Does the quantum coherence in the FMO complex have any significance to quantum computing (on a biological substrate)?

Question

The quantum effects of the FMO complex (photosynthetic light harvesting complex found in green sulfur bacteria) have been well studied as well as the quantum effects in other photosynthetic systems. One of the most common hypotheses for explaining these phenomenon (focusing on FMO complex) is Environment-Assisted Quantum Transport (ENAQT) originally described by Rebentrost et al.. This mechanism describes how certain quantum networks can "use" decoherence and environment effects to improve the efficiency of quantum transport. Note that the quantum effectss arise from the transport of excitons from one pigment (chlorophyll) in the complex to another. (There is a question that discusses the quantum effects of the FMO complex in a little more detail).

Given that this mechanism allows for quantum effects to take place at room temperatures without the negative effects of decoherence, are their any applications for quantum computing? There are some examples of artificial systems that utilize ENAQT and related quantum effects. However, they present biomimetic solar cells as a potential application and do not focus on the applications in quantum computing.

Originally, it was hypothesized that the FMO complex performs a Grover's search algorithm, however, from what I understand, it has now since been showed that this is not true.

There have been a couple studies that use chromophores and substrates not found in biology (will add references later). However, I would like to focus on systems that use a biological substrate.

Even for biological substrates there are a couple examples of engineered systems that use ENAQT. For example, a virus-based system was developed using genetic engineering. A DNA-based excitonic circuit was also developed. However, most of these examples present photovoltaics as a main example and not quantum computing.

Vattay and Kauffman was (AFAIK) the first to study the quantum effects as quantum biological computing, and proposed a method of engineering a system similar to the FMO complex for quantum computing.

How could we use this mechanism to build new types of computers? In the light harvesting case the task of the system is to transport the exciton the fastest possible way to the reaction center whose position is known. In a computational task we usually would like to find the minimum of some complex function $f_n$. For the simplicity let this function have only discrete values from 0 to K. If we are able to map the values of this function to the electrostatic site energies of the chromophores $H_{nn} = \epsilon_0 f_n$ and we deploy reaction centers near to them trapping the excitons with some rate $κ$ and can access the current at each reaction center it will be proportional with the probability to find the exciton on the chromophore $j_n ∼ κ\rho_{nn}$.

---

How can the quantum effects of the FMO complex be used on a biological substrate for quantum computing? Given that the quantum effects occur due to the transport of excitons on network structures, could ENAQT provide more efficient implementations of network-based algorithms (ex: shortest path, traveling salesman, etc.)?

---

P.S. I will add more relevant references if needed. Also, feel free to add relevant references as well.

Answer 1

I agree with most of what you've written in the first paragraph, though I would say that at roughly the same time (only 1 month apart!) as the Rebentrost et al. paper you mentioned, a very similar paper was posted to arXiv by Plenio and Huelga called "Dephasing assisted transport: Quantum networks in biomolecules" and it actually got published in the same journal as the Rebentrost et al. paper, but a few months earlier. There was also Mohseni et al.'s Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer posted on arXiv one month earlier than Rebentrost et al., and published in a journal 8 days before the Plenio-Huelga paper.

But actually 13 years before all of that, Nancy Makri and Eunji Sim wrote papers simulating the full quantum coherence for electron transfer in bacteriochlorophylls (see this and this). Also 11 years before that, Nobel Laureate Rudy Marcus used Marcus theory to study energy transfer in the same system, and wrote this review on the subject with 331 papers listed in the bibliography.

So the use of quantum mechanics to study energy transfer in bacteriochlorophyll goes back to decades before that Rebentrost et al. paper, and it was the 2007 Engel paper that you mentioned, where they connected the energy transfer to quantum computing, which created a new wave of interest (including in the quantum computing community which previously was not interested in biological/chemical energy transfer, examples being the two 2008 papers mentioned in the first paragraph, which featured authors from quantum computing such as Martin Plenio and Seth Lloyd).

