Papers

Identifying the state of a quantum bit (qubit), known as quantum state discrimination, is a crucial operation in quantum computing. However, it has been the most error-prone and time-consuming operation on superconducting quantum processors. Due to stringent timing constraints and algorithmic complexity, most qubit state discrimination methods are executed offline. In this work, we present an enhanced real-time quantum state discrimination system leveraging FPGA-based AI Engine technology. A multi-layer neural network has been developed and implemented on the AMD Xilinx VCK190 FPGA platform, enabling accurate in-situ state discrimination and supporting mid-circuit measurement experiments for multiple qubits. Our approach leverages recent advancements in architecture research and design, utilizing specialized AI/ML accelerators to optimize quantum experiments and reduce the use of FPGA resources.

Emerging theoretical frameworks suggest that physical properties of matter can be altered within an optical cavity by harnessing quantum vacuum electromagnetic fluctuations, even in the total absence of external driving fields. Among the most intriguing predictions is the potential to noninvasively manipulate superconductivity. Here, we experimentally observe modified superconductivity in niobium nitride (NbN) thin films within high-quality-factor ($Q$) terahertz cavities. Using terahertz time-domain spectroscopy, we characterize the NbN response both in free space and within a high-$Q$ photonic-crystal cavity. Our analysis reveals significant cavity-induced modifications to the optical conductivity. A theoretical model indicates that these changes originate from a substantial ($\sim13\,\%$) reduction in the superfluid density and a minor ($\sim2\,\%$) reduction in the superconducting gap, driven by cavity vacuum fluctuations. These results demonstrate a platform for engineering ground states via vacuum–matter coupling, opening frontiers in cavity materials science.

We demonstrate a dissipative protocol for ground-state preparation of a quantum spin chain on a trapped-ion quantum computer. As a first step, we derive a Kraus representation of a dissipation channel for the protocol recently proposed by Ding et al. [Phys. Rev. Res. 6, 033147 (2024)] that still holds for arbitrary temporal discretization steps, extending the analysis beyond the Lindblad dynamics regime. The protocol guarantees that the fidelity with the ground state monotonically increases (or remains unchanged) under repeated applications of the channel to an arbitrary initial state, provided that the ground state is the unique steady state of the dissipation channel. Using this framework, we implement dissipative ground-state preparation of a transverse-field Ising chain for up to 19 spins on the trapped-ion quantum computer Reimei provided by Quantinuum. Despite the presence of hardware noise, the dynamics consistently converges to a low-energy state far away from the maximally mixed state even when the corresponding quantum circuits contain as many as 4110 entangling gates, demonstrating the intrinsic robustness of the protocol. By applying zero-noise extrapolation, the resulting energy expectation values are systematically improved to agree with noiseless simulations within statistical uncertainties.

Tensor network states are an indispensable tool for the simulation of strongly correlated quantum many-body systems. In recent years, tree tensor network states (TTNS) have been successfully used for two-dimensional systems and to benchmark quantum simulation approaches for condensed matter, nuclear, and particle physics. In comparison to the more traditional approach based on matrix product states (MPS), the graph distance of physical degrees of freedom can be drastically reduced in TTNS. Surprisingly, it turns out that, for large systems in $D>1$ spatial dimensions, MPS simulations of low-energy states are nevertheless more efficient than TTNS simulations. With a focus on $D=2$ and 3, the scaling of computational costs for different boundary conditions is determined under the assumption that the system obeys an entanglement (log-)area law, implying that bond dimensions scale exponentially in the interface area of the associated subsystems.

It is commonly thought that observers in distinct branches of an Everettian multiverse cannot communicate without violating the linearity of quantum theory. Here we show a counterexample, demonstrating that inter-branch communication is in fact possible, entirely within standard quantum theory. We do this by considering a Wigner's-friend scenario, where an observer (Wigner) can have quantum control over another observer (the friend). We present a thought experiment where the friend in superposition can receive a message written by a distinct copy of themselves in the multiverse, with the aid of Wigner. The protocol involves writing the message within a branch, then Wigner running an uncomputation, branch-swap operation, and recomputation of the friend. Our thought experiment challenges conventional wisdom regarding the ultimate limits of what is possible in an Everettian multiverse. It has a surprising potential application which involves using knowledge-creation paradoxes for testing Everettian quantum theory against single-world theories.

