Periodic Reporting for period 2 - COMFTQUA (Enabling efficient computation on fault tolerant quantum computers)
Período documentado: 2024-07-01 hasta 2025-12-31
Fault-tolerant quantum computing (FTQC) offers a pathway beyond the limits of current noisy processors and classical supercomputers. Many chemically relevant systems remain intractable because achieving chemical accuracy scales beyond even the largest HPC facilities. FTQC could reduce this scaling, enabling predictive simulations for energy, catalysis and pharmaceutical discovery.
The project aims to develop quantum algorithms and software that make such simulations feasible on future FT hardware. The focus lies on reducing qubit counts, logical gate depth and runtime, since resource efficiency will determine whether simulations become practical on first-generation error-corrected devices. Methods are designed to be hardware-agnostic and compatible with photonic, superconducting and trapped-ion platforms.
Main objectives were:
• Develop quantum algorithms for electronic and nuclear dynamics using fewer qubits and gates while retaining accuracy.
• Create resource-estimation methodology for FTQC
• Optimise implementations for multiple architectures and validate through simulation and early hardware trials.
During the reporting period, multiple new algorithms and representations were developed with substantial reductions in gate complexity. Highlights include algorithms for strongly coupled Hamiltonians, relativistic electronic structure, symmetry-driven tensor factorisation, Walsh–Hadamard QROM for molecular dynamics, quantum generalised eigenvalue solving, and compact UVCC circuits for vibrational structure. We also produced the first quantum discrete-variable-representation (DVR) oracle and a dedicated quantum resource estimator.
Impact is illustrated with FeMoCo simulation. Ammonia production consumes ~4% of global energy; improved catalytic design has large economic relevance. Classical high-accuracy FeMoCo calculations remain out of reach. Our algorithms reduce quantum resources for electronic structure by ~40% and for vibrational simulation by several orders of magnitude (up to 100 000x), suggesting that FTQC could ultimately enable direct computational catalyst screening.
This progress forms a foundation for future FTQC molecular simulation, accelerating discovery of catalysts, batteries and pharmaceuticals and supporting energy-efficient industrial technologies.
The project aims to develop quantum algorithms and software that make such simulations feasible on future FT hardware. The focus lies on reducing qubit counts, logical gate depth and runtime, since resource efficiency will determine whether simulations become practical on first-generation error-corrected devices. Methods are designed to be hardware-agnostic and compatible with photonic, superconducting and trapped-ion platforms.
Main objectives were:
• Develop quantum algorithms for electronic and nuclear dynamics using fewer qubits and gates while retaining accuracy.
• Create resource-estimation methodology for FTQC
• Optimise implementations for multiple architectures and validate through simulation and early hardware trials.
During the reporting period, multiple new algorithms and representations were developed with substantial reductions in gate complexity. Highlights include algorithms for strongly coupled Hamiltonians, relativistic electronic structure, symmetry-driven tensor factorisation, Walsh–Hadamard QROM for molecular dynamics, quantum generalised eigenvalue solving, and compact UVCC circuits for vibrational structure. We also produced the first quantum discrete-variable-representation (DVR) oracle and a dedicated quantum resource estimator.
Impact is illustrated with FeMoCo simulation. Ammonia production consumes ~4% of global energy; improved catalytic design has large economic relevance. Classical high-accuracy FeMoCo calculations remain out of reach. Our algorithms reduce quantum resources for electronic structure by ~40% and for vibrational simulation by several orders of magnitude (up to 100 000x), suggesting that FTQC could ultimately enable direct computational catalyst screening.
This progress forms a foundation for future FTQC molecular simulation, accelerating discovery of catalysts, batteries and pharmaceuticals and supporting energy-efficient industrial technologies.
We developed quantum algorithms, circuit constructions and validation tooling that drastically reduce resource requirements for molecular simulation. These contributions address project goals of lowering qubit counts, shortening circuit depth, and establishing quantitative benchmarking for FTQC.
• Spin-SWAP Pauli–Breit algorithm: First scalable relativistic quantum-simulation method. Spin–orbital decoupling in the SELECT unit yields 2–3× T-gate reduction for heavy-element chemistry, with applications in battery materials, photonics and catalytic centres (FeMoCo).
• Symmetry-assisted tensor factorisation (STNF & PGSM): ~40% T-gate reduction for FeMoCo and ~37% for Ru-based CO2-to-methanol catalysts; published JCTC (2025). Establishes a general symmetry-compression scheme for electronic Hamiltonians.
