Molecular Excited States using Quantum Subspace Methods: Accuracy, Resource Reduction, and Error-Mitigated Hardware Implementation of q-sc-EOM
Srivathsan Poyyapakkam Sundar, Prince Frederick Kwao, Alexey Galda, Ayush Asthana
Abstract
Problems in quantum chemical simulations, especially achieving accurate excited-state potential energy surfaces, are among the primary applications to achieve quantum utility. On near-term quantum hardware, variants of the variational quantum eigensolver (VQE) algorithms are the primary choice for chemistry simulation. In this study, a combination of leading ground and excited state quantum algorithms for general excited states, namely, ADAPT-VQE/LUCJ and q-sc-EOM, are utilized to calculate accurate excited state potential energy surfaces in challenging bond-breaking scenarios and compared with the classical scalable EOM-CCSD method. This work investigates avenues toward quantum utility in excited-state quantum chemistry using the q-sc-EOM approach. We assess its accuracy while mitigating major scaling bottlenecks through the Davidson algorithm and basis rotation grouping, reducing the measurement scaling from O(N) to O(N), and implementing the method on quantum hardware with various error mitigation strategies to reduce gate and measurement errors in excited states. The hardware implementation of the q-sc-EOM algorithm, augmented by mitigation of M3 readout error and symmetry projection, produces reasonably accurate excited-state energies with gate noise identified as the predominant source of error. This paves the way for accurate and scalable, generally applicable quantum excited-state methods with potential for quantum utility while identifying critical problems that require advancements.
AI Impact Assessments
(3 models)Scientific Impact Assessment
Core Contribution
This paper investigates the q-sc-EOM (quantum self-consistent equation of motion) method for computing molecular excited states on quantum hardware, combining it with ADAPT-VQE and LUCJ ansätze for ground-state preparation. The work has three main thrusts: (1) accuracy benchmarking of ADAPT-VQE + q-sc-EOM against FCI and classical EOM-CCSD for bond-breaking scenarios (NH₃, H₂O); (2) resource reduction strategies combining the Davidson algorithm and basis rotation grouping (BRG) to reduce measurement scaling from O(N¹²) to O(N⁵); and (3) hardware implementation on IBM quantum processors with various error mitigation strategies. The central claim is that this combination constitutes a path toward quantum utility for excited-state chemistry.
Methodological Rigor
Strengths in simulation benchmarks: The comparison of ADAPT-VQE + q-sc-EOM against EOM-CCSD for two-bond-breaking in NH₃ and H₂O is well-motivated, as these represent genuinely challenging multi-reference scenarios where classical single-reference methods fail. The observation that the quantum method maintains accuracy in strongly correlated regimes where EOM-CCSD deteriorates is meaningful, though not unexpected given that ADAPT-VQE can capture multi-reference character by construction within the active space.
Scaling analysis concerns: The scaling reduction from O(N¹²) to O(N⁵) is claimed by combining two previously known techniques—the Davidson algorithm (Kim et al.) and BRG (Huggins et al.)—rather than developing new methodology. The paper correctly attributes these techniques but the contribution here is assembling them within the q-sc-EOM framework rather than fundamental innovation. The BRG accuracy analysis (Figure 5) showing errors below 10⁻⁶ Ha is reassuring but only tested on small hydrogen chains (H₂–H₁₀) in minimal basis.
Hardware experiments: The hardware results are the weakest aspect methodologically. The systems tested are extremely small—H₂ in minimal basis (4 qubits) and H₂O in a (2e,2o) active space (4 qubits). At these scales, classical methods trivially solve the problem exactly, making the quantum utility argument premature. The reported hardware errors of ~50 mHa for excited states are far from chemical accuracy (1.6 mHa), and the paper honestly acknowledges this. However, the error mitigation strategy exploration is somewhat incomplete: twirling and dynamic decoupling showed no benefit, ZNE was mentioned as tried but not shown, and only M3 readout mitigation plus symmetry postselection provided improvement. The statistical analysis (5 runs per configuration) is adequate but minimal.
Potential Impact
The paper addresses a genuine need—excited-state quantum chemistry is arguably a more promising application domain for quantum advantage than ground states, given the well-known classical challenges with multi-reference excited states. The resource reduction analysis is practically important: O(N¹²) is clearly intractable, and demonstrating a path to O(N⁵) makes the method more credible for future scaling.
However, several factors limit the impact:
1. Active space limitation: All calculations use small active spaces. The quantum advantage argument implicitly relies on the assumption that larger active spaces will become accessible on future hardware, but the paper provides no evidence that the method can handle the transition to utility-scale problems.
2. Comparison fairness: Comparing ADAPT-VQE (which can capture multi-reference character) against single-reference EOM-CCSD is somewhat asymmetric. A fairer comparison would include multi-reference classical methods like CASPT2 or MRCI, which also handle bond-breaking scenarios and are the actual competitors for these problem types.
3. Hardware gap: The 50 mHa errors are roughly 30× chemical accuracy. The paper correctly identifies gate noise as the primary bottleneck but offers no concrete path to closing this gap beyond hoping for better hardware and error mitigation.
Timeliness & Relevance
The paper addresses a timely topic—the search for quantum utility in chemistry. Excited states are increasingly recognized as a more promising target than ground states for near-term quantum advantage. The integration of multiple algorithmic improvements (Davidson + BRG) with hardware testing is a relevant systems-level approach. However, similar studies combining VQE-based ground states with subspace expansion methods have appeared from multiple groups, reducing the novelty somewhat.
