Constrained quantum optimization for extractive summarization on a trapped-ion quantum computer
Open accessAbstract
Realizing the potential of near-term quantum computers to solve industry-relevant constrained-optimization problems is a promising path to quantum advantage. In this work, we consider the extractive summarization constrained-optimization problem and demonstrate the largest-to-date execution of a quantum optimization algorithm that natively preserves constraints on quantum hardware. We report results with the Quantum Alternating Operator Ansatz algorithm with a Hamming-weight-preserving XY mixer (XY-QAOA) on trapped-ion quantum computer. We successfully execute XY-QAOA circuits that restrict the quantum evolution to the in-constraint subspace, using up to 20 qubits and a two-qubit gate depth of up to 159. We demonstrate the necessity of directly encoding the constraints into the quantum circuit by showing the trade-off between the in-constraint probability and the quality of the solution that is implicit if unconstrained quantum optimization methods are used. We show that this trade-off makes choosing good parameters difficult in general. We compare XY-QAOA to the Layer Variational Quantum Eigensolver algorithm, which has a highly expressive constant-depth circuit, and the Quantum Approximate Optimization Algorithm. We discuss the respective trade-offs of the algorithms and implications for their execution on near-term quantum hardware.
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Written from the paper’s full text.
TL;DR
The paper demonstrates XY-QAOA with a Hamming-weight-preserving XY mixer for extractive summarization on the Quantinuum H1-1 trapped-ion quantum computer, using up to 20 qubits and two-qubit gate depth up to 159 (765 two-qubit gates). It argues that constraints should be encoded directly into the quantum circuit because unconstrained QAOA forces a difficult trade-off between in-constraint probability and solution quality.
Key findings
- XY-QAOA was executed on H1-1 with up to 20 qubits, full-circuit two-qubit depth 159, and two-qubit gate count 765; the 20-qubit Dicke-state preparation alone required two-qubit depth 95 and 347 two-qubit gates.
- XY-QAOA natively preserves the Hamming-weight constraint, giving in-constraint probability of one in the noiseless case; hardware noise caused out-of-constraint samples, with 20-qubit XY-QAOA outputs including bitstrings as far as 10 bitflips away, while short L-VQE circuits included only bitstrings one or two bitflips away.
- QAOA gave a relatively high approximation ratio but very low in-constraint probability; for 14 qubits its in-constraint probability was below random guess due to parameter choice. L-VQE achieved high approximation ratio and in-constraint probability on the modest 14- and 20-qubit problems, but its expressiveness makes parameters hard to optimize as qubit count grows.
- A Pareto frontier for QAOA parameters showed the trade-off between approximation ratio and in-constraint probability; optimizing the penalized objective (6) can lead to an approximation ratio equal to random guess for a 20-qubit instance.
Methods
- Extractive summarization was formulated as McDonald’s NP-hard constrained optimization: maximize sentence centrality while penalizing pairwise redundancy, with a fixed summary length. Instances came from CNN/DailyMail articles (just over 300k unique news articles), using two sets of 10 instances and executions on 14 and 20 qubits; BERT sentence embeddings computed similarities and tf-idf computed centralities.
- QAOA, XY-QAOA, and L-VQE were compared. Parameters were optimized in noiseless simulation, then circuits were executed on the Quantinuum H1-1 device with 2000 shots and on an H1-1 emulator; Qiskit was used for circuit manipulation and simulation, and Quantinuum’s t transpiler for hardware compilation. No error mitigation was applied.
- Metrics were approximation ratio (Eq. 8) and in-constraint probability, estimated as the ratio of in-constraint samples to total samples. For unconstrained solvers, the penalty weight was chosen so in-constraint binary strings had greater cost than out-of-constraint strings. XY-QAOA’s initial Dicke state was prepared using a divide-and-conquer short-depth method targeting all-to-all connectivity.
Limitations
- Stated: XY-QAOA requires deeper circuits than QAOA and L-VQE because of the XY mixer and Dicke-state preparation, incurring significant cost before optimization; hardware noise in initial-state preparation and deeper circuits reduces in-constraint probability.
- Stated: L-VQE’s expressiveness makes parameters hard to optimize and may suffer barren plateaus as qubit count grows; QAOA’s parameter optimization must trade off in-constraint probability and solution quality, which is hard in general.
- Stated/evident: hardware XY-QAOA results are based on only three 14-qubit and three 20-qubit instances due to high circuit depth and running time, and no error mitigation was used. Evident from the provided text: several numerical values, including some approximation ratios and instance sizes, are omitted in the text as given.
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Claims the paper makes
0 of 13 cited sources checked · 0 supported · 0 flagged
- Findingown data
The results on hardware are on average at least as good as those obtained from the emulator.
“Additionally, we observe that the results on hardware are on average at least as good as those obtained from the emulator, making us confident that the emulator gives a good lower bound on the solution quality that can be expected on hardware.”
Quote in the paperSubstantial claim - Findingown data
The noise is sufficiently low so that the XY-QAOA output distribution is still concentrated on the in-constraint subspace.
“At the same time, the noise is sufficiently low so that the XY-QAOA output distribution is still concentrated on the in-constraint subspace.”
Quote in the paperSubstantial claim - Findingreasoning
For the modestly sized problems considered in this work, the L-VQE parameters can be optimized to obtain solutions with very high approximation ratio and in-constraint probability.
“As we consider modestly sized problems in this work, we are able to optimize the parameters and obtain solutions with very high approximation ratio and in-constraint probability.”
Quote in the paperSubstantial claim - Findingnone given
A significant part of the two-qubit gate depth of the XY-QAOA circuit comes from the circuit preparing the initial Dicke state.
“For the XY-QAOA circuit, a significant part of the two-qubit gate depth comes from the circuit preparing the initial state, which is a uniform superposition of all in-constraint states (Dicke state).”