Discrete charge fluctuations, routinely observed in semiconductor quantum dot devices, may contribute significantly to device drift and errors resulting from qubit miscalibration. Understanding the nature and origins of these discrete charge fluctuations may provide insights into material improvements or means of mitigating charge noise in semiconductor quantum dot devices. In this work, we measure multi-level charge fluctuations present in a Si/SiGe double quantum dot device over a range of device operating voltages and temperatures. To characterize the parameter-dependent dynamics of the underlying fluctuating degrees of freedom, we perform a detailed analysis of the measured noise timeseries. We perform algorithmically assisted drift detection and change point detection to detrend the data and remove a slow fluctuator component, as a preprocessing step. We perform model comparison on the post-processed time series between different $n$-level fluctuator ($n$LF) factorial hidden Markov models (FHMMs), finding that although at most sweep values the independent pair of 2LFs model would be preferred, in a particular region of voltage space the 4LF model outperforms the other models, indicating a conditional rate dependence between the two fluctuators. By tracking fluctuator transition rates, biases, and weights over a range of different device configurations, we estimate gate voltage and conductivity sensitivity. In particular, we fit a phenomenological, detailed balance model to the extracted independent 2LFs rate data, yielding lever arm estimates in the range of $-2 \mu$eV/mV up to $4 \mu$eV/mV between the two 2LFs and nearby gate electrodes. We expect that these characterization results may aid in subsequent spatial triangulation of the charge fluctuators.

Feedback-based quantum algorithms (FQAs) operate by iteratively growing a quantum circuit to optimize a given task. At each step, feedback from qubit measurements is used to inform the next quantum circuit update. In practice, the sampling cost associated with these measurements can be significant. Here, we ask whether FQA parameter sequences can be predicted using classical machine learning, obviating the need for qubit measurements altogether. To this end, we train a teacher-student model to map problem instances to associated FQA parameter curves in a single classical inference step. We first study weighted MaxCut problem instances, where numerical experiments show that this machine learning model can accurately predict FQA parameter curves across a range of problem sizes, including sizes not seen during model training. We then extend the analysis to transverse-field Ising models on graphs, and analyze how this learning strategy performs and generalizes beyond the original MaxCut setting. To evaluate performance, we compare the predicted parameter curves in simulation against FQA reference curves and linear quantum annealing schedules. We observe similar results to the former and performance improvements over the latter. These results suggest that machine learning can offer a heuristic, practical path to reducing sampling costs and resource overheads in quantum algorithms.

For a (possibly partial) Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ as well as a query complexity measure $M$ which maps Boolean functions to real numbers, define the composition limit of $M$ on $f$ by $M^*(f)=\lim_{k\to\infty} M(f^k)^{1/k}$. We study the composition limits of general measures in query complexity. We show this limit converges under reasonable assumptions about the measure. We then give a surprising result regarding the composition limit of randomized query complexity: we show $R_0^*(f)=\max\{R^*(f),C^*(f)\}$. Among other things, this implies that any bounded-error randomized algorithm for recursive 3-majority can be turned into a zero-error randomized algorithm for the same task. Our result extends also to quantum algorithms: on recursively composed functions, a bounded-error quantum algorithm can be converted into a quantum algorithm that finds a certificate with high probability. Along the way, we prove various combinatorial properties of measures and composition limits.

Understanding the energetic efficiency of quantum computers is essential for assessing their scalability and for determining whether quantum technologies can outperform classical computation beyond runtime alone. In this work, we analyze the energy required to solve the Boson Sampling problem, a paradigmatic task for quantum advantage, using a realistic photonic quantum computing architecture. Using the Metric-Noise-Resource methodology, we establish a quantitative connection between experimental control parameters, dominant noise processes, and energetic resources through a performance metric tailored to Boson Sampling. We estimate the energy cost per sample and identify operating regimes that optimize energetic efficiency. By comparing the energy consumption of quantum and state-of-the-art classical implementations, we demonstrate the existence of a quantum energetic advantage – defined as a lower energy cost per sample compared to the best-known classical implementation – that emerges before the onset of computational advantage, even in regimes where classical algorithms remain faster. Finally, we propose an experimentally feasible Boson Sampling architecture, including a complete noise and loss budget, that enables a near-term observation of quantum energetic advantage.

