Algorithms · Quantum walk
Environment-assisted quantum walks in photosynthetic energy transfer
Determine the role quantum dynamical effects play in the efficiency of exciton (energy) transfer within photosynthetic molecular arrays — such as the Fenna-Matthews-Olson (FMO) protein complex, whose long-lived coherence had recently been demonstrated experimentally — that interact with a thermal bath.
Attested & literatureUpdated
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A discrete-time quantum walk on a 4-cycle
One coin qubit, two position qubits (4 positions on a cycle), 3 steps starting at position 0.
Step 1 of 3 · Quantum walk step (4-cycle)
Probability of each outcome after this step
- 01150%
- 11050%
Flips the coin with a Hadamard, then shifts the position by +1 if the coin is |1⟩ or -1 mod 4 if the coin is |0⟩; with the coin in superposition, both shifts happen at once, entangling coin and position.
Probability leaves the outcome it was on and appears on 2 entirely different ones — not one outcome is populated both before and after. This is the step that entangles the qubits: from here on no single qubit has a state of its own, only the register as a whole does.
The same coin flip and shift, applied again.
Probability leaves all 2 outcomes it was on and appears on 4 entirely different ones — not one outcome is populated both before and after.
The same coin flip and shift, a third time.
Probability leaves all 4 outcomes it was on and appears on 2 entirely different ones — not one outcome is populated both before and after. The entanglement comes apart here: each qubit has a state of its own again.
Readout The position always reads 3, for either value of the coin: constructive interference on this small cycle concentrates the walk onto a single position after exactly 3 steps.
Open in Studio- Record typeLiterature reference
- Reference implementationquantum_walk_fmo
- Reported costNot stated by the sources read
- Papers1
Determine the role quantum dynamical effects play in the efficiency of exciton (energy) transfer within photosynthetic molecular arrays — such as the Fenna-Matthews-Olson (FMO) protein complex, whose long-lived coherence had recently been demonstrated experimentally — that interact with a thermal bath. Mohseni, Rebentrost, Lloyd and Aspuru-Guzik develop a theoretical framework for studying the role of quantum interference effects in the energy-transfer dynamics of molecular arrays that interact with a thermal bath, working within the Lindblad formalism. To do this, they generalize continuous-time quantum walks to non-unitary and temperature-dependent dynamics in Liouville space, derived from a microscopic Hamiltonian. They explore the different physical effects of coherence and decoherence processes through a universal measure of the energy-transfer efficiency and its susceptibility. Applying the framework to the Fenna-Matthews-Olson (FMO) protein complex — for which direct evidence of long-lived coherence had recently been demonstrated experimentally, citing Engel et al., Nature 446, 782 (2007) — they demonstrate that an effective interplay between the free Hamiltonian and thermal fluctuations in the environment leads to a substantial increase in the complex's energy-transfer efficiency, from about 70% to 99%. That figure is the paper's own result about the physical efficiency of energy transfer within the FMO complex, obtained from the generalized quantum-walk framework the paper develops; it is not a claim about the running time, resource cost, or speedup of an algorithm, and the abstract states none of those for the framework itself.
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
Mohseni, Rebentrost, Lloyd and Aspuru-Guzik develop a theoretical framework for studying the role of quantum interference effects in the energy-transfer dynamics of molecular arrays that interact with a thermal bath, working within the Lindblad formalism. To do this, they generalize continuous-time quantum walks to non-unitary and temperature-dependent dynamics in Liouville space, derived from a microscopic Hamiltonian. They explore the different physical effects of coherence and decoherence processes through a universal measure of the energy-transfer efficiency and its susceptibility. Applying the framework to the Fenna-Matthews-Olson (FMO) protein complex — for which direct evidence of long-lived coherence had recently been demonstrated experimentally, citing Engel et al., Nature 446, 782 (2007) — they demonstrate that an effective interplay between the free Hamiltonian and thermal fluctuations in the environment leads to a substantial increase in the complex's energy-transfer efficiency, from about 70% to 99%. That figure is the paper's own result about the physical efficiency of energy transfer within the FMO complex, obtained from the generalized quantum-walk framework the paper develops; it is not a claim about the running time, resource cost, or speedup of an algorithm, and the abstract states none of those for the framework itself. The sources read state no complexity bound for this record (The abstract of arXiv:0805.2741 states no algorithmic complexity, running time, gate count, or qubit count. Its one quantitative result is a physical efficiency figure for a specific molecular complex: "we demonstrate that for the FMO complex an effective interplay between free Hamiltonian and thermal fluctuations in the environment leads to a substantial increase in energy transfer efficiency from about 70% to 99%." That is a result about the transfer efficiency of the FMO complex itself, obtained from the paper's theoretical framework, not a bound on the cost of the generalized quantum walk or of any other algorithm; the abstract states no runtime, no query count, and no comparison of computational cost for the framework it develops. The demonstration this record covers states no complexity bound of its own. Those are the only sources read for this field, and the complexity field is left empty on purpose rather than filled with an efficiency figure that is not a complexity bound.).