Quote in the paperSubstantial claim - Findingown data
The execution of XY-QAOA on the Quantinuum H1-1 processor used all 20 qubits of H1-1.
“We use all 20 qubits of H1-1 and execute circuits with two-qubit gate depth of up to 159 and two-qubit gate count of up to 765, which is the largest such demonstration to date.”
Quote in the paperSubstantial claim
- Findingown data
The demonstration of constrained quantum optimization on gate-based quantum computers using up to 20 qubits and 765 native two-qubit gates is the largest to date.
“We show the largest to date demonstration of constrained quantum optimization on gate-based quantum computers, using up to 20 qubits and 765 native two-qubit gates (see “Related work” for a review of previous demonstrations).”
Quote in the paperSubstantial claim - Findingown data
On the H1-1 device, the initial state preparation for XY-QAOA is not fully contained in the in-constraint subspace due to noise.
“Unlike the noiseless case, the initial state is not fully contained in the in-constraint subspace.”
Quote in the paperSubstantial claim - Findingown data
The executed XY-QAOA circuits had a two-qubit gate count of up to 765.
“We use all 20 qubits of H1-1 and execute circuits with two-qubit gate depth of up to 159 and two-qubit gate count of up to 765, which is the largest such demonstration to date.”
Quote in the paperSubstantial claim - Findingreasoning
XY-QAOA natively encodes the constraints by restricting the quantum evolution to the subspace equal to the span of the computational basis states of Hamming weight M.
“XY-QAOA natively encodes the constraints by restricting the quantum evolution to the subspace equal to the span of the computational basis states of Hamming weight M.”
Quote in the paperSubstantial claim - Findingnone given
All results significantly improve on random guess.
“We observe that all results significantly improve on random guess.”
Quote in the paperSubstantial claim - Findingown data
All approximation ratios obtained, including those from the largest circuit executions on hardware, significantly improve upon random guess.
“We observe that all the approximation ratios obtained, including those from largest circuit executions on hardware, significantly improve upon random guess.”
Quote in the paperSubstantial claim - Findingreasoning
XY-QAOA requires deeper circuits as compared to QAOA and L-VQE.
“At the same time, XY-QAOA requires deeper circuits as compared to QAOA and L-VQE.”
Quote in the paperSubstantial claim - Findingreasoning
The XY-QAOA mixer operator adds additional O(N) gates in each layer of the QAOA circuit.
“It adds additional O(N) gates in each layer of QAOA circuit as it requires entangling gates on all adjacent pairs.”
Quote in the paperSubstantial claim - Findingown data
For deeper XY-QAOA circuits, bitstrings as far as 10 bitflips away are included in the output.
“On the other hand, for deeper XY-QAOA circuits, bitstrings as far as 10 bitflips away are included.”
Quote in the paperNot a substantial claim - Findingown data
XY-QAOA circuits that restrict the quantum evolution to the in-constraint subspace were successfully executed using up to 20 qubits and a two-qubit gate depth of up to 159.
“We successfully execute XY-QAOA circuits that restrict the quantum evolution to the in-constraint subspace, using up to 20 qubits and a two-qubit gate depth of up to 159.”
Quote in the paperSubstantial claim - Findingown data
The overlap with the in-constraint subspace is lower on hardware due to the presence of noise.
“Note that the overlap with the in-constraint subspace is lower on hardware due to the presence of noise.”
Quote in the paperNot a substantial claim - Findingown data
In experiments on the 20-qubit Quantinuum H1-1 system, XY-QAOA with up to 20 qubits provides results that are significantly better than random guess despite the circuit depth exceeding 100 two-qubit gates.
“In our experiments on the 20-qubit Quantinuum H1-1 system, we observe that XY-QAOA with up to 20 qubits provides results that are significantly better than random guess despite the circuit depth exceeding 100 two-qubit gates.”
Quote in the paperSubstantial claim- Rests on an assumption: The approximation ratio of random guess is a meaningful baseline for evaluating solution quality.
- Findingown data
The initial Dicke state, due to hardware noise, includes out-of-constraint states.
“Observe that the initial Dicke state, due to hardware noise, includes out-of-constraint states.”
Quote in the paperSubstantial claim - Findingreasoning
Figure 4c shows an instance where optimizing parameters with respect to (6) leads to an approximation ratio equal to that of random guess.
“Figure 4c shows an example of an instance where this leads to approximation ratio equal to that of random guess.”
Quote in the paperSubstantial claim- Rests on an assumption: The approximation ratio of random guess is a meaningful baseline for evaluating solution quality.
- Findingown data
Unlike QAOA or L-VQE, in XY-QAOA a significant amount of noise is incurred in the initial state preparation step.
“Unlike the QAOA or L-VQE, in XY-QAOA a significant amount of noise is incurred in the initial state preparation step.”
Quote in the paperSubstantial claim - Findingown data
For QAOA, even the noiseless output includes primarily out-of-constraint bitstrings due to the choice of parameters.
“For QAOA, even the noiseless output includes primarily out-of-constraint bitstrings due to the choice of parameters.”
Quote in the paperNot a substantial claim - Findingreasoning
The output distribution of QAOA circuits has a relatively small overlap with the in-constraint space even in the absence of noise.
“As discussed above, the output distribution of QAOA circuits has a relatively small overlap with the in-constraint space even in the absence of noise.”
Quote in the paperSubstantial claim - Interpretationreasoning
The trade-off between in-constraint probability and solution quality is avoided by L-VQE and XY-QAOA in two different ways.
“This trade-off is avoided by L-VQE and XY-QAOA in two different ways.”
Quote in the paperSubstantial claim - Premisecitation
L-VQE uses a very expressive parameterized circuit that can in principle solve the problem exactly with no two-qubit gates, just by optimizing the parameters of the initial single-qubit-gate layer.
