Quantum algorithms for simulating systems coupled to bosonic modes using a hybrid resonator-qubit quantum computer

Leppäkangas, Juha; Stadler, Pascal; Golubev, Dmitry; Reiner, Rolando; Reiner, Jan-Michael; Zanker, Sebastian; Wurz, Nicola; Renger, Michael; Verjauw, Jeroen; Gusenkova, Daria

Quantum algorithms for simulating systems coupled to bosonic modes using a hybrid resonator-qubit quantum computer

Juha Leppäkangas
(
- KIT, Karlsruhe, TTP
)
,
Pascal Stadler
(
- KIT, Karlsruhe, TTP
)
,
Dmitry Golubev
(
- KIT, Karlsruhe, TTP
)
,
Rolando Reiner
(
- KIT, Karlsruhe, TTP
)
,
Jan-Michael Reiner

Mar 14, 2025

25 pages

e-Print:

2503.11507 [quant-ph]

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Abstract: (arXiv)

Modeling composite systems of spins or electrons coupled to bosonic modes is of significant interest for many fields of applied quantum physics and chemistry. A quantum simulation can allow for the solution of quantum problems beyond classical numerical methods. However, implementing this on existing noisy quantum computers can be challenging due to the mapping between qubits and bosonic degrees of freedom, often requiring a large number of qubits or deep quantum circuits. In this work, we discuss quantum algorithms to solve composite systems by augmenting conventional superconducting qubits with microwave resonators used as computational elements. This enables direct representation of bosonic modes by resonators. We derive efficient algorithms for typical models and propose a device connectivity that allows for feasible scaling of simulations with linear overhead. We also show how the dissipation of resonators can be a useful parameter for modeling continuous bosonic baths. Experimental results demonstrating these methods were obtained on the IQM Resonance cloud platform, based on high-fidelity gates and tunable couplers. These results present the first digital quantum simulation including a computational resonator on a commercial quantum platform.

Note:

25 pages, 18 figures in total: 17 pages main text with 15 figures

References(98)

Figures(18)

Ĥ = Hs +

X ik

vikσi

-b̂† k + v∗ ikσi

+b̂k

+

X k

ωkb̂† kb̂k. (8)

The case of a single bosonic mode is called the JaynesCummings (JC) model, which plays a central role in our work, since it describes the natural interaction between a superconducting transmon qubit [49, 50] and a microwave resonator. It will be the key tool for creating qubit-resonator gates

[3]

Fully electronic global systems under random-phase approximation: Radical molecules

Similar models of electrons coupled to bosonic modes can also be derived for fully electronic systems when the random-phase approximation [9] (RPA) is employed

These include problems in quantum chemistry [38, 51]

The RPA maps electron-electron interactions to interactions between electrons and fictitious bosonic modes

An example is the case of radical molecules (radicals), where certain orbitals hold unpaired electrons, which makes them chemically extremely reactive. Such molecules play central roles in biology and are of high pharmaceutical interest. A notable example is an enediyne compound, which is used in antitumor antibiotics due to its exceptional reactions in the presence of

DNA. Two key orbitals are characterized by occupancies close to 1. For such diradicals, the effect of the other orbitals may be included using the RPA [38], corresponding to introducing coupling to a fictitious bosonic bath

The Hamiltonian for a diradical molecule under RPA has the form

Ĥ =

X ij tijĉ† i ĉj +

1

2

X ijj′i′ hijj′i′ ĉ† i ĉ† jĉj′ ĉi′

X ijk vijkĉ† i ĉj

b̂† k + b̂k

ωkb̂† kb̂k, (9) where the second term on the right-hand side corresponds to the Coulomb interaction of electrons in the key orbitals

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