Strengths
Limitations
Overall Assessment
This is a competent integration study that assembles known quantum algorithms for ground and excited states, applies known resource reduction techniques, and tests on real hardware. It provides useful practical insights about the current limitations of excited-state quantum chemistry on NISQ devices. However, the novelty is incremental—primarily in the assembly rather than in the components—and the scale of the calculations is far from demonstrating anything approaching quantum utility. The honest identification of gate noise as the primary barrier is perhaps the most valuable contribution for the community.
Generated Apr 8, 2026
Comparison History (40)
Paper 1 likely has higher scientific impact: it advances a broadly applicable, chemistry-relevant excited-state workflow (q-sc-EOM with ADAPT-VQE/LUCJ) and tackles key scalability barriers by reducing measurement scaling from O(N^12) to O(N^5), plus provides error-mitigated hardware demonstrations and clear identification of dominant noise sources. Excited-state potential energy surfaces are a central, timely target for quantum utility with strong real-world relevance. Paper 2 is promising but narrower (VITE ansatz discovery via DDQN) and may be more sensitive to problem-dependent RL generalization and benchmarking scope.
Paper 1 addresses a fundamental question about complexity phase transitions in continuous-variable quantum computing, establishing rigorous squeezing-level thresholds that delineate classical simulability boundaries. This provides deep theoretical insight with broad implications for the entire CV quantum computing field. Paper 2, while practically valuable, represents more incremental progress combining existing quantum algorithms (ADAPT-VQE, q-sc-EOM) with known error mitigation techniques for quantum chemistry. Paper 1's identification of a complexity phase transition is more novel and has broader theoretical impact across quantum information science.
Paper 2 addresses a critical bottleneck in quantum computing for chemistry—accurate excited-state calculations—by combining multiple algorithmic innovations (ADAPT-VQE/LUCJ with q-sc-EOM), dramatically reducing measurement scaling from O(N^12) to O(N^5), and demonstrating hardware implementation with error mitigation. This has broader impact across quantum computing and computational chemistry communities. Paper 1, while representing solid engineering progress in diamond photonics integration, is more incremental—demonstrating ensemble NV-center Purcell enhancement in a cryogenic chip package—rather than introducing fundamentally new capabilities for quantum communication.
Paper 1 presents a highly practical advancement in quantum chemistry by reducing the measurement scaling of the q-sc-EOM approach from O(N^12) to O(N^5) and demonstrating its implementation on actual quantum hardware with error mitigation. This massive resource reduction addresses critical bottlenecks in near-term quantum computing, offering immediate relevance and strong potential for real-world applications. While Paper 2 offers elegant theoretical insights bridging quantum error correction and lattice gauge theories, Paper 1's timely contributions toward 'quantum utility' in chemistry are likely to yield a broader and more immediate scientific impact.
Paper 1 tackles a critical bottleneck in quantum chemistry and demonstrates a massive theoretical reduction in measurement scaling (from O(N^12) to O(N^5)) alongside real quantum hardware implementations. Its practical steps toward 'quantum utility' in chemical applications give it a higher potential for immediate and broad scientific impact compared to Paper 2, which primarily focuses on theoretical QML frameworks for classical data estimation and relies entirely on numerical simulations.
Paper 2 addresses a critical bottleneck in near-term quantum computing by significantly reducing measurement scaling (from O(N^12) to O(N^5)) for simulating molecular excited states. Its focus on practical hardware implementation, error mitigation, and quantum chemistry applications offers much broader real-world impact and timeliness than the highly theoretical quantum information results presented in Paper 1.
Paper 1 addresses a fundamental theoretical problem in quantum information—unique determinability of quantum states from local marginals—with a universally applicable result (robustness under imperfections). It establishes a new classification framework with power-law exponents, provides rigorous mathematical proofs, and demonstrates practical applications (entanglement witnesses). Its breadth of impact spans quantum foundations, tomography, and entanglement theory. Paper 2, while practically relevant for near-term quantum computing, is more incremental—combining existing algorithms (ADAPT-VQE, q-sc-EOM) with known error mitigation techniques—and addresses a narrower domain with results limited by current hardware noise.
Paper 2 addresses a critical practical challenge in quantum computing—accurate excited-state chemistry on near-term hardware—combining algorithmic innovation (measurement scaling reduction from O(N^12) to O(N^5)), hardware implementation with error mitigation, and direct comparison with classical methods. It has broader immediate impact across quantum computing, quantum chemistry, and materials science communities. Paper 1, while theoretically elegant in proving quantum advantage for state transfer, addresses a more niche problem with less immediate practical applicability and narrower audience impact.
Paper 1 presents practical advancements in quantum chemistry algorithms for near-term quantum computers, addressing critical scaling bottlenecks and demonstrating real hardware implementation. Its focus on solving complex molecular excited states has immediate and high-value applications in chemistry and material science. In contrast, Paper 2 explores a highly theoretical and niche concept (quantum batteries near black holes) which, while novel, lacks near-term real-world applicability and empirical testability, limiting its broader scientific impact.
Paper 2 proposes improvements to Quantum Phase Estimation (QPE), a fundamental primitive underlying numerous quantum algorithms. By enhancing sensitivity efficiency and resource prefactors, its programmable framework has broad applicability across quantum computing, including sensing and Hamiltonian simulation. While Paper 1 offers significant practical advancements for near-term quantum chemistry, Paper 2's foundational improvements to a core algorithmic building block provide a broader potential theoretical and practical impact across multiple domains.