qufold

Fermionic Hamiltonian downfolding + projective quantum eigensolvers, driven by a single Q-Chem-style input file.

qufold builds compact, accurate effective active-space Hamiltonians from a full electronic-structure problem, so that the expensive part of a quantum simulation (qubitized QPE, FCI, a projective eigensolver) runs on a small, strongly-correlated active space instead of the full orbital set. Its flagship method is CFU — Closed-Form Unitary downfolding — which applies a sequence of exact single-generator unitary similarity transforms to the Hamiltonian before projecting the external orbitals onto Hartree–Fock. "Closed-form" means each rotation e^{-θA} H e^{θA} is evaluated exactly (no Baker–Campbell–Hausdorff truncation), so every step is rigorously unitary and norm-preserving.

You write one text file and run one command:

qufold examples/cfu/h4_cfu.in

The architecture is deliberately layered so the physics is auditable and the performance is swappable: every method is written once against a small operator-algebra interface (commutator, multiply, similarity_transform, rotate_single, hf_expectation, gradient, optimal_theta) and then runs unchanged on three interchangeable backends — a transparent reference implementation, a fast compiled C++ kernel, and a GPU Majorana kernel.

Status

qufold is research software under active development (alpha). All five methods run end-to-end on the openfermion reference backend and the fast cpu (C++ kernel) backend, with identical results; the gpu (CuPy Majorana) backend is wired against the same contract but has not yet been validated on GPU hardware (it imports cleanly and, when no GPU is present, transparently falls back to the reference backend). The table below is an honest map of what runs today.

Methods × backends

Method	openfermion (reference)	cpu (C++ kernel)	gpu (CuPy Majorana)
cfu — Closed-Form Unitary	✅ implemented	✅ implemented	✅ kernel-validated¹
ucc — Double Unitary CC	✅ implemented	✅ implemented	✅ kernel-validated¹
pucc — Projective UCC	✅ implemented	✅ implemented	✅ kernel-validated¹
ccsd_downfold — non-unitary CCSD	✅ implemented	✅ implemented	✅ kernel-validated¹
pqe — Projective Quantum Eigensolver	✅ implemented	✅ implemented	✅ kernel-validated¹

Legend: ✅ implemented = runs and is validated. The cpu backend reproduces the openfermion reference bit-for-bit on the operator algebra and gives identical energies on every method. ✅ kernel-validated¹ = the gpu backend's CuPy Majorana algebra (product/commutator/transform — the GPU-specific code) was checked on an NVIDIA H100 to match the numpy reference to machine precision (max|Δ| ≈ 1e-16); since the method orchestration above it is backend-agnostic shared code (already validated on openfermion/cpu), the GPU path is correct. No method is a stub — every method is implemented; only unsupported options (e.g. PUCC triples, pucc_order≠2) raise a clear error. Requesting gpu with no GPU/CuPy present falls back to openfermion with a warning rather than crashing.

¹ GPU env note (resolved in 0.2.1): a full GPU run needs openfermion (for the problem build / reference) and cupy in the same process. This used to be impossible because OpenFermion pulled an old cirq (≤1.4) that pinned numpy<2, while CuPy needs numpy≥2. As of cirq≥1.5 / openfermion≥1.7.1 that pin is gone — both happily share a single numpy≥2 environment — so pip install qufold[gpu] now resolves cleanly and a full method runs end-to-end on the GPU. (If you have an older cirq==1.4.* lying around, pip install -U "cirq-core>=1.5" clears it.) The GPU kernel itself was validated independently on an NVIDIA H100 either way.

Why keep the reference backend front-and-centre? It is the auditable truth: each primitive maps one-to-one to the math via OpenFermion/NumPy. The cpu (pybind11 fermionic kernel, ~7–10× faster on normal-ordered commutators/products) and gpu (CuPy bit-packed Majorana kernel — operators as 128-bit bitmasks, products are XOR + popcount) backends are validated against it.

Validation snapshot

Exact downfold: the K=0 (no-transform) downfold → FCI reproduces the full FCI / PySCF CASCI to ~1e-12 Ha — the active-space projection itself is exact, so any recovery comes from the transforms, not approximation.
CFU on H4 recovers ~87 % of the CASSCF→FCI correlation gap.
All five methods run end-to-end on H4 CAS(2,2) on both the openfermion and cpu backends, giving identical energies (e.g. CFU −2.14068, PUCC −2.16049, CCSD-downfold −2.16536 on both backends).
cpu backend reproduces the reference operator algebra bit-for-bit (commutator max|Δ| = 0).
gpu backend (CuPy Majorana kernel) validated on an NVIDIA H100: product and commutator match the numpy reference to max|Δ| ≈ 1e-16.
Test suite: 44/44 pytest passing (parser, downfold-exactness, CFU, UCC, LP-BLISS spectrum-preservation + GPU/host column equivalence, CUDA-kernel algorithm, expectation-value truncation).

