Vol. 0.2 Edition 2026 MIT License Open source

Quantum circuits for electron microscopy.

QuScope rebuilds transmission electron microscopy image formation as quantum circuits. The electron wavefunction is amplitude-encoded on qubits, and every optical element (specimen phase grating, Fresnel propagation, objective lens) is a diagonal unitary between quantum Fourier transforms, validated against classical references.

View on GitHub Read the papers →

By Sean D. Lam & Roberto dos Reis · Northwestern University

Quantum-circuit simulation of a phase-contrast CTEM image of a crystalline specimen, computed with QuScope: a lattice of dark atomic-column contrast in grey speckle — Fig. 01 — QuScope CTEMarXiv:2602.13438

Electron wavefunctions on qubits ✦ CTEM · STEM · Multislice ✦ Optics as diagonal gates ✦ Validated against classical references ✦ Qiskit · Aer · IBM Quantum ✦ Open source · MIT ✦ Electron wavefunctions on qubits ✦ CTEM · STEM · Multislice ✦ Optics as diagonal gates ✦ Validated against classical references ✦ Qiskit · Aer · IBM Quantum ✦ Open source · MIT ✦

The method

The microscope, rewritten as a circuit.

One circuit per image (CTEM) or per probe position (STEM); slices repeat for thick specimens.

01 //Encoding

Wavefunction on qubits

An N×N wavefield lives on 2 log₂N qubits through amplitude encoding.

02 //Circuits

Optics as diagonal gates

Phase gratings, Fresnel propagation and the lens are diagonal unitaries between quantum Fourier transforms.

03 //Verified

Validated

Noise-free circuits reproduce the classical reference implementations to unit fidelity.

04 //Backends

Simulator to hardware

Qiskit Aer statevector and shots, noise models, and IBM Quantum devices through one backend manager.

From column to circuit

Every lens has a gate.

The CTEM column, stage by stage: the classical image-formation model and its quantum-circuit counterpart. Hover or tap a stage to find it in the column (after Lam & dos Reis, arXiv:2602.13438, Fig. 1).

Conventional TEM column

Stage 01
Illumination

Classical CTEM model
Incident wave
$ψ (r) = φ (r_{⊥}, z) \exp (i k_{0} z)$

Quantum circuit
State preparation
$| ψ_{0} ⟩ = H^{\otimes n} | 0 ⟩^{\otimes n}$
Stage 02
Specimen

Classical CTEM model
Phase grating
$t (r_{⊥}) = \exp [i σ V_{proj} (r_{⊥})]$ $φ_{exit} (r_{⊥}) = t (r_{⊥}) φ_{inc} (r_{⊥})$

Quantum circuit
Diagonal phase operation
$U_{obj} = \sum_{i, j} e^{i σ V_{i j}} | i, j ⟩ ⟨ i, j |$
Stage 03
Propagation & objective lens

Classical CTEM model
Free space + lens in Fourier space
$\tilde{φ} (k_{⊥}, z) = \tilde{φ} (k_{⊥}, 0) \exp [- i π λ z k_{⊥}^{2}]$ $H (k_{⊥}) = \exp [- i χ (k_{⊥})], CTF (k) = \sin [χ (k)]$

Quantum circuit
QFT to momentum space + diagonal phases
$U_{QFT} U_{P} (z) U_{χ}$
All unitary gates.
Stage 04
Detection

Classical CTEM model
Image intensity
${| φ_{img} |}^{2}$

Quantum circuit
Inverse QFT and measurement
$| ψ_{img} ⟩ = U_{QFT}^{†} U_{χ} U_{P} (z) U_{QFT} U_{obj} | ψ_{0} ⟩$

The catalogue

Four validated imaging pipelines.

Pick a pipeline; the plate highlights the gates it uses.

Side A · Track 1

CTEM (weak phase object)

Phase grating e^iσV applied to the encoded plane wave.
QFT, the contrast transfer function of the objective lens, inverse QFT.
Bright-field image from the measured register.

quantum_ctem_circuit

Experimental: CBED · next release Frozen phonons · TDS · next release Bloch-wave QPE · later

Plate II — The circuit2 log₂N qubits

Each box is one diagonal gate or Fourier transform.

The idea, in one sentence

Every optical element of the microscope becomes a diagonal unitary between two quantum Fourier transforms.

The QuScope approach
Lam & dos Reis · arXiv 2026

The family

One project — several techniques.

QuScope aims to simulate the range of TEM techniques with quantum algorithms: imaging in the core package, ptychography and EELS in sister modules.

