Engineering Quantum-Enhanced Transport by Supertransfer

The gist The paper shows that supertransfer, an enhancement in energy transfer rates due to delocalised excitations, can be directly observed using an engineered quantum device based on a superconducting circuit.

Introduction to Collective Effects and Supertransfer

Collective effects occur when the rates of dynamical processes in a many-body system depend on its components’ interactions with each other<ref:2506.05045#pg2>. A paradigmatic collective effect is superradiance, the enhancement in the rate that radiation is emitted by a group of emitters relative to that emitted by independent emitters<ref:2506.05045#pg2>. Less studied are collective effects in energy transport, notably supertransfer, the enhancement of the rate of energy transfer from donors to acceptors due to delocalised excitations<ref:2506.05045#pg2>. Despite its proposed significance in photosynthesis, there has been no direct experimental detection of supertransfer because, in biological or molecular systems, delocalisation cannot be turned on and off to evaluate its effect on energy transfer<ref:2506.05045#pg2>. Here, we show that supertransfer could be directly observed using a quantum device based on a superconducting circuit<ref:2506.05045#pg2>.

Definition and Mathematical Description of Supertransfer

Supertransfer is defined as the enhancement of the transfer rate from an aggregate (or group) of donor sites to an aggregate of acceptor sites due to coherent delocalisation among strongly interacting donors, acceptors, or both<ref:2506.05045#pg2>. The transfer rate γ is defined by the rate of change of the acceptor population PA, dPA/dt = γPD<ref:2506.05045#pg2>. Normal transfer occurs when both eigenstates i⟩ and f⟩ are localised on individual sites, which means that each donor site independently transfers energy to acceptor sites<ref:2506.05045#pg2>. The rate of transfer from localised state i⟩ = Dj⟩ to localised state f = Ak⟩ is γloc ∝ ⟨Ak HDA Dj⟩ squared<ref:2506.05045#pg2>. Supertransfer occurs between delocalised eigenstates, and the transfer rate between the delocalised eigenstates is given by γdeloc ∝ ⟨Aβ HDA Dα⟩ squared<ref:2506.05045#pg2>. This rate is maximised for completely delocalised eigenstates (cαj = 1/√ND and cβk = 1/√NA), resulting in γmax deloc = NDNAγloc<ref:2506.05045#pg2>.

Design Rules for Engineering Supertransfer

Two design rules are proposed to optimize energy transfer using supertransfer<ref:2506.05045#pg2>.

1. Rule 1 states that the transfer must be well described by the golden-rule rate process of eq. (2), which is met if the donor aggregate is weakly coupled to the acceptor aggregate, compared to the system-environment coupling quantified by the reorganisation energies, V DA.

2. Rule 2 requires that the eigenstates of either the donor or the acceptor aggregates (or both) must be delocalised, which can be achieved if the intra-aggregate couplings V D are greater than both the static disorder in the aggregate (the variance δ D of the set of ED j) and the dynamic disorder (quantified by λ D), i.e., V D ≳ δ D, λ D<ref:2506.05045#pg2>.

Experimental Implementation using Superconducting Circuits

The simplest case of supertransfer—shown in fig. 1—could be implemented by meeting three requirements<ref:2506.05045#pg2>. First, it requires three sites: two donors and one acceptor (ND = 2 and NA = 1)<ref:2506.05045#pg2>. Second, the energies of these sites must be tunable to ensure that the acceptor energy is lower than those of the donors and to allow noise injection<ref:2506.05045#pg2>. Third, it must be possible to control delocalisation to show a higher transfer rate in the delocalised case compared to the localised one<ref:2506.05045#pg2>. This can be achieved using a superconducting circuit quantum electrodynamics (cQED) architecture where sites are implemented as transmon qubits whose energy can be tuned using an external magnetic field<ref:2506.05045#pg2>. The Hamiltonian of the required cQED circuit is Hcircuit = ED Dσ z1 + (ED D + δ D)σ z2 + EAσ zA + CDσ x1σ x2 + CDA(σ x1σxA + σ x2σxA) + h.c.<ref:2506.05045#pg2>.

