Open research questions in Quantum Computing Algorithms and Architecture

What the literature leaves open

• There are still various ways to further enrich our program logic, providing many promising avenues for us to explore. Inference on Quantum Channels Other than measurement, all the operations whose behavior we infer are unitary circuits. More general quantum operations are given by completely positive trace-preserving maps, i.e., quantum channels. Extending our logic to handle quantum channels could potentially allow us to perform inference on or validate quantum cryptography and communication protocols. A starting point for this would be to use additive predicates and disjunctions to characterize partial traces and post-selection. Implementing a fault-tolerant universal set Applications for error-correcting codes of gates transversally will reduce the overall cost of error correction. However, as this cannot be achieved using just one code, a common method used switches between two sets of codes, each having a different set of transversal gates [2]. Extending our logic to either infer the structure of or even validate the code-switching circuit given the predicates describing two codes would prove to be fruitful. Similarly, validating the encoding and decoding circuits for a code given its predicate could also be of value in verifying the implementation of error-correcting codes. Normalization for additive predicates Finding a canonical representation for additive predicates is imperative to effectively validate additive postconditions. A big roadblock to it is that, unlike with Pauli predicates, additive predicates (especially multi-qubit ones) could have terms that neither commute nor anticommute. This makes it hard to find a normalization procedure for them similar to that in §3. Additionally, this also limits our ability to make multi-qubit separability judgments in the additive case. Backwards reasoning In Remark 21 we noted that our logic can be used for backwards, as well as forwards, reasoning about quantum circuits. Right now, this is limited to unitary gates, since measurement isn’t reversible in the way unitary operations are. We could flesh out the logic to support backwards reasoning with measurement in the style of [37] and others. General measurement for additive predicates Although we have outlined some cases in §9 where we can infer the post-measurement states, this is limited to performing z-basis measurement on single and two-qubit systems. In order to fully exploit the power of additive predicates, it is essential that we have a full characterization for post-measurement states. An immediate consequence of this could be a deeper analysis of predicates for multi- qubit magic states and applications associated with them. Accepted in Quantum 2026-06-26, click title to verify. Published under CC-BY 4.0. 50 A logic for quantum programs with classical control A key component of quan- tum error correction and many quantum algorithms in practice (whether intermediate or large scale) is that they are interspersed with classical processing. This includes the use of classical control to decide which quantum operations to apply along with any pre- or post-processing. To account for this, we would need to formally extend our logic to ex- plicitly handle classical data types as well as other program elements such as conditional statements, loops, and recursion. This would involve extending both the language and the program logic itself, in the vein of the classical-quantum states of Feng and Ying [10] and Ying [36] and their associated logics.

  Hoare meets Heisenberg: A Lightweight Logic for Quantum Programs · 2026 · DOI

• Furthermore, while our study focuses on HEVC, similar simulated quantum‑circuit‑ based methods could be investigated for the Versatile Video Coding (VVC) standard, the successor to HEVC.

  Hybrid quantum CNN applied to quad-tree decision on HEVC · 2026 · DOI

• Although SQD is considered robust to noisy samples and imperfect classical inputs, its robustness across practical deployment choices has not been systematically analyzed.

  Hardware Robustness of Sample-Based Quantum Diagonalization · 2026

• Quantum machine learning on real noisy intermediate-scale quantum (NISQ) hardware has remained largely confined to binary or few-class tasks, limited by the cost of on-hardware training and the underuse of large devices at inference.

  Image Classification on IBM Quantum Computers · 2026

• Further research on NISQ-circuit programming could include (1) investigating whether succinctly encoding the structural information of the circuit into the program reduces the cost; (2) developing efficient programming schemes for local unitary gates subject to algebraic constraints, such as stabilizer gates [70] and locally symmetric unitaries [71].

  Resource quantification for programming low-depth quantum circuits · 2026 · DOI

• Crucially, the benefit is task-conditional : QASA excels on chaotic, noisy, and trend-dominated signals, while classical Transformers remain superior for clean periodic waveforms-providing a practical taxonomy for when quantum enhancement is warranted.