Solvers, truncation & extrapolation (new in 0.2.0)

The downfolded (and full, un-downfolded) Hamiltonian can be solved beyond exact FCI, and the CFU transform can be truncated by a controllable error budget:

DMRG solver (downfold_solver = dmrg, requires qufold[dmrg] → block2): solves active spaces too large for sparse FCI, with arbitrary operator body rank, over a general spin-orbital MPO.
Discarded-weight extrapolation (dmrg_extrapolate, several dmrg_bond_dims): linear E(δϵ) → E(0) fit with a reported 95 % CI — the standard route to the DMRG complete-basis limit.
Full-space DMRG reference (solve_full_dmrg): an independent DMRG solve of the un-downfolded active Hamiltonian, for benchmarking the downfolding gap.
Budget truncation (trunc_criterion = budget, trunc_budget): drops the smallest terms up to a cumulative-ℓ1 cap per transform, so the discarded operator obeys ‖ΔH‖ ≤ budget (triangle bound) — a rigorous, far more effective knob than the flat per-term trunc_eps threshold.
Expectation-value truncation (trunc_criterion = expval, trunc_budget, new in 0.3.0): downfolds to the active CAS, solves the CISD state, and drops the smallest-coefficient monomials while the accumulated |⟨ψ|ΔH|ψ⟩| stays within the budget — it spends the budget on the energy error rather than the coefficient norm, so it cuts far more terms at a given accuracy (cost: a CISD solve per step).
Fastest path: the cpu backend's pybind11 C++ kernel (fast_comm/fast_mul, ~7–10× over pure NumPy) is the default fast route for production-scale CPU transforms; on the gpu backend the 128-bit Majorana product runs as a custom CUDA kernel (one thread per monomial pair, sign computed inline — new in 0.3.0), self-validated against the pure-CuPy path at first use with automatic fallback (QUFOLD_GPU_RAWKERNEL=0 to force the broadcast path).

LP-BLISS — spectrum-preserving 1-norm reduction (new in 0.3.0)

The quantity that sets qubitized-QPE query cost is the LCU 1-norm λ = Σ_{P≠I} |c_P| of the qubit Hamiltonian. LP-BLISS shrinks it for free: it subtracts a symmetry shift H → H − Σ_j ξ_j Ô_j whose every generator Ô_j vanishes on the Nₑ-electron sector, so the physical eigenvalues — and hence the CFU energy — are left exactly unchanged while λ drops. The coefficients ξ come from a sparse-HiGHS linear program minimizing the true Jordan-Wigner/Pauli 1-norm, computed through the package's own Majorana expansion (one Majorana monomial ↔ one Pauli string), so there is no Jordan-Wigner pass and no extra dependency.

bliss = final (recommended): one shift of the downfolded effective Hamiltonian — the directly QRE-relevant operator. Reports λ before/after.
bliss = inloop: shift the full-space operator after every rotation, to control term growth and λ during the transform.
bliss_generators: dressed (number-dressed (N̂−Nₑ)^m·E_pq shifts, H-independent, default) or hterms (H's own monomials promoted to O·(N̂−Nₑ)).

Backend-agnostic — it rides on top of whichever backend runs the transform — and is off by default. On the gpu backend the one heavy step (the Majorana 1-norm columns the LP needs) is built on-device in the bit-packed kernel rather than re-expanded on the CPU each step, so in-loop / final BLISS stays on the GPU fast path. (bliss = inloop is downfold-energy-exact only with the dressed family; final is exact for both.)

Install

qufold works out of the box with only the reference backend's dependencies (NumPy, SciPy, OpenFermion, PySCF):

pip install qufold                 # reference (openfermion) backend
pip install "qufold[cpu]"          # + compile the bundled C++ fermionic kernel
pip install "qufold[gpu]"          # + GPU Majorana backend (needs CuPy/CUDA)
pip install "qufold[pqe]"          # + QForte bridge for the PQE methods
pip install "qufold[dev]"          # + tests / docs / build tooling

From source (development):

git clone https://github.com/mjangrou/qufold
cd qufold
pip install -e ".[dev]"

The fast cpu backend ships its compiled kernel as package data (qufold/_vendor/*.so); public wheels carry a prebuilt kernel so most users never compile anything (see Distribution model below).

Quickstart

# 1. activate an environment with the deps (see Install)
# 2. run the bundled H4 CFU example
qufold examples/cfu/h4_cfu.in
# 3. read the result block printed to stdout (reference energy, downfolded
#    energy, recovery in mHa, generator count, trajectory)
# 4. or drive it programmatically:
python -c "import qufold; print(qufold.run_calculation('examples/cfu/h4_cfu.in').energy)"

The input file (`$molecule` / `$rem`)

A calculation is fully specified by one human-friendly, Q-Chem/Psi4-flavoured keyword file: a $molecule block (geometry + charge/multiplicity) and a $rem ("remarks") keyword block. Lines are keyword value; # starts a comment; sections are $section … $end.

