Quantum algorithms for electronic-structure simulations are actively being developed, yet many hybrid quantum-classical approaches are bottlenecked by the measurement overhead associated with large molecular Hamiltonians. Here we introduce a diagonalization-driven framework that progressively drives the electronic Hamiltonian toward a (block-)diagonal form in the Slater-determinant basis using sequential Givens rotations. In contrast to Schrödinger-picture methods that variationally optimize a wave function, our approach adopts a Heisenberg-picture viewpoint: the Hamiltonian is iteratively transformed, and rotation angles are determined classically from low-dimensional effective blocks, reducing the quantum workload to a small, fixed set of matrix-element measurements per iteration. Candidate generators are estimated via approximate Baker-Campbell-Hausdorff updates with truncation and cumulant-based approximations that control Hamiltonian growth, complemented by stochastic selection to avoid stagnation. We further introduce an angle-merging procedure that reduces circuit depth by consolidating repeated small-angle rotations. We benchmark the framework on N$_2$ and strongly correlated hydrogen systems, assessing convergence behavior, residual-structure diagnostics, measurement-accuracy trade-offs, circuit costs, and robustness under finite sampling.
The dynamics of non-polar diatomic molecules interacting with a far-detuned narrow-band laser field, that only may drive rotational transitions, is studied. The rotation of the molecule is considered both classically and quantum mechanically, providing links to features known from the heavy symmetric top. In particular, quantum decoherence in the molecular rotation, being induced by spontaneous Raman processes, is addressed. It is shown how this decoherence modifies the rotational dynamics in phase space.
Recent works have demonstrated that large quantum circuits can be cut and decomposed into smaller clusters of quantum circuits with fewer qubits that can be executed independently on a small quantum computer. Classical post-processing then combines the results from each cluster to reconstruct the output of the original quantum circuit. However, the runtime for such hybrid quantum-classical algorithms is exponential in the number of cuts on a circuit. We propose Rotation-Inspired Circuit Cut Optimization (RICCO), an alternative method which reduces the post-processing overhead of circuit cuttin…
It is well known that a quantum correlated probe can yield better precision in estimating an unknown parameter than classically possible. However, how such a quantum probe should be measured remains somewhat elusive. We examine the role of measurements in quantum metrology by considering two types of readout strategies: coherent, where all probes are measured simultaneously in an entangled basis; and adaptive, where probes are measured sequentially, with each measurement one way conditioned on the prior outcomes. Here we firstly show that for classically correlated probes the two readout strat…
Classical rotations of asymmetric rigid bodies are unstable around the axis of intermediate momentof inertia, causing a flipping of rotor orientation. This effect, known as the tennis racket effect,quickly averages to zero in classical ensembles since the flipping period varies significantly uponapproaching the separatrix. Here, we explore the quantum rotations of rapidly spinning thermalasymmetric nanorotors and show that classically forbidden tunnelling gives rise to persistent tennisracket dynamics, in stark contrast to the classical expectation. We characterise this effect, demon-strating …
Optimal rotation control for a qubit subject to continuous measurement
Australian National University（澳大利亚国立大学）；University of California San Diego（加州大学圣地亚哥分校）；Center for Quantum Information and Control University of New Mexico（新墨西哥大学量子信息与控制中心）
Hypergraph states are generalizations of graph states where controlled-$Z$ gates on edges are replaced with generalized controlled-$Z$ gates on hyperedges. Hypergraph states have several advantages over graph states. For example, certain hypergraph states, such as the Union Jack states, are universal resource states for measurement-based quantum computing with only Pauli measurements, while graph state measurement-based quantum computing needs non-Clifford basis measurements. Furthermore, it is impossible to classically efficiently sample measurement results on hypergraph states with a constan…