“L-VQE uses a very expressive parameterized circuit that can in principle solve the problem exactly with no two-qubit gates, just by optimizing the parameters of the initial single-qubit-gate layer .”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [24] Liu, X. et al. Layer VQE: A variational approach for combinatorial optimization on noisy quantum computers. IEEE Trans. Quantum Eng. 3, 1–20. https://doi.org/10.1109/tqe.2021.3140190 (2022). source
Not checked in the free run.
- Premisenone given
The XY-QAOA mixer operator preserves the Hamming weight of the states it acts on.
“On the other hand, XY-QAOA uses a more complex mixer operator, which preserves the Hamming weight of the states it acts on.”
Quote in the paperSubstantial claim - Interpretationreasoning
The trade-off between in-constraint probability and solution quality can be avoided by encoding the constraints directly into the circuits as in XY-QAOA.
“We show how this trade-off can be avoided by either using a sufficiently expressive circuits such as L-VQE (at the cost of the increased difficulty of parameter optimization) or, more naturally, by encoding the constraints directly into the circuits as in the case of XY-QAOA.”
Quote in the paperSubstantial claim - Premisecitation
For most near-term circuit architectures, including H1-1, single-qubit gates are relatively less noisy than two-qubit entangling gates.
“For most near-term circuit architectures, including H1-1, the single qubit gates are relatively less noisy than the two-qubit entangling gates46,47.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [46] Pino, J. M. et al. Demonstration of the trapped-ion quantum CCD computer architecture. Nature 592, 209–213. https://doi.org/10.1038/s41586-021-03318-4 (2021). source
Not checked in the free run.
- cites [47] Ryan-Anderson, C. et al. Realization of real-time fault-tolerant quantum error correction. Phys. Rev. X 11, 041058. https://doi.org/10.1103/PhysRevX.11.041058 (2021). source
Not checked in the free run.
- Interpretationreasoning
The trade-off between in-constraint probability and solution quality can be avoided by using sufficiently expressive circuits such as L-VQE.
“We show how this trade-off can be avoided by either using a sufficiently expressive circuits such as L-VQE (at the cost of the increased difficulty of parameter optimization) or, more naturally, by encoding the constraints directly into the circuits as in the case of XY-QAOA.”
Quote in the paperSubstantial claim - Interpretationreasoning
The trade-off between in-constraint probability and solution quality makes choosing good parameters difficult in general.
“We show that this trade-off makes choosing good parameters difficult in general.”
- Also stated in: § Introduction · hedged
“This trade-off suggests the need to carefully engineer the parameter optimization strategy, which is difficult in general.”
Quote in the paperSubstantial claim - Also stated in: § Introduction · hedged
- Interpretationreasoning
For the Hamming-weight constraint, the XY-QAOA evolution is restricted to the span of computational basis states with Hamming weight M.
“Given that commutes with , the evolution produced by the resulting circuit is restricted to the span of computational basis states with Hamming weight M, as desired.”
Quote in the paperSubstantial claim - Interpretationreasoning
The deeper circuits of XY-QAOA are due to the higher gate count cost of the XY-QAOA mixer operator and the initial state preparation.
“This is due to the higher gate count cost of the XY-QAOA mixer operator and the initial state preparation.”
Quote in the paperSubstantial claim - Interpretationcitation
A penalty term introduces a trade-off between the in-constraint probability and the quality of the in-constraint solution.
“Moreover, a penalty term introduces a trade-off between the in-constraint probability and the quality of the in-constraint solution, as discussed in “Quantum circuit needs to preserve constraints”.”
Quote in the paperSubstantial claim - Interpretationreasoning
The low in-constraint probability of QAOA makes its high approximation ratio less significant.
“Here we simply note that the low in-constraint probability of QAOA makes the high approximation ratio less significant.”
Quote in the paperSubstantial claim - Premisecitation
The Quantum Alternating Operator Ansatz algorithm overcomes the limitation of unconstrained algorithms by using a parameterized circuit that limits the quantum evolution to a constraint-preserving subspace.
“The Quantum Alternating Operator Ansatz algorithm22 overcomes this limitation by using a parameterized circuit which limits the quantum evolution to a constraint-preserving subspace.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [22] Hadfield, S. et al. From the quantum approximate optimization algorithm to a quantum alternating operator ansatz. Algorithms 12, 34. https://doi.org/10.3390/a12020034 (2019). source
Not checked in the free run.
- Interpretationown data
The emulator gives a good lower bound on the solution quality that can be expected on hardware.
“Additionally, we observe that the results on hardware are on average at least as good as those obtained from the emulator, making us confident that the emulator gives a good lower bound on the solution quality that can be expected on hardware.”
Quote in the paperSubstantial claim - Interpretationreasoning
The QAOA mixer unitary does not add much noise to the evolution.
“As a result, the mixer unitary does not add much noise to the evolution.”
Quote in the paperNot a substantial claim - Premisecitation
Implementing the XY-QAOA initial Dicke state requires a circuit with O(N) two-qubit gate depth.
“This state is non-trivial to implement, as it requires a circuit with O(N) two-qubit gate depth41.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [41] Bärtschi, A. & Eidenbenz, S. Deterministic preparation of Dicke states. In Fundamentals of Computation Theory 126–139 (Springer International Publishing, 2019). https://doi.org/10.1007/978-3-030-25027-0_9. source
Not checked in the free run.
- Interpretationown data
There is a trade-off between the in-constraint probability and the quality of the solution when unconstrained quantum optimization methods are applied to constrained problems.
“We demonstrate the necessity of directly encoding the constraints into the quantum circuit by showing the trade-off between the in-constraint probability and the quality of the solution that is implicit if unconstrained quantum optimization methods are used.”
- Also stated in: § Introduction · plain
“Second, we motivate our algorithm choice by highlighting the trade-off between the quality of the solution and the in-constraint probability which is implicit in applying unconstrained near-term quantum optimization algorithms to constrained problems.”
Quote in the paperSubstantial claim - Also stated in: § Introduction · plain
- Interpretationreasoning
As the number of qubits grows, optimizing L-VQE parameters will become increasingly infeasible.