Corev0.2.1

QuScopeQuantum-circuit TEM simulation

CTEM, STEM and multislice imaging as quantum circuits, with a 5th-order lens model, Kirkland potentials, materials workflows and Aer or IBM Quantum backends.

GitHub →Documentation →

Sister moduleIn preparation

ptyqoQuantum algorithms for electron ptychography · said “ptycho”

Dose limits of electron ptychography for beam-sensitive specimens: STEM probe and multislice circuits validated against abTEM, electron counting, quantum and classical Fisher information and thermal vibrations, with gas and liquid cells as the demanding in-situ test cases.

Repository coming soon

PlaceholderComing soon

qeelsQuantum EELS

Quantum algorithms for electron energy-loss spectroscopy, the next technique in the family.

Repository coming soon

q-matsuiteMaterials data, ready for quantum simulation

Open-source tools linking materials databases to fault-tolerant quantum algorithms, starting with QMatBridge.

q-matsuite.com →GitHub →

The lab

dos Reis LabMaterials Science · Northwestern

Roberto dos Reis's materials science lab at Northwestern University, home of the QuScope project.

robertodosreis.com →

In print

The papers.

Preprints on arXiv, quantum physics with materials-science cross-lists.

arXiv:2608.02782Aug 2026

QuScope: An Open-Source Python Framework for Quantum-Circuit Simulation of Transmission Electron Microscopy

Sean D. Lam, Roberto dos Reis

The framework: conventional, multislice and scanning TEM pipelines as quantum circuits, validated against a classical reference, with resource estimates and an analysis of diagonal-gate synthesis on near-term hardware.

Read on arXiv →

arXiv:2602.13438Feb 2026

Quantum Algorithm Framework for Phase-Contrast Transmission Electron Microscopy Image Simulation

Sean D. Lam, Roberto dos Reis

Phase-contrast image formation on a gate-based quantum computer, validated on MoS₂ against classical multislice, with a discussion of where circuits may help: Fourier-space queries, global image statistics and phase-coherent observables.

Read on arXiv →

Admit one · Get started

Install QuScope in one line.

pip install quscope

Latest fixes (0.2.1): git clone -b v0.2.x https://github.com/QuScope/QuScope

from quscope.quantum_ctem import QuantumCTEMCircuit, QuantumCTEMParameters
import numpy as np

params = QuantumCTEMParameters(acceleration_voltage=200e3, grid_size=8,
                               pixel_size=0.5, defocus=-659.7, cs=1.3)
result = QuantumCTEMCircuit(params).simulate(np.random.rand(8, 8) * 100)
print(result["intensity"].shape)   # (8, 8)

Ticket No.

0.2.1

★ Star on GitHub Read the docs

Valid on Python 3.9+

Cite

@article{lam2026quscope,
  title   = {QuScope: An Open-Source Python Framework for Quantum-Circuit
             Simulation of Transmission Electron Microscopy},
  author  = {Lam, Sean D. and dos Reis, Roberto},
  journal = {arXiv preprint arXiv:2608.02782},
  year    = {2026}
}

@article{lam2026quantum,
  title   = {Quantum Algorithm Framework for Phase-Contrast Transmission
             Electron Microscopy Image Simulation},
  author  = {Lam, Sean D. and dos Reis, Roberto},
  journal = {arXiv preprint arXiv:2602.13438},
  year    = {2026}
}

Quantum circuits for electron microscopy.

The microscope, rewritten as a circuit.

Wavefunction on qubits

Optics as diagonal gates

Validated

Simulator to hardware

Every lens has a gate.

Illumination

Incident wave

State preparation

Specimen

Phase grating

Diagonal phase operation

Propagation & objective lens

Free space + lens in Fourier space

QFT to momentum space + diagonal phases

Detection

Image intensity

Inverse QFT and measurement

Four validated imaging pipelines.

CTEM (weak phase object)

CTEM multislice

STEM (single slice)

STEM multislice

One project — several techniques.

QuScopeQuantum-circuit TEM simulation

ptyqoQuantum algorithms for electron ptychography · said “ptycho”

qeelsQuantum EELS

q-matsuiteMaterials data, ready for quantum simulation

dos Reis LabMaterials Science · Northwestern

The papers.

QuScope: An Open-Source Python Framework for Quantum-Circuit Simulation of Transmission Electron Microscopy

Quantum Algorithm Framework for Phase-Contrast Transmission Electron Microscopy Image Simulation

Install QuScope in one line.

How to contribute.

Report a bug

Submit code

Docs and tests

Share an example