We describe two procedures which, given access to one copy of a quantum state and a sequence of two-outcome measurements, can distinguish between the case that at least one of the measurements accepts the state with high probability, and the case that all of the measurements have low probability of acceptance. The measurements cannot simply be tried in sequence, because early measurements may disturb the state being tested. One procedure is based on a variant of Marriott-Watrous amplification. The other procedure is based on the use of a test for this disturbance, which is applied with low pro…
We study the estimation of an infinitesimal rotation of a spin-j system, characterized by two unknown phases, and compare the estimation precision achievable with two different strategies. The first is a standard `joint estimation' strategy, in which a single probe state is used to estimate both parameters, while the second is a `sequential' strategy in which the two phases are estimated separately, each on half of the total number of system copies. In the limit of small angles we show that, although the joint estimation approach yields in general a better performance, the two strategies posse…
The quantum fidelity was introduced by Peres to study some fingerprints of classically chaotic behavior in the quantum dynamics of the corresponding systems. In the present paper the signatures of classical dynamics near elliptic points and of interactions between particles are characterized for kicked systems. In particular, the period of the fidelity resulting of the interactions is found using analytical and numerical calculations. A mechanism leading to the oscillations with the intermediate period is proposed. It is of a semiclassical origin and results of the interplay between the oscill…
An accurate description of electron transport at a molecular level requires a precise treatment of quantum effects. These effects play a crucial role in determining the electron transport properties of single molecules, such as current-voltage curves, which can be challenging to simulate classically. Here we introduce a quantum algorithm to efficiently calculate the electronic current through single-molecule junctions in the weak-coupling regime. We show that a quantum computer programmed to simulate vibronic transitions between different charge states of a molecule can be used to compute sequ…
We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant factor in time complexity, this is wrong in a space bounded setting. We observe that for all storage bounds n/\log n\ge S\ge \log^3 n, one can devise a quantum algorithm that sorts n numbers (using comparisons only) in time T=O(n^{3/2}\log^{3/2} n/\sqrt S). We then show the following lower bound on the time-space tradeoff for sorting $n$ numbers from a polynom…
Quantum--classical break-even in electronic dynamics of macrocyclic molecules
Mitsubishi Chemical Corporation（三菱化学株式会社）；Keio University（庆应义塾大学）；Deloitte Tohmatsu LLC（德勤松永有限责任公司）；TCG Centres for Research and Education in Science and Technology（科学与技术研究教育TCG中心）；IBM Research（IBM研究院）；JSR Corporation（JSR株式会社）
PARITY is the problem of determining the parity of a string $f$ of $n$ bits given access to an oracle that responds to a query $x\in\{0,1,...,n-1\}$ with the $x^{\rm th}$ bit of the string, $f(x)$. Classically, $n$ queries are required to succeed with probability greater than 1/2 (assuming equal prior probabilities for all length $n$ bitstrings), but only $\lceil n/2\rceil$ quantum queries suffice to determine the parity with probability 1. We consider a generalization to strings $f$ of $n$ elements of $\Z_k$ and the problem of determining $\sum f(x)$. By constructing an explicit algorithm, we…
Quantum resources, such as entanglement, can decrease the uncertainty of a parameter-estimation procedure beyond what is classically possible. This phenomenon is well described for noiseless systems with asymptotically many measurement resources by the Quantum Cramer-Rao Bound, but no general description exists for the regime of limited measurement resources. We address this problem by defining a Bayesian quantifier for uncertainty suitable for the regime of limited resources, and by developing a mathematical description for a parameter-estimation procedure which uses qubit probes to estimate …
Rotation Collision based Quantum Lattice Boltzmann Methods
School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）；College of Engineering, Shantou University（汕头大学工学院）；Institute of Interdisciplinary Research for Mathematics and Applied Science, Huazhong University of Science and Technology（华中科技大学数学与应用科学交叉研究院）；Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology（华中科技大学工程建模与科学计算湖北省重点实验室）；The State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology（华中科技大学智能装备制造与技术国家重点实验室）
