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arXiv · 2509.18854

Trading modes against energy

Lukas Brenner·Beatriz Dias·Robert Koenig
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Abstract

We ask how much energy is required to weakly simulate an $n$-qubit quantum circuit (i.e., produce samples from its output distribution) by a unitary circuit in a hybrid qubit-oscillator model. The latter consists of a certain number of bosonic modes coupled to a constant number of qubits by a Jaynes-Cummings Hamiltonian. We find that efficient approximate weak simulation of an $n$-qubit quantum circuit of polynomial size with inverse polynomial error is possible with (1) a linear number of bosonic modes and a polynomial amount of energy, or (2) a sublinear (polynomial) number of modes and a subexponential amount of energy, or (3) a constant number of modes and an exponential amount of energy. Our construction encodes qubits into high-dimensional approximate Gottesman-Kitaev-Preskill (GKP) codes. It provides new insight into the trade-off between system size (i.e., number of modes) and the amount of energy required to perform quantum computation in the continuous-variable setting.

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Lukas Brenner, Beatriz Dias, Robert Koenig. 2025-09-23. Trading modes against energy. https://arxiv.org/abs/2509.18854

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