  Quantum Adaptive Self-Attention for Quantum Transformer Models · 2026 · DOI

• Abstract Integrating quantum computing into deep learning architectures is a promising but poorly understood endeavor: when does a quantum layer actually help, and how much quantum is enough? We address both questions through Quantum Adaptive Self-Attention (QASA), a hybrid Transformer that replaces the value projection in a single encoder layer with a parameterized quantum circuit (PQC), while keeping all other layers classical.

  Quantum Adaptive Self-Attention for Quantum Transformer Models · 2026 · DOI

• It remains unclear whether allowing working qubits can reduce the number of CZ operations. We hope that the combinatorial viewpoint developed in this paper will be useful for further studies on graph-state preparation, stabilizer-state transformations, and resource states for MBQC.

  Complexity of graph-state preparation by Clifford circuits · 2026 · DOI

• Both place the ML codeword at the ground state under sufficient constraint enforcement, but they have not been compared under the constraints that neuromorphic hardware imposes.

  A Comparative Analysis of Ising Formulations for Neuromorphic Maximum-Likelihood Channel Decoding · 2026

• Although current quantum annealing hardware remains insufficient for cryptographically relevant parameters, the proposed methodology offers a structured basis for studying lattice-based problems in quantum optimization settings without implying a practical threat to standardized post-quantum schemes.

  QUBO Modeling of Module Learning With Errors: Stability and Scaling in Post-Quantum Cryptography · 2026

• These results show that dissipation can enhance the learnability of open quantum dynamics, but that fidelity alone is insufficient to distinguish genuine dynamical learning from steady-state trivialization: dissipative contraction and trajectory simplification are distinct effects that peak in different regimes and should be disentangled when evaluating learned quantum-dynamical surrogates.

  When does dissipation help neural surrogates learn open quantum dynamics? · 2026

• While some academic proofs of concept have been studied, such as the "Hamming weight with a spike" (HWS) problem, the algorithmic gains of this effect remain underexplored.

  Log-concavity and tunneling: adiabatic quantum optimization for convex functions (with a spike) · 2026

• n − − 1, D, n 1, D, n and LU orbits of ((n We proved that a certain construction gives a bijection between LU orbits of normal- ized perfect tensors in (CD)⊗ 2 ))D MDS codes, extend- ing prior work of Rains, Huber, and Grassl [19, 22]. Furthermore, the local symmetries of an r-uniform state tell us about the transversal gates of its corresponding MDS code; this adds to the practical meaning of a state’s local symmetries, which is known to give information about a state’s reachability [4]. On the other hand, the transversal gates of a ((n 2 ))D code do not determine the local symmetries of its corresponding per- fect tensor unless the local symmetries are all LU operators. A possible avenue for future research is to consider more general situations where perfect tensors only have LU local symmetries. In the present work, we focus on the 4-qutrit AME state and the ((3, 3, 2))3 code. This is motivated by a connection to the graded Lie algebra e6, which allows for the application of Vinberg’s theory. As mentioned in Sect. 4.5, the state space of four qubits can also be embedded in a graded Lie algebra; the author intends to study further the consequences of this in future work.

  Transversal gates of the ((3,3,2)) qutrit code and local symmetries of the absolutely maximally entangled state of four qutrits · 2026 · DOI

• The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for demonstrating quantum advantage on near-term devices, yet the physical origins of its efficacy remain poorly understood.

  Mechanism of Efficacy in QAOA for Random k-SAT: From Adiabatic Manifold to Sublinear Parameter Optimization · 2026

• As quantum cloud services grow and hardware platforms get better, future research should focus on direct comparisons between different types of devices to confirm modeling results and finetune noise models. Das, "Quantum secure authentication and key agreement protocols for IoT-enabled applications: A comprehensive survey and open challenges," Computer Science Review, doi: vol. Diop, "IoT Security in the Quantum Era: State of the Art and Open Challenges," 2025 5th International Conference on Innovative Research in Applied Science, Engineering and Technology (IRASET), pp.