Variational quantum circuits have become a widely used tool for performing quantum machine learning (QML) tasks on labeled quantum states. In some specific tasks or for specific variational ansätze, one may perform measurements on a restricted part of the overall input state. This is the case for, e.g., quantum convolutional neural networks (QCNNs), where after each layer of the circuit a subset of qubits of the processed state is measured or traced out, and at the end of the network one typically measures a local observable. In this work, we demonstrate that measuring observables with restricted support results in larger label prediction variance in regression QML tasks. We show that the reason for this is, essentially, the number of distinct eigenvalues of the observable one measures after the application of a variational circuit.

Quantum error correction is one of the fundamental building blocks of digital quantum computation. The Quantum Lego formalism has introduced a systematic way of constructing new stabilizer codes out of basic lego-like building blocks, which in previous work we have used to generate improved error correcting codes via an automated reinforcement learning process. Here, we take this a step further and show the use of a hybrid classical-quantum algorithm. We combine classical reinforcement learning with calls to two commercial quantum devices to search for a stabilizer code to correct errors specific to the device, as well as an induced photon loss error.

Adding a constant energy offset leaves classical dynamics unchanged. In quantum mechanics it changes the phase velocity of the wavefunction. The inclusion of the constant rest energy in the Klein-Gordon formulation leads to significantly higher phase velocities compared with the Schrödinger equation. The Schrödinger equation predicts an attenuation of the wavefunction along one of the paths in a Sagnac interferometer when a beamsplitter's trajectory along that path includes a segment where its speed exceeds the phase velocity of a free particle. Such an attenuation does not occur for electromagnetic waves nor for eigenstates of momentum in the Klein-Gordon equation since the speed of the beamsplitter cannot then exceed the phase velocity of the wave. This attenuation reduces the amplitude without introducing a phase shift, preserving the overall structure of the transmitted wave group. While a Klein-Gordon wave group undergoes three traversals of the beamsplitter that moved, it experiences attenuation equivalent to only a single pass, whereas the Schrödinger equation predicts the expected attenuation for three passes. This discrepancy highlights a fundamental incompatibility between the Klein-Gordon equation and the Schrödinger equation in a regime where their predictions should converge.

Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of applications and the quest for enhanced theorem-proving capabilities remains a prominent pursuit in artificial intelligence. Here, we propose a generic framework for quantum automated theorem proving, where the intrinsic quantum superposition and entanglement features would lead to potential advantages. In particular, we introduce quantum representations of knowledge bases and propose corresponding reasoning algorithms for a variety of tasks. We show how automated reasoning can be achieved with quantum resolution in both propositional and first-order logic with quadratically reduced query complexity. In addition, we propose the quantum algebraic proving method for geometric theorems, extending Wu's algebraic approach beyond the classical setting. Through concrete examples, including geometry problems from the International Mathematical Olympiad, we demonstrate how a quantum computer may prove geometric theorems with quadratic better query complexity. Our results establish a primary approach towards building quantum automatic theorem provers, which would be crucial for practical applications of both near-term and future quantum technologies.

The Universal Operator Growth Hypothesis formulates time evolution of operators through Lanczos coefficients. In practice, however, numerical instability and memory cost limit the number of coefficients that can be exactly computed. In response to these challenges, the standard approach relies on fitting early coefficients to asymptotic forms, but such procedures can miss subleading, history-dependent structures in the coefficients that subsequently affect reconstructed observables. In this work, we treat the Lanczos coefficients as a causal time sequence and introduce a transformer-based model to autoregressively predict future Lanczos coefficients from short prefixes. For classical and quantum chaotic systems, our model outperforms asymptotic fits in both coefficient extrapolation and physical observable reconstruction, and achieves an order-of-magnitude reduction in error. The model also accurately extrapolates coefficients in integrable regimes, where no universal asymptotic fit exists. Remarkably, our model transfers across system sizes: it can be trained on smaller systems and then be used to extrapolate coefficients on a larger system without retraining. By probing the learned attention patterns and performing targeted attention ablations, we identify portions of the coefficient history that are most influential for accurate forecasts. Our results demonstrate that modern sequence models can serve as practical surrogates for probing operator dynamics deep in Krylov space, where brute-force Lanczos iteration can be computationally prohibitive.

