quantum-computing

Ladder Operator Block-Encoding

William A. Simon, Carter M. Gustin, Kamil Serafin, Alexis Ralli, Gary R. Goldstein, and Peter J. Love

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Researchers from Tufts University and collaborators introduced a novel framework for block-encoding ladder operators acting on fermionic and bosonic modes, published in December 2025. The method directly applies operator actions to quantum states while isolating undesired effects outside the encoded subspace. The framework eliminates overhead from basis expansion by using subspace rotations based on system occupation states. Benchmarks against Pauli-basis methods show reductions in non-Clifford operations, ancillae qubits, and rescaling factors for models like quartic oscillators and φ⁴/Yukawa Hamiltonians. Numerical tests demonstrate favorable scaling with bosonic mode occupancy, total mode count, and operator locality. This efficiency could significantly lower resource requirements for quantum simulations of field theories and molecular systems. An open-source Python package implements the technique, enabling broader adoption. The approach integrates with quantum algorithms like phase estimation and QSVT, potentially accelerating near-term applications. The work advances quantum simulation by providing a resource-efficient alternative to traditional block-encoding methods, particularly for complex quantum field theory models.

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AbstractWe describe and analyze LOBE (Ladder Operator Block-Encoding), a framework for block-encoding ladder operators that act upon fermionic and bosonic modes. In this framework, we achieve efficient block-encodings by applying the desired action of the operator onto the quantum state and pushing any undesired effects outside of the encoded subspace. This direct approach avoids any overhead caused by expanding the operators in another basis. We numerically benchmark these constructions using models arising in quantum field theories including the quartic harmonic oscillator, and $\phi^4$ and Yukawa Hamiltonians on the light front. These benchmarks show that LOBE often produces block-encodings with fewer non-Clifford operations, fewer block-encoding ancillae and overall number of qubits, and lower rescaling factors for various operators as compared to frameworks that expand the ladder operators in the Pauli basis. LOBE constructions also demonstrate favorable scaling with respect to key parameters, including the maximum occupation of bosonic modes, the total number of fermionic and bosonic modes, and the locality of the operators. LOBE is implemented as an open-source python package to enable further applications.Featured image: The Ladder Operator Block-Encoding (LOBE) framework generates quantum circuits that block encode products and linear combinations of fermionic and bosonic ladder operators. These circuits use fewer quantum resources than other methods by performing a subspace rotation based on the occupation state of the system, and then directly updating the state of the system based on the intended action of the operator. This figure shows the LOBE circuit for a product of fermionic ladder operators plus its Hermitian conjugate.Brown Interdisciplinary Quantum Seminar Popular summarySimulating quantum systems is a promising application for useful quantum computation. "Block encoding" refers to a method of encoding information regarding non-unitary operators – such as a Hamiltonian – inside a larger unitary. Block encodings are a building block for many promising quantum algorithms, such as probabilistic state preparation, quantum phase estimation, and the Quantum Singular Value Transformation (QSVT). In this work, we describe the Ladder Operator Block-Encoding (LOBE) framework for constructing efficient block encodings of operators written in terms of fermionic and bosonic ladder operators. LOBE reduces the number of qubits and gates needed to block encode these operators compared to other techniques. This reduces the cost of quantum algorithms employing these block encodings by several orders of magnitude in many cases. LOBE also has favorable scaling with the maximum occupancy of bosonic modes and the locality of the ladder operators. 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URL https://doi.org/10.1103/RevModPhys.21.392. https://doi.org/10.1103/RevModPhys.21.392Cited byOn Crossref's cited-by service no data on citing works was found (last attempt 2025-12-28 10:46:46). Could not fetch ADS cited-by data during last attempt 2025-12-28 10:46:47: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractWe describe and analyze LOBE (Ladder Operator Block-Encoding), a framework for block-encoding ladder operators that act upon fermionic and bosonic modes. In this framework, we achieve efficient block-encodings by applying the desired action of the operator onto the quantum state and pushing any undesired effects outside of the encoded subspace. This direct approach avoids any overhead caused by expanding the operators in another basis. We numerically benchmark these constructions using models arising in quantum field theories including the quartic harmonic oscillator, and $\phi^4$ and Yukawa Hamiltonians on the light front. These benchmarks show that LOBE often produces block-encodings with fewer non-Clifford operations, fewer block-encoding ancillae and overall number of qubits, and lower rescaling factors for various operators as compared to frameworks that expand the ladder operators in the Pauli basis. LOBE constructions also demonstrate favorable scaling with respect to key parameters, including the maximum occupation of bosonic modes, the total number of fermionic and bosonic modes, and the locality of the operators. LOBE is implemented as an open-source python package to enable further applications.Featured image: The Ladder Operator Block-Encoding (LOBE) framework generates quantum circuits that block encode products and linear combinations of fermionic and bosonic ladder operators. These circuits use fewer quantum resources than other methods by performing a subspace rotation based on the occupation state of the system, and then directly updating the state of the system based on the intended action of the operator. This figure shows the LOBE circuit for a product of fermionic ladder operators plus its Hermitian conjugate.Brown Interdisciplinary Quantum Seminar Popular summarySimulating quantum systems is a promising application for useful quantum computation. "Block encoding" refers to a method of encoding information regarding non-unitary operators – such as a Hamiltonian – inside a larger unitary. Block encodings are a building block for many promising quantum algorithms, such as probabilistic state preparation, quantum phase estimation, and the Quantum Singular Value Transformation (QSVT). In this work, we describe the Ladder Operator Block-Encoding (LOBE) framework for constructing efficient block encodings of operators written in terms of fermionic and bosonic ladder operators. LOBE reduces the number of qubits and gates needed to block encode these operators compared to other techniques. This reduces the cost of quantum algorithms employing these block encodings by several orders of magnitude in many cases. LOBE also has favorable scaling with the maximum occupancy of bosonic modes and the locality of the ladder operators. LOBE is implemented as an open-source python package to enable further applications.► BibTeX data@article{Simon2025ladderoperatorblock, doi = {10.22331/q-2025-12-22-1953}, url = {https://doi.org/10.22331/q-2025-12-22-1953}, title = {Ladder {O}perator {B}lock-{E}ncoding}, author = {Simon, William A. and Gustin, Carter M. and Serafin, Kamil and Ralli, Alexis and Goldstein, Gary R. and Love, Peter J.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {9}, pages = {1953}, month = dec, year = {2025} }► References [1] Richard P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21 (6): 467–488, 1982. 10.1007/BF02650179. URL https://doi.org/10.1007/BF02650179. https://doi.org/10.1007/BF02650179 [2] Seth Lloyd. Universal quantum simulators. Science, 273 (5278): 1073–1078, 1996. 10.1126/science.273.5278.1073. 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