arXiv subjects

Attila Portik

Publications and source records attributed to Attila Portik.

6 recordsLinked to original sources

arXiv2026

Persistence of Fractal Structures in Iterated Quantum Protocols: Robustness to Preparation and Gate Errors

Repeatedly combining entangling gates on an ensemble of qubits with measurement and postselection on a part of them induces a nonlinear evolution of the unmeasured qubits' state, whose fractal convergence boundaries make the outcome sensitive to the initial state. We study a family of iterated protocols in which $n$ identical qubits are coupled by CNOT gates, $n-1$ of them are postselected, and a parametrized single-qubit unitary acts on the survivor. For orders $n=2$ to $5$, we map the box-counting dimension of the pure-state Julia sets over the complex parameter plane and identify the symmetries that constrain it. Allowing mixed initial states, we find that moderate preparation noise preserves the main parameter-dependent trends of the boundary dimension over much of the studied range, and that the three-dimensional quasi-Julia boundary in the Bloch ball has a dimension that is approximately equal to the dimension of the pure-state Julia set plus one. We further model gate imperfections by an effective depolarizing channel and by fixed coherent interactions. Weak errors leave the estimated dimensions consistent with their ideal values even where the convergence regions visibly deform, and $ZZ$ errors are shown to be exactly conjugate to the ideal protocol at a rotated parameter. Finally, we analyze the postselection and storage cost of an implementation and propose a diagnostic test combining conditional fidelity with acceptance statistics, which we demonstrate on IQM Emerald and Rigetti Cepheus-1-108Q.

quant-ph↗

arXiv2026

Chaos, Fractals, and Ergodicity in Nonlinear Quantum Protocols

Iterated nonlinear quantum protocols provide a straightforward way of realizing nonlinear dynamics in quantum systems through measurement and postselection. We investigate a family of protocols in which the order of the induced nonlinearity is controlled by the number of qubits involved in a single step. By examining the resulting rational maps and applying a set of numerical diagnostics, we identify extended parameter regions that exhibit ergodic-like dynamics for protocol orders $n=3,4,$ and $5$. We further characterize the associated chaotic behavior through the distribution of Lyapunov exponents. Our results show that ergodic-like dynamics persists beyond the quadratic case, while the geometry of the corresponding parameter regions and the typical degree of chaoticity depend strongly on the order of the nonlinear transformation.

quant-ph↗

arXiv2026

Clifford Volume and Free Fermion Volume: Complementary Scalable Benchmarks for Quantum Computers

As quantum computing advances toward the late-NISQ and early fault-tolerant eras, scalable and platform-independent benchmarks are essential for quantifying computational capacity in a classically verifiable manner. We introduce two volumetric benchmarks, Clifford Volume and Free Fermion Volume, that assess quantum hardware by testing the execution of random Clifford and free fermion operations. These two groups of unitaries possess a combination of properties that make them ideal for benchmarking: (i) each is individually efficient to simulate classically, enabling verification at scale; (ii) together they form a universal gate set; (iii) they serve as essential algorithmic primitives in practical applications (including shadow tomography and quantum chemistry); and (iv) their definitions are formulated abstractly, without explicit reference to hardware-specific features such as qubit connectivity or native gate sets. This framework thus enables scalable and fair cross-platform comparisons and tracks meaningful computational advancement. We demonstrate the practical feasibility of these benchmarks through extensive numerical simulations across realistic noise parameters and through experimental validation on Quantinuum's H2-1 trapped-ion quantum computer, which achieves a Clifford Volume of 34.

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arXiv2025

Ergodic dynamics in iterated quantum protocols

We study measurement-induced nonlinear dynamics generated by an iterated quantum protocol combining an entangling gate, a single-qubit rotation, and post-selection. For pure single-qubit inputs, a particular choice of the single-qubit unitary yields globally chaotic, strongly mixing dynamics that explores the entire Bloch sphere, providing a physical realization of ergodic behavior in a complex map. We extend the analysis to realistic, noisy preparation by considering mixed initial states and the induced nonlinear evolution inside the Bloch sphere. Numerical results show that the maximally mixed state is an attractor for mixed inputs, although many trajectories exhibit transient increases in purity before ultimately converging. To quantify robustness against noise, we introduce a practical notion of quasi-ergodicity: ensembles prepared in a small angular patch at fixed purity rapidly spread to cover all directions, while the purity gradually decreases toward its minimal value. By varying the final single-qubit gate, we identify a broad family of protocols that remain ergodic-like for pure states, supported by consistent diagnostics including the absence of attracting cycles, agreement of time and ensemble statistics, rapid spreading from localized regions, and exponential sensitivity to initial conditions. Away from the special globally mixing case, the mixed-state dynamics can change qualitatively: for most ergodic-like parameters, a finite subset of noisy inputs is driven toward purification rather than complete mixing, demonstrating the coexistence of statistical mixing and purification within a single iterated protocol.

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arXiv2025

The EU Quantum Flagship's Key Performance Indicators for Quantum Computing

As quantum processors continue to scale in size and complexity, the need for well-defined, reproducible, and technology-agnostic performance metrics becomes increasingly critical. Here we present a suite of scalable quantum computing benchmarks developed as key performance indicators (KPIs) within the EU Quantum Flagship. These proposed benchmarks are designed to assess holistic system performance rather than isolated components, and to remain applicable across both noisy intermediate-scale quantum (NISQ) devices and future fault-tolerant architectures. We introduce four core benchmarks addressing complementary aspects of quantum computing capability: large multi-qubit circuit execution via a Clifford Volume benchmark, scalable multipartite entanglement generation through GHZ-state preparation, a benchmark based on the application of Shor's period-finding subroutine to simple functions, and a protocol quantifying the benefit of quantum error correction using Bell states. Each benchmark is accompanied by clearly specified protocols, reporting standards, and scalable evaluation methods. Together, these KPIs provide a coherent framework for transparent and fair performance assessment across quantum hardware platforms and for tracking progress late-NISQ toward early fault-tolerant quantum computation.

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arXiv2023

Robustness of chaotic behavior in iterated quantum protocols

One of the simplest possible quantum circuits, consisting of a CNOT gate, a Hadamard gate and a measurement on one of the outputs is known to lead to chaotic dynamics when applied iteratively on an ensemble of equally prepared qubits. The evolution of pure initial quantum states is characterized by a fractal (in the space of states), formed by the border of different convergence regions. We examine how the ideal evolution is distorted in the presence of both coherent error and incoherent initial noise, which are typical imperfections in current implementations of quantum computers. It is known that under the influence of initial noise only, the fractal is preserved, moreover, its dimension remains constant below a critical noise level. We systematically analyze the effect of coherent Hadamard gate errors by determining fixed points and cycles of the evolution. We combine analytic and numerical methods to explore to what extent the dynamics is altered by coherent errors in the presence of preparation noise as well. We show that the main features of the dynamics, and especially the fractal borders, are robust against the discussed noise, they will only be slightly distorted. We identify a range of error parameters, for which the characteristic properties of the dynamics are not significantly altered. Hence, our results allow to identify reliable regimes of operation of iterative protocols.

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