arXiv subjects

Muhammad Erew

Publications and source records attributed to Muhammad Erew.

5 recordsLinked to original sources

arXiv2025

Extremizing Measures of Magic on Pure States by Clifford-stabilizer States

Magic states enable universal, fault-tolerant quantum computation within the stabilizer framework. Their non-stabilizerness supplies the resource needed to bypass the Eastin-Knill theorem while allowing fault-tolerant distillation. Although many measures of magic exist, not every nonzero-magic state is known to be distillable, and many of currently known distillable states are special cases of Clifford-stabilizer states, defined as pure states uniquely stabilized by finite Clifford subgroups. We develop a general framework for group-covariant functionals on Hermitian operators, introducing the notions of $G$-stabilizer spaces, states, and codes for arbitrary finite subgroups $G \subset \mathrm{U}(\mathcal{H})$. We define analytic families of $G$-covariant functionals and prove that any $G$-invariant pure state is extremal for a broad class of derived functionals, including symmetric, max-type, and R\'enyi-type functionals, whenever the underlying family is $G$-covariant. This extremality holds for purity-preserving variations orthogonal to the stabilized subspace. Specializing to the Pauli and Clifford groups, we recover the extremality structure of canonical magic measures such as mana, stabilizer R\'enyi entropies, generalized R\'enyi entropies, and stabilizer fidelity, and show that Clifford-stabilizer states extremize them. We classify such states for qubits, qutrits, ququints, and two-qubit systems, identifying new candidates for magic distillation. We further propose an inefficient distillation protocol for a two-qubit magic state with stabilizer fidelity exceeding standard benchmarks, and conjecture that SIC-POVM fiducial states are Clifford-stabilizer states.

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arXiv2025

Pre-Distillation of Magic States via Composite Schemes

Magic state distillation (MSD) is a cornerstone of fault-tolerant quantum computing, enabling non-Clifford gates via state injection into stabilizer circuits. However, the substantial overhead of current MSD protocols remains a major obstacle to scalable implementations. We propose a general framework for pre-distillation, based on composite pulse sequences that suppress systematic errors in the generation of magic states. While most composite designs target simple gates such as X, Z, or Hadamard, our schemes directly implement the non-Clifford T gate with enhanced robustness to the targeted systematic errors. We develop composite sequences tailored to the dominant control imperfections in superconducting, trapped-ion, neutral-atom, and integrated photonic platforms. To quantify improvement in the implementation, we introduce an operationally motivated fidelity measure specifically tailored to the T gate: the T-magic error, which captures the gate's effectiveness in preparing high-fidelity magic states. We further show that the error in the channel arising from the injection of faulty magic states scales linearly with the leading-order error of the states. Within the systematic-error-dominated regimes considered, this approach lowers the number of required distillation levels by up to three across the platforms we study, translating to substantial qubit-overhead savings and offering a practical route toward more resource-efficient universal quantum computation.

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arXiv2024

Efficient Robust Spontaneous Parametric Down-Conversion via Detuning Modulated Composite Segments Designs

Spontaneous Parametric Down Conversion (SPDC) holds a pivotal role in quantum physics, facilitating the creation of entangled photon pairs, heralded single photons and squeezed light, critical resources for many applications in quantum technologies. However, their production is susceptible to physical variations, posing limitations on their robust utility. To overcome these limitations, this work introduces a method to significantly enhance the reliability of entangled photon pair generation. This approach involves introducing a composite design scheme to the SPDC process. The design is based on the development of a theoretical composite segments framework for SU(1,1), offering increased error resilience and robustness of the process. The practical application is experimentally demonstrated by modulating the nonlinear coefficient of a KTP crystal for degenerate 532 nm to 1064 nm conversion, resulting in an effective sevenfold improvement in stability of photon-pair generation and coincidence rate against temperature fluctuations compared to conventional quasi-phase-matching techniques. Furthermore, the presented concept is applicable to other physical systems that exhibit SU(1,1) dynamics. This methodology can create a leap forward in quantum technologies by significantly enhancing stability and error tolerance, thus paving the way for a new generation of entangled photon sources, holding promise for quantum information processing, communication, and precision measurement applications.

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arXiv2022

Segmented Composite Design of Robust Single-Qubit Quantum Gates

Error mitigation schemes and error-correcting codes have been the center of much effort in quantum information processing research over the last few decades. While most of the successful proposed schemes for error mitigation are perturbative in the noise and assume deterministic systematic errors, studies of the problem considering the full noise and errors distribution are still scarce. In this work, we introduce an error mitigation scheme for robust single-qubit unitary gates based on composite segmented design, which accounts for the full distribution of the physical noise and errors in the system. We provide two optimization approaches to construct these robust segmented gates: perturbative and non-perturbative, that addresses all orders of errors. We demonstrate our scheme in the photonics realm for the dual-rail directional couplers realization. We show that the 3-segmented composite design for the fundamental single-qubits unitary operations reduces the error by an order of magnitude for a realistic distribution of errors, and that the two approaches are compatible for small errors. This is shown to significantly reduce the overhead of modern error correction codes. Our methods are rather general and can be applied to other realizations of quantum information processing units.

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arXiv2020

Complete Population Transfer of Maximally Entangled States in $2^{2N}$-level Systems via Pythagorean Triples Coupling

Maximally entangled states play a central role in quantum information processing. Despite much progress throughout the years, robust protocols for manipulations of such states in many-level systems are still scarce. Here we present a control scheme that allow efficient manipulation of complete population transfer between two maximally entangled states. Exploiting the self-duality of $\mathrm{SU}\left(2\right)$, we present in this work a family of ${\mathrm{2}}^{\mathrm{2}N}$-level systems with couplings related to Pythagorean triples that make a complete population transfer from one state to another (orthogonal) state, using very few couplings and generators. We relate our method to the recently-developed retrograde-canon scheme and derive a more general complete transfer recipe. We also discuss the cases of $\left(2n\right)^2$-level systems, $\left(2n+1\right)^2$-level systems and other unitary groups.

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