Fault-tolerant quantum computing requires extremely precise knowledge and control of qubit dynamics during the application of a gate. We develop a data-driven learning protocol for characterizing quantum gates that builds off previous work on learning the Nakajima-Mori-Zwanzig (NMZ) formulation of open system dynamics from time series data, which allows detailed reconstruction of quantum evolution, including non-Markovian dynamics. We demonstrate this learning technique on three different systems: a simulation of a qubit whose dynamics are purely Markovian, a simulation of a driven qubit coupled to stochastic noise produced by an Ornstein-Uhlenbeck process, and trapped-ion experimental data of a driven qubit whose noise environment is not characterized ahead of time. Our technique is able to learn the generators of time evolution, or the NMZ operators, in all three cases and can learn the timescale in which the qubit dynamics can no longer be accurately described by a purely Markovian model. Our technique complements existing quantum gate characterization methods such as gate set tomography by explicitly capturing non-Markovianity in the gate generator, thus allowing for more thorough diagnosis of noise sources.

Since its inception, Bohmian mechanics has been surrounded by a halo of controversy. Originally proposed to bypass the limitations imposed by von Neumann's theorem on the impossibility of hidden-variable models in quantum mechanics, it faced strong opposition from the outset. Over time, however, its use in tackling specific problems across various branches of physics has led to a gradual shift in attitude, turning the early resistance into a more moderate acceptance. A plausible explanation for this change may be that, since the late 1990s and early 2000s, Bohmian mechanics has been taking on a more operational and practical role. The original hidden-variable idea has gradually faded from its framework, giving way to a more pragmatic approach that treats it as a suitable analytical and computational tool. This discussion explores how and why such a shift in perspective has occurred and, therefore, answers questions such as whether Bohmian mechanics should be considered once and for all a legitimate quantum representation (i.e., worth being taught in elementary quantum mechanics courses) or, by extension, whether these ideas can be transferred to and benefit other fields. Here, the Schrödinger equation and several specific numerical examples are re-examined in the light of a less restrictive view than the standard one usually adopted in quantum mechanics.

This work provides a step-by-step quantum computing derivation of the unitary coupled cluster singles and doubles ansatz. We show how the structure of the ansatz emerges from fermionic algebra under unitary constraints. By explicitly connecting second quantization, Jordan-Wigner mapping, and quantum circuit synthesis, we clarify conceptual gaps between quantum physics and quantum computing implementations, particularly regarding operator locality, commutation structure, and hardware realization. We exemplify the procedure on the singles and doubles coupled cluster ansatz for the hydrogen molecule.

We explore the experimental predictions of the local scale invariant, non-Hermitian pilot-wave (de Broglie-Bohm) formulation of quantum theory introduced in arXiv:2601.03567. We use Weyl's definition of gravitational radius of charge to obtain the fine-structure constant for non-integrable scale effects $\alpha_S$. The minuteness of $\alpha_S$ relative to $\alpha$ ($\alpha_S/\alpha \sim 10^{-21}$) effectively hides the effects in usual quantum experiments. In an Aharonov-Bohm double-slit experiment, the theory predicts that the position probability density depends on which slit the particle trajectory crosses, due to a non-integrable scale induced by the magnetic flux. This experimental prediction can be tested for an electrically neutral, heavy molecule with mass $m \sim 10^{-19} \text{g}$ at a $\sim 10^5 \text{ esu}$ flux regime. We analyse the Weyl-Einstein debate on the second-clock effect using the theory and show that spectral frequencies are history-independent. We thereby resolve Einstein's key objection against local scale invariance, and obtain two further experimental predictions. First, spectral intensities turn out to be history-dependent. Second, energy eigenvalues are modified by tiny imaginary corrections that modify spectral linewidths. We argue that the trajectory dependence of the probabilities renders our theory empirically distinguishable from other quantum formulations that do not use pilot-wave trajectories, or their mathematical equivalents, to derive experimental predictions.

Hybrid quantum systems combine the unique advantages of different physical platforms with the goal of realizing more powerful and practical quantum information processing devices. Mechanical systems, such as bulk acoustic wave resonators, feature a large number of highly coherent harmonic modes in a compact footprint, which complements the strong nonlinearities and fast operation times of superconducting quantum circuits. Here, we demonstrate an architecture for mechanical resonator-based quantum computing, in which a superconducting qubit is used to perform quantum gates on a collection of mechanical modes. We show the implementation of a universal gate set, composed of single-qubit gates and controlled arbitrary-phase gates, and showcase their use in the quantum Fourier transform and quantum period finding algorithms. These results pave the way toward using mechanical systems to build crucial components for future quantum technologies, such as quantum random-access memories.