TakesNothingWhat joins here
No input port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
ReturnsNothingWhat joins here
No output port at this edge: the record publishes no gate sequence and no register, so there is nothing here to read one off — and unlike a declared hole, nothing has been recorded about what belongs here.
Nothing in the Atlas meets this end.
This record publishes no gate sequence and no register, so there is nothing here to read an interface off. Absent rather than empty. See all 152 →
- Record type
- Literature reference
- Reference implementation
- quantum_walk_fmo
- Reported cost
- Not stated by the sources read
- Complexity basis
- The abstract of arXiv:0805.2741 states no algorithmic complexity, running time, gate count, or qubit count. Its one quantitative result is a physical efficiency figure for a specific molecular complex: "we demonstrate that for the FMO complex an effective interplay between free Hamiltonian and thermal fluctuations in the environment leads to a substantial increase in energy transfer efficiency from about 70% to 99%." That is a result about the transfer efficiency of the FMO complex itself, obtained from the paper's theoretical framework, not a bound on the cost of the generalized quantum walk or of any other algorithm; the abstract states no runtime, no query count, and no comparison of computational cost for the framework it develops. The demonstration this record covers states no complexity bound of its own. Those are the only sources read for this field, and the complexity field is left empty on purpose rather than filled with an efficiency figure that is not a complexity bound.
- Circuit
- Not supplied
This record is not a concrete circuit.
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ALGORITHM: Environment-assisted quantum walks in photosynthetic energy transfer
PROBLEM: Determine the role quantum dynamical effects play in the efficiency of exciton (energy) transfer within photosynthetic molecular arrays — such as the Fenna-Matthews-Olson (FMO) protein complex, whose long-lived coherence had recently been demonstrated experimentally — that interact with a thermal bath.
IDEA: Mohseni, Rebentrost, Lloyd and Aspuru-Guzik develop a theoretical framework for studying the role of quantum interference effects in the energy-transfer dynamics of molecular arrays that interact with a thermal bath, working within the Lindblad formalism. To do this, they generalize continuous-time quantum walks to non-unitary and temperature-dependent dynamics in Liouville space, derived from a microscopic Hamiltonian. They explore the different physical effects of coherence and decoherence processes through a universal measure of the energy-transfer efficiency and its susceptibility. Applying the framework to the Fenna-Matthews-Olson (FMO) protein complex — for which direct evidence of long-lived coherence had recently been demonstrated experimentally, citing Engel et al., Nature 446, 782 (2007) — they demonstrate that an effective interplay between the free Hamiltonian and thermal fluctuations in the environment leads to a substantial increase in the complex's energy-transfer efficiency, from about 70% to 99%. That figure is the paper's own result about the physical efficiency of energy transfer within the FMO complex, obtained from the generalized quantum-walk framework the paper develops; it is not a claim about the running time, resource cost, or speedup of an algorithm, and the abstract states none of those for the framework itself.
REPORTED COST: Not stated by the sources read
BASIS: The abstract of arXiv:0805.2741 states no algorithmic complexity, running time, gate count, or qubit count. Its one quantitative result is a physical efficiency figure for a specific molecular complex: "we demonstrate that for the FMO complex an effective interplay between free Hamiltonian and thermal fluctuations in the environment leads to a substantial increase in energy transfer efficiency from about 70% to 99%." That is a result about the transfer efficiency of the FMO complex itself, obtained from the paper's theoretical framework, not a bound on the cost of the generalized quantum walk or of any other algorithm; the abstract states no runtime, no query count, and no comparison of computational cost for the framework it develops. The demonstration this record covers states no complexity bound of its own. Those are the only sources read for this field, and the complexity field is left empty on purpose rather than filled with an efficiency figure that is not a complexity bound.
PRIMARY SOURCE: Masoud Mohseni, Patrick Rebentrost, Seth Lloyd, Alán Aspuru-Guzik (2008), Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer — https://arxiv.org/abs/0805.2741
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References
- Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer
Masoud Mohseni, Patrick Rebentrost, Seth Lloyd, Alán Aspuru-Guzik · 2008
Primary source: it develops the Lindblad-formalism theoretical framework and the generalization of continuous-time quantum walks to non-unitary, temperature-dependent Liouville-space dynamics, and reports the resulting increase in the FMO complex's energy-transfer efficiency from about 70% to 99%. Consult it for the universal efficiency-and-susceptibility measure, the microscopic Hamiltonian the dynamics are derived from, and the derivation connecting the free-Hamiltonian/thermal-fluctuation interplay to the reported efficiency figure, none of which the abstract states in detail.