  Comparative Analysis of Quantum and Classical Computing: Performance, Error Rates, and Hybrid Architectures · 2026 · DOI

• It remains an open question as to whether these barriers can be surpassed, or can be strengthened to a complete impossibil- ity theorem for random self-reductions. There are also several open questions centered around strengthening both the positive and negative results we give about reductions among quantum decoding.

  Average-Case Complexity of Quantum Stabilizer Decoding · 2026 · DOI

• Siva Sai, Rajkumar Buyya Fellow, ACM; Fellow, IEEE 1 6 2 0 2 y a M 5 1 ] I A. s c [ 2 v 4 8 8 9 0. 1 1 5 2: v i X r a the stringent robustness, constraints of the fusion of artificial Abstract—Mission critical (MC) applications such as defense operations, energy management, cybersecurity, and aerospace control require reliable, deterministic, and low-latency decision making under uncertainty. Although the classical Artificial Intelligence (AI) approaches are effective, they often struggle to meet timing, explainability, and safety in the MC domains. Quantum Artificial Intelligence (QAI), intelligence and quantum computing (QC), can potentially provide transformative solutions to the challenges faced by classical ML models. QAI is a broader umbrella than Quantum Machine Learning (QML) and additionally includes quantum optimization, search, and reasoning; we use QAI throughout the paper for the field at large, and QML only for learning-specific subroutines. The principal contributions of this work are: (i) a systematic survey of QAI methods analyzed through the lens of MC requirements like certification, robustness, and timing; (ii) a conceptual quantum cloud resource management and scheduling framework with deployment assumptions, complexity analysis, and failure-mode discussion; and (iii) an identification of the gaps between current QAI capabilities and MC systems requirements. We also propose a conceptual model for management of quantum resources and scheduling of applications driven by timeliness constraints. including trainability limits, We discuss multiple challenges, data access, and loading bottlenecks, verification of quantum components, and adversarial QAI. Finally, we outline future research directions toward achieving interpretable, scalable, and hardware-feasible QAI models for MC application deployment. Index Terms—Quantum computing, Quantum artificial systems, Aerospace, Defense, grid intelligence, Mission critical Disaster management, Cybersecurity, Energy management, Technical foundations and I. INTRODUCTION Mission critical (MC) applications are those that must not fail because failure can lead to severe harm, injury, loss of life, large economic damage, or major outages. An MC system aim to build a structured safety case that traces hazards, requirements, designs, and tests, so that acceptable risk is argued with evidence rather than based on assumption. An air traffic control system, where even a slight malfunction can endanger hundreds of lives is an example of an MC application. The industrial control systems in nuclear plants and power grids are also mission critical applications, since their failure could cause catastrophic accidents or large-scale blackouts.

  Quantum Artificial Intelligence for mission-critical systems: Foundations, architectural elements, and future directions · 2026 · DOI

• Developing such a model remains an open problem. Whether this perspective can be developed into a more complete theoretical framework remains an open question, but the results presented here indicate that it is a direction worthy of further investigation. Additional datasets—particularly those with different geometries, measurement protocols, or system sizes—should be examined to determine the generality of the observed behavior.

  Paper 39 The Schrödinger Equation as Expansion-Dominated Relational Evolution · 2026 · DOI

• Fortunately, for the specific example of four parity check rounds, even with currently achievable readout fidelities73, the increase in the cost SNT is limited by a factor of ≲7, which could be further reduced to ≲1. 1 where the reach is limited by the bias of the QEM.

  Near-term fermionic simulation with subspace noise tailored quantum error mitigation · 2026 · DOI

• Training is conducted with a single optimizer (Adam) and fixed hyperparameter ranges (learning_rate=0.01, weight_decay=0.0); the effect of different optimization algorithms and regularization intensities on quantum information metrics and their correlation with generalization remains untested.

