Quantum coherence allows photosynthesis to operate at nearly 100% efficiency. If this effect could be used for photovoltaics.
2009-07-15: Converting the photosynthesis of rice from the less-efficient C3 form to the C4 form would increase yields by 50% and would also use water 2x as efficiently.
2014-01-09: Rubisco. This little molecule underwrites your lavish lifestyle. It isn’t a very prolific sugar daddy:

Typical enzymes can process 1000 molecules per second, but rubisco fixes only 3 CO2 molecules per second.

2015-03-28: 2x photosynthesis?

“We have unprecedented computational resources that allow us to model every stage of photosynthesis and determine where the bottlenecks are, and advances in genetic engineering will help us augment or circumvent those steps that impede efficiency. Long suggested several strategies.

Add pigments. “Our lab and others have put a gene from cyanobacteria into crop plants and found that it boosts the photosynthetic rate by 30%. Some bacteria and algae contain pigments that utilize more of the solar spectrum than plant pigments do. If added to plants, those pigments could bolster the plants’ access to solar energy.

Add the blue-green algae system. Some scientists are trying to engineer C4 photosynthesis in C3 plants, but this means altering plant anatomy, changing the expression of many genes and inserting new genes from C4 plants.

“Another, possibly simpler approach is to add to the C3 chloroplast the system used by blue-green algae”. This would increase the activity of Rubisco, an enzyme that catalyzes a vital step of the conversion of atmospheric CO2 into plant biomass. Computer models suggest adding this system would increase photosynthesis as much as 60%.

More sunlight for lower leaves. Computer analyses of the way plant leaves intercept sunlight have revealed other ways to improve photosynthesis. Many plants intercept too much light in their topmost leaves and too little in lower leaves; this probably allows them to outcompete their neighbors, but in a farmer’s field such competition is counterproductive. Studies aim to make plants’ upper leaves lighter, allowing more sunlight to penetrate to the light-starved lower leaves.

Eliminate traffic jams. “The computer model predicts that by altering this system by up-regulating some genes and down-regulating others, a 60% improvement could be achieved without any additional resource”.

In silico simulation. “The next step is to create an in silico plant to virtually simulate the amazingly complex interactions among biological scales. This type of model is essential to fill current gaps in knowledge and better direct our engineering efforts.”

2015-03-31: Improving photosynthetic efficiency from the current 1-2% would be very profound.

worldwide agricultural yields must increase by 50% by 2050. And that ambitious goal does not factor in the effects of climate change. RIPE researchers demonstrated for the first time that it was possible to improve crop yields in the field by engineering photosynthesis. By increasing the expression levels of 3 genes involved in processing light, they improved tobacco yields by 20%

2015-05-03: Artificial photosynthesis

a nanowire array captures light, and bacteria convert CO2 into acetate. The bacteria directly interact with light-absorbing materials, the first example of “microbial photoelectrosynthesis.” Another kind of bacteria then transforms the acetate into chemical precursors that can be used to make a wide range of everyday products from antibiotics to paints, replacing fossil fuels and electrical power

2016-06-05: Bionic leaf

the work addresses 2 fundamental goals: storing the energy of the sun, and building something useful from CO2 in the atmosphere, thereby reducing a major greenhouse gas.

For the new bionic leaf, Nocera’s team has designed a system in which bacteria use hydrogen from the water split by the artificial leaf plus CO2 from the atmosphere to make a bioplastic that the bacteria store inside themselves as fuel. “I can then put the bug [bacteria] in the soil because it has already used the sunlight to make the bioplastic. Then the bug pulls nitrogen from the air and uses the bioplastic, which is basically stored hydrogen, to drive the fixation cycle to make ammonia for fertilizing crops.” The researchers have used their approach to grow 5 crop cycles of radishes. The vegetables receiving the bionic-leaf-derived fertilizer weigh 150% more than the control crops. The next step is to boost throughput so that 1 day, farmers in India or sub-Saharan Africa can produce their own fertilizer with this method.

there’s also

Researchers have engineered a potentially game-changing solar cell that cheaply and efficiently converts atmospheric CO2 directly into usable hydrocarbon fuel, using only sunlight for energy.

2019-01-11: More on improving RuBisCO:

Unfortunately, RuBisCO is, well, terrible at its job. It might not be obvious based on the plant growth around us, but the enzyme is not especially efficient at catalyzing the CO2 reaction. And, worse still, it often uses oxygen instead. This produces a useless byproduct that, if allowed to build up, will eventually shut down photosynthesis entirely. It’s estimated that crops such as wheat and rice lose anywhere from 20-50% of their growth potential due to this byproduct. While plants have evolved ways of dealing with this byproduct, they’re not especially efficient. So a group of researchers at the University of Illinois, Urbana decided to step in and engineer a better way. The result? In field tests, the engineered plants grew up to 40% more mass than ones that relied on the normal pathways.

2020-08-10: Plants are Green to reduce Photosynthesis Noise. Plants ignore the most energy-rich part of sunlight because stability matters more than efficiency
2022-07-04: Acetate could be a photosynthesis alternative

Experiments showed that a wide range of food-producing organisms can be grown in the dark directly on the acetate-rich electrolyzer output, including green algae, yeast, and fungal mycelium that produce mushrooms. Producing algae with this technology is 4x more energy efficient than growing it photosynthetically. Yeast production is 18x more energy efficient than how it is typically cultivated using sugar extracted from corn. “We found that a wide range of crops could take the acetate we provided and build it into the major molecular building blocks an organism needs to grow and thrive. With some breeding and engineering that we are currently working on we might be able to grow crops with acetate as an extra energy source to boost crop yields.”

2022-08-22: Better gene regulation increases yield by 20%

“Plants dissipate potentially damaging excess absorbed light energy in full sunlight by inducing a mechanism termed nonphotochemical quenching (NPQ),” the investigators explained. However, when the leaves are shaded (by other leaves, clouds, or the sun moving in the sky) this photoprotection needs to switch off so the leaves can continue the photosynthesis process with a reserve of sunlight.

It takes several minutes for the plant to switch off the protective mechanism, costing plants valuable time that could have been used for photosynthesis. “… NPQ mechanisms are slow to relax following the frequent sun–shade transitions that occur within crop canopies”. This results in 7.5% to 30% loss of photochemical energy that could otherwise be used for photosynthesis. “For soybean crop canopies, this slow NPQ relaxation upon sun–shade transitions was calculated to cost >11% of daily CO2 assimilation”. Modifications resulted in a 20% increase in yield, and importantly, without impacting seed quality. “Despite higher yield, seed protein content was unchanged. This suggests some of the extra energy gained from improved photosynthesis was likely diverted to the nitrogen-fixing bacteria in the plant’s nodules.”