“However, as the number of qubits grows, this will become increasingly infeasible.”
Quote in the paperSubstantial claim - Interpretationreasoning
In XY-QAOA a significant cost is incurred before any optimization is performed.
“Therefore in XY-QAOA a significant cost is incurred before any optimization is performed.”
Quote in the paperSubstantial claim - Interpretationreasoning
QAOA is not a good algorithm for the problem considered here despite having a relatively high approximation ratio.
“Combined with the complexity of parameter setting arising from the trade-off, this means that QAOA is not a good algorithm for the problem we consider here despite having a relatively high approximation ratio.”
Quote in the paperSubstantial claim - Interpretationreasoning
If the circuit does not preserve the constraints, the in-constraint probability and the quality of the in-constraint solution have to be traded-off against each other.
“If the circuit does not preserve the constraints, the in-constraint probability and the quality of the in-constraint solution have to be traded-off against each other.”
Quote in the paperSubstantial claim - Interpretationown data
This work is the largest demonstration to date of constrained optimization on a gate-based quantum computer (or quantum hardware).
“In this work, we show the largest demonstration to date of constrained optimization on a gate-based quantum computer.”
- Also stated in: § Discussion · plain
“In this work, we present the largest to date demonstration of constrained optimization on quantum hardware.”
Quote in the paperSubstantial claim- Rests on an assumption: The survey of previous quantum optimization demonstrations in Table 2 is complete enough to establish that this work is the largest demonstration to date.
- Also stated in: § Discussion · plain
- Interpretationreasoning
Circuits that are sufficiently expressive to solve the problem exactly would by necessity have many parameters that are hard to optimize.
“However, such circuits by necessity would have many parameters that are hard to optimize.”
Quote in the paperSubstantial claim - Interpretationreasoning
The small overlap of QAOA output distribution with the in-constraint space is due to the trade-off between the in-constraint probability and the approximation ratio, which is implicit in the choice of the parameter optimization strategy.
“This is due to the trade-off between the in-constraint probability and the approximation ratio, which is implicit in the choice of the parameter optimization strategy.”
Quote in the paperSubstantial claim - Premisecitation
In many cases, such expressive circuits would suffer from gradients of the objective vanishing exponentially with the number of qubits (barren plateaus), making optimization impossible.
“Additionally, in many cases they would suffer from gradients of the objective vanishing exponentially with the number of qubits (“barren plateaus”)45, making optimization impossible.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [45] Holmes, Z., Sharma, K., Cerezo, M. & Coles, P. J. Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum.https://doi.org/10.1103/prxquantum.3.010313 (2022). source
Not checked in the free run.
- Interpretationreasoning
The most practical solution is encoding constraints directly into the quantum circuit, as is the case for XY-QAOA.
“Therefore the most practical solution is encoding constraints directly into the quantum circuit, as is the case for XY-QAOA.”
Quote in the paperNot a substantial claim - Interpretationnone given
Optimizing parameters with respect to objective (6) would lead to prioritizing the in-constraint probability.
“As an example, optimizing parameters with respect to (6) would lead to prioritizing the in-constraint probability.”
Quote in the paperNot a substantial claim - Interpretationreasoning
The paper shows the necessity of embedding constraints directly into the quantum circuit being used.
“We additionally show the necessity of embedding the constraints directly into the quantum circuit being used.”
Quote in the paperSubstantial claim
- Classified as probably not a substantial claim. 16
- May combine two claims. 15
Probably not a substantial claim: may not pass S3 (load-bearing).
Findingown dataThe in-constraint probability of QAOA is below random guess for 14 qubits due to the choice of parameters.
“The in-constraint probability of QAOA is below random guess for 14 qubits due to the choice of parameters; see discussion in “Quantum circuit needs to preserve constraints”.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataFor the short L-VQE circuits, the amount of noise accumulated during circuit execution is small, and only bitstrings that are one or two bitflips away are included in the output.
“Note that for the short L-VQE circuits, the amount of noise accumulated during the circuit execution is small, and only the bitstrings that are one or two bitflips away are included in the output.”
Quote in the paperNot a substantial claimMay combine two claims.
Findingown dataAs noise is added, the in-constraint probability decreases and the output begins to include out-of-constraint bitstrings.
“We can see that as the noise is added, the in-constraint probability decreases and the output begins to include out-of-constraint bitstrings.”
Quote in the paperSubstantial claimMay combine two claims.
FindingreasoningQAOA gives a relatively high approximation ratio but a very low in-constraint probability.
“We begin by noting that QAOA gives a relatively high approximation ratio, but a very low in-constraint probability.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Findingnone givenInitial state preparation for QAOA and L-VQE requires no two-qubit gates.
“Initial state preparation for QAOA and L-VQE requires no two-qubit gates.”
Quote in the paperNot a substantial claimMay combine two claims.
PremisecitationThe expressiveness of the L-VQE circuit makes the parameters hard to optimize, both due to their high number and due to gradients vanishing as the number of qubits grows in some cases.
“At the same time, the expressiveness of L-VQE circuit makes the parameters hard to optimize, both due to their high number and due to the gradients vanishing as the number of qubits grows in some cases44,45.”
Quote in the paperSubstantial claim0 of 2 sources checked- cites [44] McClean, J. R., Boixo, S., Smelyanskiy, V. N., Babbush, R. & Neven, H. Barren plateaus in quantum neural network training landscapes. Nat. Commun.https://doi.org/10.1038/s41467-018-07090-4 (2018). source
Not checked in the free run.
- cites [45] Holmes, Z., Sharma, K., Cerezo, M. & Coles, P. J. Connecting ansatz expressibility to gradient magnitudes and barren plateaus. PRX Quantum.https://doi.org/10.1103/prxquantum.3.010313 (2022). source
Not checked in the free run.
May combine two claims.
