Algorithms · QAOA
Quantum Simulation-Based Optimization (QuSO) for cooling system design
Evaluate candidate designs for a simplified cooling system within an engineering design process that normally requires numerous computationally intensive numerical simulations, in a way that avoids the data input/output overhead that otherwise erodes any quantum speedup on such simulation tasks.
Attested & literatureUpdated
A small worked example, computed in your browser. It is not a result from this record's papers.
QAOA, p=1, MaxCut on a 4-cycle
4 qubits on a 4-cycle (edges 0-1, 1-2, 2-3, 3-0), one QAOA layer with gamma=pi/8, beta=3*pi/8.
Step 1 of 2 · Hadamard layer(4)
Probability of each outcome after this step
- 00006%
- 00016%
- 00106%
- 00116%
- 01006%
- 01016%
- 01106%
- 01116%
- 8 more outcomes50%
Starts from the uniform superposition over all 16 possible cuts.
Probability spreads from 1 outcome to 16. All 16 are equally likely.
The cost layer (RZZ(2*gamma) on each of the 4 edges) rewards cuts that separate connected qubits, then the mixer (RX(2*beta) on every qubit) lets amplitude move between cuts.
Probability moves between the same 16 outcomes. Up: 0101 6.3% → 26.6%, 1010 6.3% → 26.6%. Down: 0001 6.3% → 1.6%. 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.
Readout 0101 and 1010 are the two optimal cuts of a 4-cycle (alternating around the ring); at these angles measuring the register returns one of them clearly more often than any other cut.
Open in Studio- Record typeLiterature reference
- Reference implementationcooling_systems_optimization
- Reported costFor a single QuSO iteration, the paper's gate-level complexity analysis shows that the cost function can be coherently computed, over a superposition of exponentially many configurations, using circuits of polynomial complexity — but the abstract states this does not yield a speedup for a single simulation instance; any advantage is left as a potential one arising from the subsequent QAOA-based search over many such iterations, not a speedup proven here. The abstract also states that it expresses the scaling in terms of problem parameters and QAOA depth and iterations, without giving that expression itself, so no explicit formula, exponent, or constant for that scaling is recorded above.
- Papers1
Evaluate candidate designs for a simplified cooling system within an engineering design process that normally requires numerous computationally intensive numerical simulations, in a way that avoids the data input/output overhead that otherwise erodes any quantum speedup on such simulation tasks. Hölscher, Müller, Samimi and Danzig start from a tension in the literature: quantum algorithms promise substantial speedups for specific tasks relevant to engineering simulations, but those advantages quickly vanish once the cost of data input and output on quantum computers is considered. They build on the recently introduced Quantum Simulation-Based Optimization (QuSO) framework, which they describe as circumventing that limitation by treating simulations as subproblems within a larger optimization problem rather than running each simulation as a standalone computation with its own input/output cost. The authors adapt and implement QuSO for a simplified cooling system design problem, validate its correctness in statevector simulations, and present a detailed gate-level complexity analysis for a single QuSO iteration, expressing the scaling in terms of problem parameters and QAOA depth and iterations. They show that the cost function of the design problem can be coherently computed over a superposition of exponentially many configurations using circuits of polynomial complexity, but they state plainly that this does not by itself yield a speedup for a single simulation instance; instead, they say it enables potential advantages that could arise from the subsequent QAOA-based search over configurations. The authors describe the study as a proof-of-concept for integrating fault-tolerant quantum subroutines with simulation-based optimization in engineering workflows, and say it is meant to clarify both the promise and the practical limitations of that integration.
