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arXiv:2610.29762

Encoding a bosonic mode into qubits for simulating boson-matter interactions

Maarten Stroeks, Jelena Mackeprang, Yaroslav Herasymenko, Barbara Terhal

quant-phSubmitted Oct 21, 2026• Announced Oct 22, 2026• 0 citations• Revised Oct 26, 2026 (v2)
v1 · Oct 21, 2026v2 · Oct 26, 2026
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Abstract

We explore the space-time cost of encoding of a bosonic mode into a set of qubits via various encodings, and their resilience to noise. In particular, we compare the performance of the unary Fock state encoding, an unexplored encoding of Fock states into Dicke states (``Dicke'' encoding), and the binary quadrature encoding. We do so by considering a displacement as well as a simulation of a Dicke model, coupling a bosonic mode to a set of atoms represented as qubits. Using classical simulations, we assess the accuracy and optimized space-time costs in terms of number of qubits, circuit depth and CNOT count of a quantum simulation of the time dynamics using these encodings. Although our study is far from comprehensive, we find that the binary quadrature encoding is overall most favorable in terms of being very space-efficient and relatively time-efficient due to the use of the quantum Fourier transform. Our novel Dicke encoding leads to very shallow circuits, but pays in terms of using many more qubits. We probe the use of an H2-2 Quantinuum trapped-ion qubit device (56 qubits) for displacement and Dicke model simulation in the low boson-number regime, where we find that noise leads to visible deviations from ideal circuit dynamics.

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Updated references for v2

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We explore the space-time cost of encoding of a bosonic mode into a set of qubits via various encodings, and their resilience to noise. In particular, we compare the performance of the unary Fock state encoding, an unexplored encoding of Fock states into Dicke states (``Dicke'' encoding), and the binary quadrature encoding. We do so by considering a displacement as well as a simulation of a Dicke model, coupling a bosonic mode to a set of atoms represented as qubits. Using classical simulations, we assess the accuracy and optimized space-time costs in terms of number of qubits, circuit depth and CNOT count of a quantum simulation of the time dynamics using these encodings. Although our study is far from comprehensive, we find that the binary quadrature encoding is overall most favorable in terms of being very space-efficient and relatively time-efficient due to the use of the quantum Fourier transform. Our novel Dicke encoding leads to very shallow circuits, but pays in terms of using many more qubits. We probe the use of an H2-2 Quantinuum trapped-ion qubit device (56 qubits) for displacement and Dicke model simulation in the low boson-number regime, where we find that noise leads to visible deviations from ideal circuit dynamics.
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi- Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.
We compare the basic resource requirements for first and second quantized bosonic mappings in a system consisting of NNN particles in MMM modes. In addition to the standard binary first quantized mapping, we investigate the unary first quantized mapping. Our comparison focuses on the kkk-body reduced density matrix (kkk-RDM) and two standard bosonic Hamiltonians. The first quantized mappings use less resources for off-diagonal terms of the kkk-RDM by a factor of $ \sim N^k$, compared to the second quantized mappings. The number of gates for the first quantized binary mapping increases faster with MMM compared to the other mappings. Nevertheless, a detailed numeric analysis reveals that the binary first quantized mapping still requires fewer gates than the binary and unary second quantized ones for realistic combinations of NNN and MMM, while requiring exponentially fewer qubits than the unary mappings. Additionally, the number of CNOT and Rz(φ)R_z(φ)Rz​(φ) gates necessary to express a single Trotter step of the Hamiltonian in the binary first quantized mapping is comparable to the (most efficient for a single Trotter step) unary first quantized one when M=2nM = 2^nM=2n for both the Bose-Hubbard model and the harmonic trap with short-range interactions. Additionally the binary mapping leads to lower one-norms than the unary mapping making it the overall most efficient choice for qubitization-based quantum phase estimation.
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The Dicke model provides a fundamental description of collective light-matter interactions and has long served as a testbed for exploring a wide range of physical phenomena in quantum optics and condensed matter physics. In this work, we develop a variational framework for investigating the finite-size Dicke model on both fully qubit-based (digital) and hybrid qubit boson based (digital-analogue) quantum computing platforms. We show that the resulting model reproduces the characteristic critical behavior of the Dicke model in the appropriate large-spin limit while remaining suitable for implementation on both classical emulators of quantum computers and actual trapped ion quantum computers, albeit in the case of latter somewhat limited by noise. Finally, we introduce a complementary hybrid qubit-bosonic variational ansatz that directly exploits the bosonic degree of freedom to reduce quantum resources and discuss its potential implementation on hybrid quantum hardware. Our results establish a scalable, symmetry-aware framework for variational quantum simulations of collective light-matter systems and provide a pathway toward efficient simulations of more general spin-boson models on near-term quantum devices.
Efficient simulation of interacting fermionic systems is a key application of near-term quantum computers, but is hindered by the overhead required to encode fermionic operators on qubit hardware. Here, we consider models with NNN fermionic modes in which each participates in at most a constant number ddd of interactions and study the circuit depth required to implement the Trotterized time evolution on qubit hardware with all-to-all connectivity. We introduce an encoding that augments each physical fermionic mode with a small number of auxiliary fermions, enabling the removal of Jordan--Wigner strings. Although the preparation of the auxiliary fermion state incurs an initial overhead, this state remains invariant under time evolution. As a result, long-time evolution can be implemented with asymptotically optimal circuit depth, reducing a previously multiplicative O(log⁡N)O(\log N)O(logN) overhead to an additive overhead. Our results thus establish that the simulation of sparse fermionic models on qubit hardware matches the performance achievable on ideal fermionic hardware up to constant factors and O(dN)O(dN)O(dN) ancillary qubits.
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