Non-stabilizerness, also known as “magic,” quantifies how far a quantum state departs from the stabilizer set. It is a central resource behind quantum advantage and a useful probe of the complexity of quantum many-body states. Yet standard magic quantifiers, such as the stabilizer Rényi entropy (SRE) for qubits and the mana for qutrits, are costly to evaluate numerically, with the computational complexity growing rapidly with the number $N$ of qudits. Here we introduce efficient, numerically exact algorithms that exploit the fast Hadamard transform to compute the SRE for qubits ($d=2$) and the mana for qutrits ($d=3$) for pure states given as state vectors. Our methods compute SRE and mana at cost $O(N d^{2N})$, providing an exponential improvement over the naive $O(d^{3N})$ scaling, with substantial parallelism and straightforward GPU acceleration. We further show how to combine the fast Hadamard transform with Monte Carlo sampling to estimate the SRE of state vectors, and we extend the approach to compute the mana of mixed states. All algorithms are implemented in the open-source Julia package HadaMAG ( https://github.com/bsc-quantic/HadaMAG.jl/ ), which provides a high-performance toolbox for computing SRE and mana with built-in support for multithreading, MPI-based distributed parallelism, and GPU acceleration. The package, together with the methods developed in this work, offers a practical route to large-scale numerical studies of magic in quantum many-body systems.

Analog coprocessors are intensively developing nowadays with the aim to optimize energy computations of neural networks. In this work we focus on the possibility of using detection of collective oscillations in optical systems for computational purposes. We show that in a system of coupled resonators, collective oscillations can be used to implement matrix-vector multiplication. The matrix is formed by the coupling constants between the resonators, and the input vector is formed by the initial occupancies of the involved modes. The frequency of the collective oscillations is growing with the number of the involved modes, similarly to Rabi oscillations. The time needed for their detection, i.e., averaging, decreases with an increase in the input vector dimension. We discuss the limitations imposed on parallel computation in the system by restriction of the allowed optical frequency band.

We analyze the interplay of disorder and long-range hopping in a paradigmatic one dimensional model of quantum transport. While typically the current is expected to decrease as the disorder strength increases due to localization effects, in systems with infinite range hopping it was shown in Chavez et al, Phys. Rev. Lett. 126, 153201 (2021), that the current can increase with disorder in the Disorder-Enhanced-Transport (DET) regime. Here, by analyzing models with variable hopping range decaying as $1/r^{\alpha}$ with the distance $r$ among the sites, we show that the DET regime is a general feature of long-range hopping systems and it occurs, not only in the strong long-range limit $\alpha<1$ but even for weak long-range $1 \le \alpha \le 3$. Specifically, we show that, after an initial decrease, the current grows with the disorder strength until it reaches a local maximum. Both disorder thresholds at which the DET regime starts and ends are determined. Our results open the path to understand the effect of disorder on transport in many realistic systems where long range hopping is present.

We investigate the superradiant phase transition in a two-component Bose-Einstein condensate with distinct atomic detunings, confined in an optical cavity and driven by a transverse pump laser. By combining perturbation theory and numerical simulations, we demonstrate that the phase transition is dominated by the red-detuned component, resulting in a phase diagram completely different from that of a single-component case under blue-detuned condition. The system exhibits spontaneous phase separation between the two components, manifested as alternating stripe patterns in the normal phase and distinct Bragg gratings in the superradiant phase. Furthermore, the Bogoliubov excitation spectrum reveals roton-type mode softening, indicating that the phase transition also corresponds to the superfluid-to-lattice supersolid transition. Our findings provide insights into the interplay between atomic detunings and collective quantum many-body phenomena, offering potential applications in quantum simulation and optical switching technologies.