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 →
Hölscher, Müller, Samimi and Danzig start from a tension in the literature: quantum algorithms promise substantial speedups for specific tasks relevant to engineering simulations, but those advantages quickly vanish once the cost of data input and output on quantum computers is considered. They build on the recently introduced Quantum Simulation-Based Optimization (QuSO) framework, which they describe as circumventing that limitation by treating simulations as subproblems within a larger optimization problem rather than running each simulation as a standalone computation with its own input/output cost. The authors adapt and implement QuSO for a simplified cooling system design problem, validate its correctness in statevector simulations, and present a detailed gate-level complexity analysis for a single QuSO iteration, expressing the scaling in terms of problem parameters and QAOA depth and iterations. They show that the cost function of the design problem can be coherently computed over a superposition of exponentially many configurations using circuits of polynomial complexity, but they state plainly that this does not by itself yield a speedup for a single simulation instance; instead, they say it enables potential advantages that could arise from the subsequent QAOA-based search over configurations. The authors describe the study as a proof-of-concept for integrating fault-tolerant quantum subroutines with simulation-based optimization in engineering workflows, and say it is meant to clarify both the promise and the practical limitations of that integration. Reported cost: For a single QuSO iteration, the paper's gate-level complexity analysis shows that the cost function can be coherently computed, over a superposition of exponentially many configurations, using circuits of polynomial complexity — but the abstract states this does not yield a speedup for a single simulation instance; any advantage is left as a potential one arising from the subsequent QAOA-based search over many such iterations, not a speedup proven here. The abstract also states that it expresses the scaling in terms of problem parameters and QAOA depth and iterations, without giving that expression itself, so no explicit formula, exponent, or constant for that scaling is recorded above..
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
- cooling_systems_optimization
- Reported cost
- For a single QuSO iteration, the paper's gate-level complexity analysis shows that the cost function can be coherently computed, over a superposition of exponentially many configurations, using circuits of polynomial complexity — but the abstract states this does not yield a speedup for a single simulation instance; any advantage is left as a potential one arising from the subsequent QAOA-based search over many such iterations, not a speedup proven here. The abstract also states that it expresses the scaling in terms of problem parameters and QAOA depth and iterations, without giving that expression itself, so no explicit formula, exponent, or constant for that scaling is recorded above.
- Complexity basis
- abstract of arXiv:2504.15460, the only source read for this record: "Here we adapt and implement QuSO for a simplified cooling system design problem, validate correctness in statevector simulations, and present a detailed gate-level complexity analysis for a single QuSO iteration." Its scaling statement names the variables but not the formula: "We express the scaling in terms of problem parameters and QAOA depth and iterations." Its complexity finding is: "We show that the cost function can be coherently computed over a superposition of exponentially many configurations using circuits of polynomial complexity." And its speedup finding, quoted in full because upgrading it would misstate the paper: "This does not yield a speedup for a single simulation instance, but it enables potential advantages arising from the subsequent QAOA-based search over configurations." No exponent, no explicit function of the problem parameters, QAOA depth or iteration count, and no qubit or gate count is quoted anywhere in the abstract; "polynomial complexity" and "exponentially many configurations" are the only complexity-class descriptors it gives, and "potential advantages" is the abstract's own hedge on the one place it points to an advantage at all. The demonstration this record covers states no bound. This record fills the complexity field with the paper's stated complexity class rather than leaving it empty, because the abstract does give one, but every clause above is carried with the hedge the abstract itself attaches to it.
- Circuit
- Not supplied
This record is not a concrete circuit.
Quantum vs classical
Classical baseline
Compare QAOA with the strongest classical method for the same instance, input budget, and output metric.
Quantum claim
This reference exposes a quantum circuit pattern; it does not imply an application-level speedup without a matched benchmark.
How to compare
Report input loading, circuit depth, repetitions, classical preprocessing, post-processing, and wall-clock time together.
Nobody has reviewed this record for gaps yet.
ALGORITHM: Quantum Simulation-Based Optimization (QuSO) for cooling system design
PROBLEM: Evaluate candidate designs for a simplified cooling system within an engineering design process that normally requires numerous computationally intensive numerical simulations, in a way that avoids the data input/output overhead that otherwise erodes any quantum speedup on such simulation tasks.