• Quantum Resource Estimator (QRE): Software that returns exact qubit, Toffoli and runtime requirements for QPE-based chemistry. Used internally for verification, available for partner analysis and scalable to future algorithm classes.
• First DVR quantum oracle: O(N) volume versus O(N²) state-synthesis. Enables direct vibrational and bosonic-mode simulation and forms the basis for our most advanced dynamics work.
• Walsh–Hadamard QROM molecular dynamics: Incorporates curvilinear kinetic operators and general non-SOP PES. Up to 10⁵× resource reduction for H2O and >10⁶× for 30-dimensional models; a 12-atom benchmark solvable in ~3 months on <300 logical qubits versus >30 000 years classically.
• Generalised eigenvalue solver: Matrix-inversion-free spectral estimation via QPE + amplitude amplification. Quartic speedup, robust scaling and applicability to dense excited-state spectra.
• Low-depth UVCC: Removes redundant unary-encoded subspaces, reducing entangling gates by up to 50%. Hardware tests on Quantinuum H1-1 improved fidelity by up to 172%. Published in J. Chem. Phys. (2025).
Together these advances form a new generation of scalable FTQC algorithms for chemistry and materials science.
• Spin-SWAP Pauli–Breit algorithm: First scalable relativistic quantum-simulation method. Spin–orbital decoupling in the SELECT unit yields 2–3× T-gate reduction for heavy-element chemistry, with applications in battery materials, photonics and catalytic centres (FeMoCo).
• Symmetry-assisted tensor factorisation (STNF & PGSM): ~40% T-gate reduction for FeMoCo and ~37% for Ru-based CO2-to-methanol catalysts; published JCTC (2025). Establishes a general symmetry-compression scheme for electronic Hamiltonians.
• Quantum Resource Estimator (QRE): Software that returns exact qubit, Toffoli and runtime requirements for QPE-based chemistry. Used internally for verification, available for partner analysis and scalable to future algorithm classes.
• First DVR quantum oracle: O(N) volume versus O(N²) state-synthesis. Enables direct vibrational and bosonic-mode simulation and forms the basis for our most advanced dynamics work.
• Walsh–Hadamard QROM molecular dynamics: Incorporates curvilinear kinetic operators and general non-SOP PES. Up to 10⁵× resource reduction for H2O and >10⁶× for 30-dimensional models; a 12-atom benchmark solvable in ~3 months on <300 logical qubits versus >30 000 years classically.
• Generalised eigenvalue solver: Matrix-inversion-free spectral estimation via QPE + amplitude amplification. Quartic speedup, robust scaling and applicability to dense excited-state spectra.
• Low-depth UVCC: Removes redundant unary-encoded subspaces, reducing entangling gates by up to 50%. Hardware tests on Quantinuum H1-1 improved fidelity by up to 172%. Published in J. Chem. Phys. (2025).
Together these advances form a new generation of scalable FTQC algorithms for chemistry and materials science.
The project pushed quantum simulation well beyond current capabilities, demonstrating that FTQC can handle systems unreachable for HPC alone. Algorithms reduce resource requirements, extend applicability to relativistic, vibrational and strongly-coupled regimes, and provide concrete estimates for when quantum advantage becomes realistic.
The QRE tool enables accurate feasibility planning for future quantum capacity. The Spin-SWAP algorithm brings relativistic simulation into the fault-tolerant regime. STNF/PGSM reduce T-gate cost ≥40% for industrial catalyst families. The DVR oracle and Walsh–Hadamard QROM establish the first practical route to high-dimensional vibrational dynamics, reducing total quantum volume by 5–6 orders of magnitude. The eigenvalue solver removes matrix-inversion barriers, while UVCC provides a validated low-depth ansatz.
These results establish measurable thresholds for quantum advantage and provide a basis for commercial exploitation, patent protection and eventual deployment on FT hardware.
The QRE tool enables accurate feasibility planning for future quantum capacity. The Spin-SWAP algorithm brings relativistic simulation into the fault-tolerant regime. STNF/PGSM reduce T-gate cost ≥40% for industrial catalyst families. The DVR oracle and Walsh–Hadamard QROM establish the first practical route to high-dimensional vibrational dynamics, reducing total quantum volume by 5–6 orders of magnitude. The eigenvalue solver removes matrix-inversion barriers, while UVCC provides a validated low-depth ansatz.
These results establish measurable thresholds for quantum advantage and provide a basis for commercial exploitation, patent protection and eventual deployment on FT hardware.