Interpretationown dataBoth the algorithm design and the hardware noise affect the in-constraint probability.
“Both the algorithm design and the hardware noise affect the in-constraint probability.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S4 (based).
Premisenone givenThe initial state used by QAOA or L-VQE requires no two-qubit gates to prepare.
“This is in sharp contrast with the initial state used by QAOA or L-VQE, which requires no two-qubit gates to prepare.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim. May combine two claims.
Premisenone givenQAOA and L-VQE can tackle constrained-optimization problems in which the constraint is enforced by a penalty term, but their output is not guaranteed to satisfy the constraint.
“While QAOA and L-VQE can tackle constrained-optimization problems in which the constraint is enforced by a penalty term, the output of these algorithms is not guaranteed to satisfy the constraint.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
InterpretationreasoningImproved hardware fidelity would lead to more accurate initial state preparation and higher overall in-constraint probability.
“Improved hardware fidelity would lead to more accurate initial state preparation and higher overall in-constraint probability.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
InterpretationreasoningThe running time of the algorithm scales inversely proportionally to the in-constraint probability due to the need to obtain at least one in-constraint sample.
“In practice, the running time of the algorithm scales inversely proportionally to the in-constraint probability due to the need to obtain at least one in-constraint sample.”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationreasoningXY-QAOA leads to an in-constraint probability of one and a high approximation ratio, if no noise is present.
“This leads to an in-constraint probability of one and a high approximation ratio, if no noise is present.”
Quote in the paperSubstantial claimMay combine two claims.
PremisecitationThe extractive summarization formulation that maximizes centrality and minimizes redundancy under a fixed summary length constraint has been proposed by R. McDonald and shown to be NP-hard to solve exactly.
“This formulation of ES has been proposed by R. McDonald and shown to be -hard to solve exactly19.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [19] McDonald, R. A study of global inference algorithms in multi-document summarization. In Advances in Information Retrieval, ECIR’07 557–564 (Springer, Berlin, 2007). https://doi.org/10.5555/1763653.1763720. source
Not checked in the free run.
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThere have been very large-scale demonstrations of QAOA on analog quantum simulators.
“Lastly, there have been very large-scale demonstrations of QAOA on analog quantum simulators.”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [64] Pagano, G. et al. Quantum approximate optimization of the long-range ising model with a trapped-ion quantum simulator. Proc. Natl. Acad. Sci 117, 25396–25401. https://doi.org/10.1073/pnas.2006373117 (2020). source
Not checked in the free run.
- cites [15] Ebadi, S. et al. Quantum optimization of maximum independent set using rydberg atom arrays. Science 376, 1209–1215. https://doi.org/10.1126/science.abo6587 (2022). source
Not checked in the free run.
Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.
Interpretationown dataOur results demonstrate how algorithmic and hardware progress are bringing the prospect of quantum advantage in constrained optimization closer, which can be leveraged in many industries including finance.
“Our results demonstrate how algorithmic and hardware progress are bringing the prospect of quantum advantage in constrained optimization closer, which can be leveraged in many industries including finance65,66.”
Quote in the paperNot a substantial claim0 of 2 sources checked- cites [65] Herman, D. et al. A survey of quantum computing for finance. https://doi.org/10.48550/ARXIV.2201.02773 (2022). source
Not checked in the free run.
- cites [66] Pistoia, M. et al. Quantum machine learning for finance iccad special session paper. In 2021 IEEE/ACM International Conference On Computer Aided Design (ICCAD), 1–9. https://doi.org/10.1109/ICCAD51958.2021.9643469 (2021). source
Not checked in the free run.
Classified as probably not a substantial claim.
InterpretationreasoningExecution of complex circuits for constrained optimization benefits from the underlying hardware's all-to-all connectivity, as the circuit depth would increase significantly if the circuit had to be compiled to a nearest-neighbor architecture.
“Our execution of complex circuits for constrained optimization benefits from the underlying hardware’s all-to-all connectivity, as the circuit depth would increase significantly if the circuit had to be compiled to a nearest-neighbor architecture.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing). May combine two claims.
Interpretationnone givenFurther advances are needed to reduce the hardware requirements of implementing such circuits and improve the fidelities of the hardware.
“At the same time, we show that further advances are needed to reduce the hardware requirements of implementing such circuits and improve the fidelities of the hardware.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
InterpretationreasoningSince analog devices do not implement universal gate sets, their results are not directly comparable to ours.
“However, since these analog devices do not implement universal gate sets, the results are not directly comparable to ours.”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationcitationOther hardware demonstrations of QAOA using alternative mixers to the transverse field were either not applied to hard-constrained problems or did not use an in-constraint initial state.
“While there have been other hardware demonstrations of QAOA using alternative mixers to the transverse field, they were either not applied to hard-constrained problems or did not use an in-constraint initial state.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Interpretationnone givenTo the authors' knowledge, there has only been one other demonstration of QAOA with constrained mixers and Dicke-state initialization on quantum hardware.
“To the authors’ knowledge, there has only be one other demonstration of QAOA with constrained mixers and Dicke-state initialization on quantum hardware.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Interpretationnone givenOne potential solution to the challenge of choosing parameters is using a circuit that is sufficiently expressive to solve the problem exactly, such as the circuit used in L-VQE.
“One potential solution to this challenge is using a circuit that is sufficiently expressive to solve the problem exactly, such as the circuit used in L-VQE.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim. May combine two claims.
Study design and conductnone givenThe results presented here were obtained with no error mitigation, which is not the case for many previous demonstrations.
“The results we present here were obtained with no error mitigation, which is not the case for many of the previous demonstrations.”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningThe trade-off between in-constraint probability and approximation ratio is an important weakness of unconstrained quantum algorithms applied to constrained problems, necessitating the development and implementation of quantum algorithms that natively preserve constraints.
“This trade-off is an important weakness of unconstrained quantum algorithms applied to constrained problems, necessitating the development and implementation of quantum algorithms that natively preserve constraints.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S4 (based).