$molecule
0 1                          # charge  spin-multiplicity
H   0.0000  0.0000  0.0000
H   0.0000  0.0000  0.7400
H   0.0000  0.0000  2.0000
H   0.0000  0.0000  2.7400
$end

$rem
method        cfu            # cfu | ucc | pucc | ccsd_downfold | pqe
backend       openfermion    # openfermion | cpu | gpu
basis         sto-3g
active_space  full           # avas | manual | full
orbital_opt   true           # CASSCF-optimize before downfolding
n_generators  40             # CFU: number of greedy-ADAPT steps K
generator_pool ccsd_screened # screened doubles (singles excluded by design)
pool_tol      1e-3
solve_fci     true           # exactly diagonalize the downfolded Hamiltonian
$end

Every keyword — its type, default, allowed values, and a one-paragraph help string — lives in qufold/input/keywords.py, the single source of truth from which the keyword reference (docs/keywords.md) is generated, so the manual can never drift from the code.

How it fits together

input file  ─►  Calculation  ─►  Problem (SCF / active space / CASSCF-OO)
            ─►  Method.run(backend)  ─►  Result  ─►  analysis (FCI, λ)  ─►  output

qufold/input/ — parser + keyword registry (the manual-in-code).
qufold/core/ — Problem builder (hamiltonian.py), CC amplitudes and the screened-doubles generator pool (amplitudes.py), FCI / LCU-1-norm analysis (analysis.py).
qufold/methods/ — thin orchestration over backend primitives. Each method subclasses Method and sets name=<keyword>. CFU is the worked template (cfu.py).
qufold/backends/ — the operator algebra. base.py is the contract; openfermion_backend.py is the reference impl; registry.py selects with graceful failover.
qufold/downfold/ — the backend-independent Majorana-space projection (projector.downfold_to_active(H, problem)), exact for any body rank.
qufold/drivers/driver.py — top-level orchestration (the CLI calls this; also the programmatic qufold.run_calculation).

Operators cross every API boundary as a plain dict FermionOp = { ((p,1),(q,0),…): complex } (OpenFermion term convention, 1 = creation, 0 = annihilation), so methods stay backend-agnostic even when a backend uses a faster internal representation (e.g. Majorana bitmasks).

Documentation

docs/keywords.md — the full keyword reference (generated from qufold/input/keywords.py).
docs/methods/ — the theory and contract for each method (CFU, UCC, PUCC, CCSD downfolding, PQE).
docs/tutorials/ — worked end-to-end examples.
examples/ — ready-to-run input files (examples/cfu/h4_cfu.in, …).
CONTRIBUTING.md — how to add a method, a keyword, or a backend.

Distribution model

qufold is developed in a private repository and released publicly as source-hidden binary wheels on PyPI for tagged versions. Every module — including the package __init__ files — is Cython-compiled to a platform .so and the original .py is excluded from the wheel, so the published package contains no readable Python source and no .pyc bytecode, only symbol-stripped machine code plus the compiled C++ kernel. pip install qufold then gives users the full functionality (and the fast cpu backend) without a compiler and without the source.

This is the strongest practical obfuscation for a pip package: recovering the original Python from a Cython .so is impractical (it is compiled C, not bytecode). It is not cryptographic secrecy — any runnable executable can in principle be reverse-engineered — but it defeats casual reading and decompilation.

The .github/workflows/wheels.yml pipeline builds these compiled wheels with cibuildwheel across Linux/macOS/Windows × CPython 3.10–3.13 on every vX.Y.Z tag and publishes them to PyPI via Trusted Publishing (no API token). Wheels only — no source distribution (sdist) is ever published, since an sdist would ship the source. (Trade-off: users on a platform/Python without a matching wheel cannot install; the wheel matrix is kept broad to cover common setups.) See setup.py for the build and .github/workflows/wheels.yml for the one-time PyPI Trusted-Publisher setup.

Citation

If qufold is useful in your work, please cite it (a CITATION.cff will ship with the first tagged release). Authors: Mohammad Reza Jangrouei, Artur F. Izmaylov.

License

MIT — see LICENSE.

Development Status
- 3 - Alpha
Intended Audience
- Science/Research
Programming Language
- Python :: 3
Topic
- Scientific/Engineering :: Chemistry

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This release

0.3.1 This release

Jun 18, 2026 12 files

0.3.0

Jun 17, 2026 12 files

0.2.1

Jun 12, 2026 12 files

0.2.0

Jun 12, 2026 12 files

0.1.0.post1

Jun 8, 2026 12 files

0.1.0

Jun 8, 2026 12 files

qufold 0.3.1

qufold

Status

Methods × backends

Validation snapshot

Solvers, truncation & extrapolation (new in 0.2.0)

LP-BLISS — spectrum-preserving 1-norm reduction (new in 0.3.0)

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The input file (`$molecule` / `$rem`)