I was lucky to get the chance to see Bob Silbey's talk at the Royal Society meeting called "Quantum coherent energy transfer: Implications for biology and new energy technologies" fewer than 6 months before he died, and he traced quantum biology back to Chapter 4 of Schrödinger's book "What is Life?" which talks about mutations being causd by electron transfer (which we now learn in high school biology: UV radiation causes excitations that cause thymine dimers to form, leading to cancer).

---

Things get interesting in your second paragraph when you say:

Given that this mechanism allows for quantum effects to take place at room temperatures without the negative effects of decoherence, are their any applications for quantum computing?

In my answer to this I pointed out that if the excitations were in a vacuum with no vacuum modes (in QED, even a vacuum has modes that can interact with the excitations), then the energy would just transfer back and forth (Rabi oscillations) indefinitely due to the quantum version of the Poincaré recurrence theorem. You can see that when I turned on the decoherence, these Rabi oscillations didn't just get damped, but also the excitation was "funneled" towards the reaction center, hence allowing it to fuel the subsequent photosynethesis. This is why it's called "decoherence-driven" energy transfer, and why you say that quantum effects take place "without the negative effects of decoherence".

The implications for quantum computing are more subtle though.

Notice that the coherence was practically gone after 1ps (notice the Rabi oscillations are gone at 1ps). This means the decoherence is still bad, in fact much worse than in some quantum computer candidates such as phosphorous-doped silicon.

Said another way, the coherence is killed in the FMO within about 1ps, whereas in phosphorous-doped silicon it was made to last more than a trillion times longer than 1ps. You should not be surprised by this difference of 12 orders of magnitude, since the FMO was not meant to be a quantum computer (it is a wet, noisy, environment full of decoherence sources), while the phosphorous-doped silicon experiments were purposely done in conditions that would allow the authors to get the longest room-temperature coherence time possible.

---

So in summary:

• decoherence helps photosynthesis work,
• decoherence happens rapidly in the FMO (roughly 1ps, vs seconds for some QC candidates)
• circuit-based quantum computers require long coherence times
• circuit-based quantum computers will not perform well if coherence is completely lost after 1ps, especially if the quantum gates take 100ns each (which is a realistic estimate for superconducting QCs).
• Therefore I would not choose excitations in chromophores for the qudits in a circuit-based quantum computer. Such a quantum computer is less likely to be as capable as the machines currently being made by the real companies who are trying very hard to make good quantum computers: IBM, Google, D-Wave, Rigetti, Intel, Alibaba, etc. all use superconducting systems, not biological chromophores).

The bottom line is that it is very interesting that we are able to observe quantum coherence in the energy transfer of the FMO via coherent 2D spectroscopy, but this coherence does not last nearly as long as we need it to for fault-tolerant quantum computing, and QCs that have been engineered in the lab specifically to perform well at quantum computing, have much longer coherence times. Otherwise, IBM, Google, D-Wave, Rigetti, Intel, Alibaba, etc. would be using biological chromophores, not superconducting qubits. Those companies are well-aware of the quantum coherence in the FMO. In fact as stated in my first paragraph, Mohseni was the first to write about coherence in the FMO (in 2008) in this wave that started after Engel's 2007 paper. Guess where Mohseni works? Google. You said ENAQT was originally proposed by Patrick Rebentrost. Patrick works at Xanadu, a company trying to make photonic QCs, not chromophoric QCs. Patrick's PhD supervisor Alan Aspuru-Guzik who authored (at least) 4 of the mentioned papers, including the DNA one you posted, was also the PhD adviser of multiple other people in Google and Rigetti's quantum teams. These companies know about coherence in the FMO, employ many of the lead authors on those FMO papers, and if it was a good idea to build an FMO-inspired quantum computer, they would know it, but instead they all use superconducting qubits and sometimes ion-traps or photonics.