The transition to the High-Luminosity Large Hadron Collider (HL-LHC) presents a computational challenge where particle reconstruction complexity may outpace classical computing resources. While quantum computing offers potential speedups, standard algorithms like Harrow-Hassidim-Lloyd (HHL) require prohibitive circuit depths for near-term hardware. Here, we introduce the 1-Bit Quantum Filter, a domain-specific adaptation of HHL that reformulates tracking from matrix inversion to binary ground-state filtering. By replacing high-precision phase estimation with a single-ancilla spectral threshold and exploiting the Hamiltonian's sparsity, we achieve an asymptotic gate complexity of $O(\sqrt{N} \log N)$, given Hamiltonian dimension $N$. We validate this approach by simulating LHCb Vertex Locator events with a toy model, and benchmark performance using the noise models of Quantinuum H2 trapped-ion and IBM Heron superconducting processors. This work establishes a resource-efficient track reconstruction method capable of solving realistic event topologies on noise-free simulators and smaller tracking scenarios within the current constraints of the Noisy Intermediate Scale Quantum (NISQ) era.

Most numerical methods for time integration use real-valued time steps. Complex time steps, however, can provide an additional degree of freedom, as we can select the magnitude of the time step in both the real and imaginary directions. We show that specific paths in the complex time plane lead to expanded stability regions, providing clear computational advantages for complex-valued systems. In particular, we highlight the Schrödinger equation, for which complex time integrators can be uniquely optimal. Furthermore, we demonstrate that these benefits extend to certain classes of real-valued stiff systems by coupling complex time steps with the Projective Integration method.

This research presents a novel approach in quantum computing by transforming ARM assembly instructions for use in quantum algorithms. The core achievement is the development of a method to directly map the ARM assembly language, a staple in classical computing, to quantum computing paradigms. The practical application of this methodology is demonstrated through the computation of the Fibonacci sequence. This example serves to validate the approach and underscores its potential in simplifying quantum algorithms. Grover's Algorithm was realized through the use of quantum-specific instructions. These transformations were developed as part of an open-source assembly-to-quantum compiler (github.com/arhaverly/AssemblyToQuantumCompiler). This effort introduces a novel approach to utilizing classical instruction sets in quantum computing and offers insight into potential future developments in the field. The AssemblyToQuantumCompiler streamlines quantum programming and enables computer scientists to transition more easily from classical to quantum computer programming.

We have observed Hong-Ou-Mandel interference of high-brightness synchrotron x-rays with a Mach-Zehnder interferometer, yielding two-photon states of potential interest for x-ray quantum optics.

Tegmark's decoherence bound is derived under the assumption of a strictly memoryless environment. We show that this result corresponds to the singular limit of a finite-memory theory. For exponentially correlated environments decoherence is generically quadratic at short times and the decoherence time scales as the square root of the bath correlation time. For the Ornstein-Uhlenbeck bath we derive the exact non-Markovian coherence equation and verify the predicted scaling using an exact pseudomode mapping. Tegmark's bound is recovered only in the vanishing-memory limit.

Although the original EPR paradox was formulated in terms of position and momentum, most studies of these phenomena have focused on measurement scenarios with only a discrete number of possible measurement outcomes. Here, we present a framework for studying non-locality that is agnostic to the dimension of the physical systems involved, allowing us to probe purely continuous-variable, discrete-variable, and hybrid continuous/discrete non-locality. Our approach allows us to find the optimal Bell inequality for any given measurement scenario and quantifies the amount of non-locality that is present in measurement statistics. This formalism unifies the existing literature on continuous-variable non-locality and allows us to identify new states in which Bell non-locality can be probed through homodyne detection. Notably, we find the first example of two-mode continuous-variable non-locality that cannot be mapped to a binary Bell inequality. Moreover, we provide several examples of simple hybrid DV-CV entangled states that could lead to near-term violation of Bell inequalities.

In this work, we present analytical solutions of Schrödinger equation for Coulomb potential in presence of a Dunkl reflection operator. Expressions are offered for eigenvalues, eigenfunctions and radial densities for H-isoelectronic series (Z=1-3). The degeneracy in energy in absence and presence of the reflection has been discussed. The standard deviation, Shannon entropy, Rényi entropy in position space have been derived for arbitrary quantum states. Then several important complexity measures like López-Ruiz-Mancini-Calbet (LMC), Shape-Rényi complexity (SRC), Generalized Rényi complexity (GRC), Rényi complexity ratio (RCR) are considered in the analytical framework. Representative results are given for three one-electron atomic ions in tabular and graphical format. Changes in these measures with respect to parity and Dunkl parameter have been given in detail. Most of these results are offered here for the first time.