Interpretationnone givenThe trade-off behavior between in-constraint probability and approximation ratio applies to all unconstrained quantum algorithms that are not expressive enough to solve the problem exactly.
“This trade-off behavior is not specific to QAOA and indeed applies to all unconstrained quantum algorithms that are not expressive enough to solve the problem exactly.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Study design and conductown dataOnly three 14-qubit and three 20-qubit XY-QAOA instances were solved on H1-1 due to high circuit depth and correspondingly high running time on trapped-ion hardware.
“All the statistics we report are computed over 10 problem instances for each number of qubits, with the exception of XY-QAOA on H1-1 where only three 14-qubit and three 20-qubit instances are solved due to the high circuit depth and correspondingly high running time on trapped-ion hardware.”
Quote in the paperNot a substantial claim
The paper relies on this without support.
The CNN/DailyMail articles used to generate the optimization instances are representative of practical extractive summarization problems.
“To generate the optimization problems to be solved, we use articles from the CNN/DailyMail dataset36.”
The paper relies on this without support.
The survey of previous quantum optimization demonstrations in Table 2 is complete enough to establish that this work is the largest demonstration to date.
“In this work, we show the largest demonstration to date of constrained optimization on a gate-based quantum computer.”
“To the authors’ knowledge, there has only be one other demonstration of QAOA with constrained mixers and Dicke-state initialization on quantum hardware.”
The paper relies on this without support.
The approximation ratio of random guess is a meaningful baseline for evaluating solution quality.
“the thin dotted line marks the approximation ratio of a random solution”
“provides results that are significantly better than random guess”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The number of two-qubit gates is ≈10^3 at N = 18, putting our experiments among the largest quantum optimization demonstrations on quantum hardware to date.
“We remark that the number of two-qubit gates is ≈103 at N = 18, putting our experiments among the largest quantum optimization demonstrations on quantum hardware to date (36–38).”
From Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem (2024) · cites this paper as [38]
The high-round and large-problem-size QAOA circuits evaluated in this paper are the largest QAOA experimental implementations yet presented with respect to gate counts and depths of the circuits that the authors are aware of.
“however the high round and large problem size QAOA circuits evaluated in this paper are the largest QAOA experimental implementations yet presented with respect to gate counts and depths of the circuits that the authors are aware of.”
From High-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices (2023) · cites this paper as [38]
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“( 34– 38) In this work we execute QAOA circuits with p = 1 using parameters β , γ optimized in noiseless simulation, followed by a projective measurement in the computational basis.”
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Alignment between initial state and mixer improves QAOA performance for constrained optimization
He, Z., Shaydulin, R., Chakrabarti, S., Herman, D., Li, C., Sun, Y., & Pistoia, M. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00787-5 · Cited by 51 · see citing works
Self-citationShort-depth QAOA circuits and quantum annealing on higher-order ising models
Pelofske, E., Bärtschi, A., & Eidenbenz, S. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00825-w · Cited by 49 · see citing works
Quantum Annealing vs. QAOA: 127 Qubit Higher-Order Ising Problems on NISQ Computers
Pelofske, E., Bärtschi, A., & Eidenbenz, S. (2023) · Lecture Notes in Computer Science · doi:10.1007/978-3-031-32041-5_13 · Cited by 47 · see citing works
Constrained optimization via quantum Zeno dynamics
Herman, D., Shaydulin, R., Sun, Y., Chakrabarti, S., Hu, S., Minssen, P., Rattew, A. G., Yalovetzky, R., & Pistoia, M. (2023) · Communications Physics · doi:10.1038/s42005-023-01331-9 · Cited by 43 · see citing works
Self-citationCherrat, E. A., Raj, S., Kerenidis, I., Shekhar, A., Wood, B., Dee, J., Chakrabarti, S., Chen, R., Herman, D., Hu, S., et al. (2023) · Quantum · doi:10.22331/q-2023-11-29-1191 · Cited by 37 · see citing works
Self-citationA practitioner’s guide to quantum algorithms for optimisation problems
Symons, B. C. B., Galvin, D., Sahin, E., Alexandrov, V., & Mensa, S. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad00f0 · Cited by 37 · see citing works
Montañez-Barrera, J. A., & Michielsen, K. (2025) · npj Quantum Information · doi:10.1038/s41534-025-01082-1 · Cited by 34 · see citing works
Maciejewski, F. B., Hadfield, S., Hall, B., Hodson, M. J., Dupont, M., Evert, B., Sud, J., Alam, M. S., Wang, Z., Jeffrey, S., et al. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.22.044074 · Cited by 22 · see citing works
Preparing valence-bond-solid states on noisy intermediate-scale quantum computers
Murta, B., Cruz, P. M. Q., & Fernández-Rossier, J. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.013190 · Cited by 21 · see citing works
Transfer learning of optimal QAOA parameters in combinatorial optimization
Montañez-Barrera, J. A., Willsch, D., & Michielsen, K. (2025) · Quantum Information Processing · doi:10.1007/s11128-025-04743-4 · Cited by 19 · see citing works