IDEA: Hölscher, Müller, Samimi and Danzig start from a tension in the literature: quantum algorithms promise substantial speedups for specific tasks relevant to engineering simulations, but those advantages quickly vanish once the cost of data input and output on quantum computers is considered. They build on the recently introduced Quantum Simulation-Based Optimization (QuSO) framework, which they describe as circumventing that limitation by treating simulations as subproblems within a larger optimization problem rather than running each simulation as a standalone computation with its own input/output cost. The authors adapt and implement QuSO for a simplified cooling system design problem, validate its correctness in statevector simulations, and present a detailed gate-level complexity analysis for a single QuSO iteration, expressing the scaling in terms of problem parameters and QAOA depth and iterations. They show that the cost function of the design problem can be coherently computed over a superposition of exponentially many configurations using circuits of polynomial complexity, but they state plainly that this does not by itself yield a speedup for a single simulation instance; instead, they say it enables potential advantages that could arise from the subsequent QAOA-based search over configurations. The authors describe the study as a proof-of-concept for integrating fault-tolerant quantum subroutines with simulation-based optimization in engineering workflows, and say it is meant to clarify both the promise and the practical limitations of that integration.
REPORTED COST: For a single QuSO iteration, the paper's gate-level complexity analysis shows that the cost function can be coherently computed, over a superposition of exponentially many configurations, using circuits of polynomial complexity — but the abstract states this does not yield a speedup for a single simulation instance; any advantage is left as a potential one arising from the subsequent QAOA-based search over many such iterations, not a speedup proven here. The abstract also states that it expresses the scaling in terms of problem parameters and QAOA depth and iterations, without giving that expression itself, so no explicit formula, exponent, or constant for that scaling is recorded above.
BASIS: abstract of arXiv:2504.15460, the only source read for this record: "Here we adapt and implement QuSO for a simplified cooling system design problem, validate correctness in statevector simulations, and present a detailed gate-level complexity analysis for a single QuSO iteration." Its scaling statement names the variables but not the formula: "We express the scaling in terms of problem parameters and QAOA depth and iterations." Its complexity finding is: "We show that the cost function can be coherently computed over a superposition of exponentially many configurations using circuits of polynomial complexity." And its speedup finding, quoted in full because upgrading it would misstate the paper: "This does not yield a speedup for a single simulation instance, but it enables potential advantages arising from the subsequent QAOA-based search over configurations." No exponent, no explicit function of the problem parameters, QAOA depth or iteration count, and no qubit or gate count is quoted anywhere in the abstract; "polynomial complexity" and "exponentially many configurations" are the only complexity-class descriptors it gives, and "potential advantages" is the abstract's own hedge on the one place it points to an advantage at all. The demonstration this record covers states no bound. This record fills the complexity field with the paper's stated complexity class rather than leaving it empty, because the abstract does give one, but every clause above is carried with the hedge the abstract itself attaches to it.
PRIMARY SOURCE: Leonhard Hölscher, Lukas Müller, Or Samimi, Tamuz Danzig (2025), Quantum Simulation-Based Optimization for Cooling System Design — https://arxiv.org/abs/2504.15460
This is a literature reference record, not an executable circuit.A reference record, not runnable source. Leona cannot execute it, so it cannot be saved to your Library as a circuit.
Related entries
- QAOA MaxCut on a 5-node ring
Algorithms
- Ising cost Hamiltonian
Operators
- Quantum simulated annealing
Algorithms
- Ising formulations of NP-complete and NP-hard problems
Algorithms
References
- Quantum Simulation-Based Optimization for Cooling System Design
Leonhard Hölscher, Lukas Müller, Or Samimi, Tamuz Danzig · 2025
Primary source: it adapts and implements the Quantum Simulation-Based Optimization (QuSO) framework for a simplified cooling system design problem, validates correctness in statevector simulations, presents a gate-level complexity analysis for a single QuSO iteration, and states that the resulting polynomial-complexity circuits do not yield a speedup for a single simulation instance, only a potential downstream advantage from a QAOA-based search. Consult it for the scaling expression in problem parameters and QAOA depth/iterations, the gate-level analysis itself, and the QuSO framework this paper builds on but does not originate.