  Quantum Information Framework for Neural Network Generalization: A Comprehensive Experimental Analysis · 2026 · DOI

• Weight entropy is computed using histogram binning with a fixed bin count of 50; the sensitivity of classical weight entropy calculations to bin selection and alternative entropy estimators (e.g., kernel density estimation) in the context of quantum information framework validation has not been addressed.

  Quantum Information Framework for Neural Network Generalization: A Comprehensive Experimental Analysis · 2026 · DOI

• The training analysis collects quantum information metrics only from the last hidden layer when layer_key is None; the paper does not investigate how von Neumann entropy, purity, and effective rank evolve across different layers during training or how these metrics differ between shallow versus deep architectures.

  Quantum Information Framework for Neural Network Generalization: A Comprehensive Experimental Analysis · 2026 · DOI

• The modular arithmetic dataset generation supports only three operations (x+y, x²+y, x³+xy) with a fixed modulus of 97; systematic investigation of how operation complexity, modulus size, and arithmetic structure affect quantum information metrics during neural network training is absent.

  Quantum Information Framework for Neural Network Generalization: A Comprehensive Experimental Analysis · 2026 · DOI

• The quantum analyzer computes density matrices from activation patterns using a single method (likely outer product construction); alternative density matrix formulations and their impact on von Neumann entropy and purity measurements for neural network activations remain unexplored, creating ambiguity about metric robustness.

  Quantum Information Framework for Neural Network Generalization: A Comprehensive Experimental Analysis · 2026 · DOI

• The quantum information framework is evaluated exclusively on synthetic datasets (spiral data and modular arithmetic operations); the generalization behavior of von Neumann entropy, purity, and effective rank metrics has not been validated on real-world datasets with natural data distributions, limiting claims about the framework's applicability to practical neural network training scenarios.

  Quantum Information Framework for Neural Network Generalization: A Comprehensive Experimental Analysis · 2026 · DOI

Most-cited papers in Quantum Computing Algorithms and Architecture

• Quantum error correction below the surface code threshold · Nature · 2024 · 616 citations
• High-threshold and low-overhead fault-tolerant quantum memory · Nature · 2024 · 405 citations
• Systematic literature review: Quantum machine learning and its applications · Computer Science Review · 2024 · 207 citations
• Distributed quantum computing: A survey · Computer Networks · 2024 · 207 citations
• Quantum Computing for High-Energy Physics: State of the Art and Challenges · PRX Quantum · 2024 · 184 citations
• A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits · Nature Communications · 2024 · 148 citations
• Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays · Nature Physics · 2024 · 146 citations
• Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges · Nature Communications · 2024 · 145 citations
• Quantum machine learning for image classification · Machine Learning Science and Technology · 2024 · 136 citations
• Verification of Quantum Computation: An Overview of Existing Approaches · Theory of Computing Systems · 2018 · 134 citations

Most recent work

• Noise-induced shallow circuits and the absence of barren plateaus · Nature Physics · 2026
• Compressed representation of quantum states via orthogonal polynomials for flow field analysis · Acta Mechanica Sinica · 2026
• Quantum Amplitude Estimation for Wright-Fisher Parameter Inference: Theoretical Query Complexity Advantages Conditional on Efficient Oracle Construction · International Journal of Modern Physics C · 2026
• Fully convolutional 3D neural network decoders for surface codes with syndrome circuit noise · Quantum Science and Technology · 2026
• Estimating quantum relative entropies on quantum computers · Communications Physics · 2026
• Readout of a solid state spin ensemble at the projection noise limit · Nature Communications · 2026
• QuCheck: A Property-based Testing Framework for Quantum Programs in Qiskit · ACM Transactions on Quantum Computing · 2026
• Quantum Doeblin Coefficients: Interpretations and Applications · Quantum · 2026
• A quantum state transfer protocol with Ising Hamiltonians · Quantum Science and Technology · 2026
• Quantum logic operations and algorithms in a single 25-level atomic qudit · Nature Communications · 2026

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