Multiangle QAOA Does Not Always Need All Its Angles
Shi, K., Herrman, R., Shaydulin, R., Chakrabarti, S., Pistoia, M., & Larson, J. M. (2022) · IEEE/ACM Symposium on Edge Computing (SEC) · doi:10.1109/sec54971.2022.00062 · Cited by 17 · see citing works
Self-citationQuantum Approximate Bayesian Optimization Algorithms With Two Mixers and Uncertainty Quantification
Kim, J. E., & Wang, Y. (2023) · IEEE Transactions on Quantum Engineering · doi:10.1109/tqe.2023.3327055 · Cited by 17 · see citing works
Montañez-Barrera, J. A., van den Heuvel, P., Willsch, D., & Michielsen, K. F. L. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00067 · Cited by 17 · see citing works
Fermionic quantum approximate optimization algorithm
Yoshioka, T., Sasada, K., Nakano, Y., & Fujii, K. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.023071 · Cited by 17 · see citing works
Shaydulin, R., & Pistoia, M. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00121 · Cited by 16 · see citing works
Self-citationHigh-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices
Pelofske, E., Bärtschi, A., Golden, J., & Eidenbenz, S. (2023) · 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00064 · Cited by 15 · see citing works
Quantum Approximate Optimization Algorithm for Test Case Optimization
Wang, X., Ali, S., Yue, T., & Arcaini, P. (2024) · IEEE Transactions on Software Engineering · doi:10.1109/tse.2024.3479421 · Cited by 15 · see citing works
Performance of quantum approximate optimization with quantum error detection
He, Z., Amaro, D., Shaydulin, R., & Pistoia, M. (2025) · Communications Physics · doi:10.1038/s42005-025-02136-8 · Cited by 15 · see citing works
Self-citationDíez-Valle, P., Luis-Hita, J., Hernández-Santana, S., Martínez-García, F., Díaz-Fernández, Á., Andrés, E., García‐Ripoll, J. J., Sánchez-Martínez, E., & Porras, D. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/ace474 · Cited by 15 · see citing works
Exploiting In-Constraint Energy in Constrained Variational Quantum Optimization
Hao, T., Shaydulin, R., Pistoia, M., & Larson, J. M. (2022) · IEEE/ACM International Workshop on Quantum Computing Software (QCS) · doi:10.1109/qcs56647.2022.00017 · Cited by 14 · see citing works
Self-citationGate-Based Variational Quantum Algorithm for Truss Structure Size Optimization Problem
Xu, Y., Wang, X., & Wang, Z. (2024) · AIAA Journal · doi:10.2514/1.j064518 · Cited by 13 · see citing works
Symmetric tensor networks for generative modeling and constrained combinatorial optimization
Lopez-Piqueres, J., Chen, J., & Perdomo‐Ortiz, A. (2023) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ace0f5 · Cited by 13 · see citing works
Perelshtein, M. R., Pakhomchik, A. I., Мельников, А. А., Podobrii, M., Termanova, A., Kreidich, I., Nuriev, B., Iudin, S., Mansell, C., & Vinokur, V. M. (2023) · Quantum · doi:10.22331/q-2023-11-21-1186 · Cited by 11 · see citing works
He, Z., Shaydulin, R., Herman, D., Li, C., Raymond, R., Sureshbabu, S. H., & Pistoia, M. (2024) · doi:10.1145/3676536.3697128 · Cited by 10 · see citing works
Self-citationPhysics-informed neural networks for an optimal counterdiabatic quantum computation
Ferrer-Sánchez, A., Flores-Garrigós, C., Hernani‐Morales, C., Orquín-Marqués, J. J., Hegade, N. N., Cadavid, A. G., Montalban, I., Solano, E., Vives‐Gilabert, Y., & Martín‐Guerrero, J. D. (2024) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ad450f · Cited by 9 · see citing works
Navigating the noise-depth tradeoff in adiabatic quantum circuits
Azses, D., Dupont, M., Evert, B., Reagor, M. J., & Torre, E. G. D. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.125127 · Cited by 8 · see citing works
Acharya, A., Yalovetzky, R., Minssen, P., Chakrabarti, S., Shaydulin, R., Raymond, R., Sun, Y., Herman, D., Andrist, R. S., Salton, G., et al. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.023142 · Cited by 9 · see citing works
Self-citationProgress and Challenges in Quantum Computing Algorithms for NP-Hard Problems
Younis, M. I., Jamil, A. S., Abdulrazzaq, A. H., Mawla, N. A., Khudhair, R. M., & Vasiliu, Y. (2024) · Conference of Open Innovations Association (FRUCT) · doi:10.23919/fruct64283.2024.10749878 · Cited by 7 · see citing works
LX-mixers for QAOA: Optimal mixers restricted to subspaces and the stabilizer formalism
Fuchs, F. G., & Bassa, R. P. (2024) · Quantum · doi:10.22331/q-2024-11-25-1535 · Cited by 5 · see citing works
Bounding entanglement entropy with Clifford double cosets
Keeler, C. A., Munizzi, W., & Pollack, J. (2025) · Physical Review A · doi:10.1103/hfhg-2z68 · Cited by 5 · see citing works
Invited: Challenges and Opportunities of Quantum Optimization in Finance
He, Z., Chakrabarti, S., Herman, D., Kumar, N., Li, C., Minssen, P., Niroula, P., Shaydulin, R., Sun, Y., Sureshbabu, S. H., et al. (2024) · ACM/IEEE Design Automation Conference (DAC) · doi:10.1145/3649329.3664193 · Cited by 4 · see citing works
Self-citationThe Lie algebra of XY-mixer topologies and warm starting QAOA for constrained optimization
Kordonowy, S., & Leipold, H. (2026) · npj Quantum Information · doi:10.1038/s41534-026-01192-4 · Cited by 3 · see citing works
Experimental Demonstration of Fermionic QAOA with One-Dimensional Cyclic Driver Hamiltonian
Yoshioka, T., Sasada, K., Nakano, Y., & Fujii, K. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00041 · Cited by 3 · see citing works
Variational Quantum Algorithm Landscape Reconstruction by Low-Rank Tensor Completion
Hao, T., He, Z., Shaydulin, R., Pistoia, M., & Tannu, S. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00139 · Cited by 2 · see citing works