Demonstration of Scaling and Robustness

The simulation results in fig. 5b confirm the scaling law of eq. (9), showing that the supertransfer rate increases in proportion to the number of sites participating in the delocalised donor and acceptor aggregates, according to eq. (9)<ref:2506.05045#pg2>. The robustness of supertransfer to experimental noise simplifies implementation by reducing the need for precise parameter engineering<ref:2506.05045#pg2>. The two proposed implementations—direct coupling in Circuit 1 and indirect coupling in Circuit 2—have complementary advantages<ref:2506.05045#pg2>. In Circuit 1, there is complete flexibility in selecting all of the couplings, which means that the mapping of the supertransfer Hamiltonian is direct and straightforward<ref:2506.05045#pg2>. In contrast, in Circuit 2, the couplings are achieved through a bus, facilitating scalability as illustrated in fig. 5a<ref:2506.05045#pg2>. The simulation results show that when Rule 2 (V D ≳ δ D, λ D) is met, the supertransfer enhances the transfer rate γ (fig. 4)<ref:2506.05045#pg2>. The maximum supertransfer rate 2γ0 (for ND = 2 and NA = 1) gradually decreases to γ0 if the donor parameters leave the region defined by Rule 2<ref:2506.05045#pg2>.

Conclusion

We showed that a quantum device based on a cQED circuit could be engineered to conclusively demonstrate supertransfer<ref:2506.05045#pg2>. The simplest supertransfer case is achieved with ND = 2 and NA = 1, with larger arrangements also possible, as shown in fig. 5<ref:2506.05045#pg2>. Circuits 1 and 2 are achievable with current engineering capabilities in cQED, as all required components have been experimentally demonstrated<ref:2506.05045#pg2>. The necessary couplings can be implemented using either of direct capacitive coupling [33–35] or buses for indirect qubit coupling [29, 38, 41]<ref:2506.05045#pg2>. Finally, our proposal can be implemented using simulation times that are an order of magnitude shorter that typical transmon decoherence times of 50–120 µs [2506.050451>.

References

[1] R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev. 93, 99 (1954).

[2] M. Gross and S. Haroche, Superradiance: An essay on the theory of collective spontaneous emission, Phys. Rep. 93, 301–396 (1982).

[3] K. D. B. Higgins, S. C. Benjamin, T. M. Stace, G. J. Milburn, B. W Lovett, and E M Gauger, Superabsorption of light via quantum engineering, Nat Commun 5 4705 (2014).

[4] J Q Quach, K E McGhee, L Ganzer, D M Rouse, B W Lovett, E M Gauger, J Keeling, G Cerullo, D G Lidzey, and T Virgili Superabsorption in an organic microcavity: Toward a quantum battery Sci Adv 8 eabk3160 (2022).

[5] J Q Quach and W J Munro, Using Dark States to Charge and Stabilize Open Quantum Batteries Phys Rev Appl 14 024092 (2020).

1. Supertransfer enhanced energy transport in quantum AI systems can be implemented by engineering superconducting circuits to create controllable delocalization of quantum states, allowing for tunable energy transfer rates.

2. The improved AI system can achieve higher efficiency in artificial light-harvesting devices by designing energy transfer mechanisms that utilize supertransfer, potentially surpassing normal transfer rates by a factor of NDNA over the normal rate.

3. Quantum hardware design rules can be applied to optimize energy transport, ensuring that the transfer must be well described by the golden-rule rate process of eq. (2) and that the eigenstates of either the donor or the acceptor aggregates (or both) must be delocalised.

4. A superconducting circuit based quantum electrodynamics cQED architecture can be used to realize this supertransfer, where transmon qubits are tuned via external magnetic fields to control site energies and couplings.

5. The AI system can demonstrate scaling of supertransfer by adding more donor and acceptor sites to circuits, as the supertransfer rate increases in proportion to the number of sites participating in the delocalised donor and acceptor aggregates, according to eq. (9).

6. The system can exhibit robustness against experimental noise because the gradual change with the parameters makes supertransfer robust to small changes in either the static (delta) or dynamic (lambda) disorders.