalar QFT

ApproachFault-tolerant quantum algorithm (FT · theory)

ResultPolynomial-time scattering amplitudes, exponential speedup at strong coupling — foundational, not yet run

Jordan-Lee-Preskill quantum algorithms for QFT

Klco et al. 2018 — Quantum-classical computation of Schwinger-model dynamics arXiv 1803.03326 · PRA 98, 032331

Physics1+1D QED (Schwinger model), real-time dynamics

ApproachIBM superconducting qubits, hybrid variational (digital)

Resulte⁺e⁻ pair production & vacuum persistence on 2 qubits — small demo w/ error mitigation

Bauer, de Jong, Nachman & Provasoli 2019 — A quantum algorithm for high-energy-physics simulations arXiv 1904.03196 · PRL 126, 062001

PhysicsCollider parton showers with quantum interference

ApproachQuantum circuit / algorithm, IBMQ demo (digital)

ResultCaptures interfering emission histories classical Markov showers miss — toy-model demo

Hall, Roggero, Baroni & Carlson 2021 — Simulation of collective neutrino oscillations on a quantum computer arXiv 2102.12556 · PRD 104, 063009

PhysicsCollective (many-body) neutrino flavor oscillations

ApproachSuperconducting qubits (IBM / Rigetti) (digital)

ResultTracked inversion probability for 2–4 neutrinos; error mitigation needed — proof-of-principle

Dumitrescu et al. 2018 — Cloud quantum computing of an atomic nucleus arXiv 1801.03897 · PRL 120, 210501

PhysicsDeuteron binding energy (nuclear structure)

ApproachIBM QX5 & Rigetti 19Q, cloud VQE, 2–3 qubits (digital)

ResultDeuteron ground-state energy via pionless EFT — first atomic nucleus on a QC

Landsman et al. 2019 — Verified quantum information scrambling arXiv 1806.02807 · Nature 567, 61

PhysicsQuantum information scrambling / black-hole teleportation

ApproachTrapped-ion 7-qubit processor (digital)

ResultTeleportation-fidelity witness verifies scrambling; wormhole-inspired protocol — small-scale demo

Andersen et al. (Google) 2023 — Non-Abelian braiding of graph vertices in a superconducting processor arXiv 2210.10255 · Nature 618, 264

PhysicsNon-Abelian topological order & anyon braiding

ApproachSuperconducting qubits (Sycamore-class) (digital)

ResultCreated & braided non-Abelian anyons; braids change the measured state — step toward topological QC

Cosmology in the lab FDM / neutrino cosmology Neutral-atom / lattice Digital QPU QC · chemistry & materials QC · HEP / nuclear / info ✓ our reproductions (VACUA · QVLASOV)

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