Self-citationAccelerated VQE: Parameter Recycling for Similar Recurring Problem Instances
Rohe, T., Mansky, M. B., Kölle, M., Stein, J., Sünkel, L., & Linnhoff–Popien, C. (2025) · Communications in computer and information science · doi:10.1007/978-3-031-94263-1_5 · Cited by 2 · see citing works
Alonso, M., Martínez, R., Díez-Valle, P., Garbayo, A., García‐Santiago, X., & Gil, G. B. (2025) · IEEE Access · doi:10.1109/access.2025.3578780 · Cited by 2 · see citing works
Comparison of C# and Qiskit Runtimes on K-Means Clustering
Szatmáry, K. S., & Kozlovszky, P. M. (2023) · IEEE International Conference and Workshop Óbuda on Electrical and Power Engineering (CANDO-EPE) · doi:10.1109/cando-epe60507.2023.10418018 · Cited by 2 · see citing works
Multiclass portfolio optimization via variational quantum Eigensolver with Dicke state ansatz
Scursulim, J. V. S., Langeloh, G. M., Beltran, V. L., & Brito, S. (2026) · Scientific Reports · doi:10.1038/s41598-026-36333-4 · Cited by 1 · see citing works
Near-Term Application Engineering Challenges in Emerging Superconducting Qudit Processors
Venturelli, D., Gustafson, E., Kürkçüog̃lu, D. M., & Zorzetti, S. (2025) · International Conference on Dependable Systems and Networks workshops · doi:10.1109/dsn-w65791.2025.00061 · Cited by 1 · see citing works
Q-CHOP: Quantum constrained Hamiltonian optimization
Perlin, M. A., Shaydulin, R., Hall, B., Minssen, P., Li, C., Dubey, K., Rines, R., Anschuetz, E. R., Pistoia, M., & Gokhale, P. (2025) · ACM Transactions on Quantum Computing · doi:10.1145/3778864 · Cited by 1 · see citing works
Self-citationSideband cooling of a trapped ion in strong sideband coupling regime
Zhang, S., Huang, Z.-P., Tian, T.-C., Wu, Z., Zhang, J., Bao, W., & Guo, C. (2023) · Optics Express · doi:10.1364/oe.505844
What is the perception of the Hungarian quantum community regarding the future of quantum computing?
Szatmáry, K. S., & Kozlovszky, M. (2023) · IEEE International Symposium on Computational Intelligence and Informatics (CINTI) · doi:10.1109/cinti59972.2023.10382091
Quantum Algorithms: Application and Feasibility
Bui, D., Halunen, K., Nguyen, N., & Röning, J. (2024) · Lecture notes in computer science · doi:10.1007/978-3-031-78392-0_10
A method of modeling saddle point movement driven by multiple radio frequency fields
Jun, M. A. I., Wang, Z., Chang, Y. U. A. N., Jie, X. I. A. O., Ma, W., & Xu, W. A. N. G. (2025) · Acta Physica Sinica · doi:10.7498/aps.74.20241552
Yoshioka, T., Sasada, K., Nakano, Y., & Fujii, K. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00061
The Art of Quantum Computing for Finance: Brief Overview and ProspectsPreprint
Mengara, O. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5373357
The Art of Quantum Computing for Finance: Brief Overview and ProspectsPreprint
Mengara, O. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5362526
QAOA for Hard-to-solve Instances of Maximum Independent Set ProblemPreprint
Li, X., Hu, S., Liu, W., He, X., Wang, D., & Liu, Z. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6669349
Self-citationQuantum Optimization and Local Search on Conflict Graphs for Radio Resource Allocation
Gavrilovskaia, M., & Chen, K. (2026) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2026.3690424
Dmitriev, I. A., Bogdanov, Y. I., Bantysh, B. I., Koksharov, K. B., & Lukichev, V. F. (2026) · Russian Microelectronics · doi:10.1134/s1063739725600943
Tensor Network QAOA for Document Graphs: Narrative Map Extraction from News
Keith, B., & Flores-Bustos, C. (2026) · Electronics · doi:10.3390/electronics15112487
Polynomial Time Quantum Approximation Schemes for Constrained OptimizationPreprint
Onah, C., & Michielsen, K. F. L. (2026) · Research Square · doi:10.21203/rs.3.rs-11280943/v1
Min, G., Seo, Y., & Heo, J. (2026) · Scientific Reports · doi:10.1038/s41598-026-65365-z
Data-driven, multi-objective QUBO-based optimization for multi-phase alloy design
Plehn, T., Barragán-Yani, D., Breitbarth, E., Requena, G., & Melching, D. (2026) · Digital Discovery · doi:10.1039/d6dd00126b
DİRLİK, G. (2026) · Research Square · doi:10.21203/rs.3.rs-10821375/v1
Guru, R. R., Vinothini, T., Jemin, V. M., Nithin, A. A., & Kumar, B. P. (2026) · International Conference on Emerging Techniques in Computational Intelligence (ICETCI) · doi:10.1109/icetci71772.2026.11710293
- Authors
- Niroula, P., Shaydulin, R., Yalovetzky, R., Minssen, P., Herman, D., Hu, S., & Pistoia, M.
- Affiliations
- JPMorgan Chase & Co (United States) (US)
- Corresponding author
- Shaydulin, Ruslan
- ORCID
- Venue
- Scientific Reports
- Published
- 2022-10-13
- Volume
- 12
- Issue
- 1
- Pages
- 17171-17171
- ISSN
- 2045-2322 (ISSN-L)
- PMC
- PMC9563071
- OpenAlex
- W4304893331
- Semantic Scholar
- 62ead0dab2cd666d89ca5155165d9de44210e46c
- Cited by
- 59
- References
- 74
- Citations by year
- 2026: 9 · 2025: 12 · 2024: 15 · 2023: 21 · 2022: 2
- FWCI
- 4.12
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Scientific Reports (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- arXiv (Cornell University) (cc-by)
- Funders
- U.S. Department of Energy (DE-SC0020312)
- National Science Foundation
- Air Force Office of Scientific Research
- Defense Advanced Research Projects Agency
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- extractive summarization, trapped-ion quantum computer, Quantum Alternating Operator Ansatz, quantum approximate optimization algorithm, constraint encoding, quantum advantage, natural language processing
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