arXiv subjects

Shayan Majidy

Publications and source records attributed to Shayan Majidy.

12 recordsLinked to original sources

arXiv2026

Entangling logical qubits without physical operations

Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom codes-quantum error-correcting codes that realize entangling gates between all logical qubits in a code block purely through relabelling of physical qubits during compilation, yielding perfect fidelity with no spatial or temporal overhead. We present a systematic study of such codes. First, we identify phantom codes using complementary numerical and analytical approaches. We exhaustively enumerate all $2.71 \times 10^{10}$ inequivalent CSS codes up to $n=14$ and identify additional instances up to $n=21$ via SAT-based methods. We then construct higher-distance phantom-code families using quantum Reed-Muller codes and the binarization of qudit codes. Across all identified codes, we characterize other supported fault-tolerant logical Clifford and non-Clifford operations. Second, through end-to-end noisy simulations with state preparation, full QEC cycles, and realistic physical error rates, we demonstrate scalable advantages of phantom codes over the surface code across multiple tasks. We observe a one-to-two order-of-magnitude reduction in logical infidelity at comparable qubit overhead for GHZ-state preparation and Trotterized many-body simulation tasks, given a modest preselection acceptance rate. Our work establishes phantom codes as a viable architectural route to fault-tolerant quantum computation with scalable benefits for workloads with dense local entangling structure, and introduces general tools for systematically exploring the broader landscape of quantum error-correcting codes.

quant-ph↗

arXiv2025

Architectural mechanisms of a universal fault-tolerant quantum computer

Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architectures is an outstanding scientific challenge. Here we utilize reconfigurable arrays of up to 448 neutral atoms to implement all key elements of a universal, fault-tolerant quantum processing architecture and experimentally explore their underlying working mechanisms. We first employ surface codes to study how repeated QEC suppresses errors, demonstrating 2.14(13)x below-threshold performance in a four-round characterization circuit by leveraging atom loss detection and machine learning decoding. We then investigate logical entanglement using transversal gates and lattice surgery, and extend it to universal logic through transversal teleportation with 3D [[15,1,3]] codes, enabling arbitrary-angle synthesis with logarithmic overhead. Finally, we develop mid-circuit qubit re-use, increasing experimental cycle rates by two orders of magnitude and enabling deep-circuit protocols with dozens of logical qubits and hundreds of logical teleportations with [[7,1,3]] and high-rate [[16,6,4]] codes while maintaining constant internal entropy. Our experiments reveal key principles for efficient architecture design, involving the interplay between quantum logic and entropy removal, judiciously using physical entanglement in logic gates and magic state generation, and leveraging teleportations for universality and physical qubit reset. These results establish foundations for scalable, universal error-corrected processing and its practical implementation with neutral atom systems.

quant-ph↗

arXiv2025

Scalable and fault-tolerant preparation of encoded k-uniform states

$k$-uniform states are valuable resources in quantum information, enabling tasks such as teleportation, error correction, and accelerated quantum simulations. The practical realization of $k$-uniform states, at scale, faces major obstacles: verifying $k$-uniformity is as difficult as measuring code distances, and devising fault-tolerant preparation protocols further adds to the complexity. To address these challenges, we present a scalable, fault-tolerant method for preparing encoded $k$-uniform states, and we illustrate our approach using surface and color codes. We first present a technique to determine $k$-uniformity of stabilizer states directly from their stabilizer tableau. We then identify a family of Clifford circuits that ensures both fault tolerance and scalability in preparing these states. Building on the encoded $k$-uniform states, we introduce a hybrid physical-logical strategy that retains some of the error-protection benefits of logical qubits while lowering the overhead for implementing arbitrary gates compared to fully logical algorithms. We show that this hybrid approach can outperform fully physical implementations for resource-state preparation, as demonstrated by explicit constructions of $k$-uniform states.

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arXiv2024

Thermodynamic limitations on fault-tolerant quantum computing

We investigate the thermodynamic limits on scaling fault-tolerant quantum computers due to heating from quantum error correction (QEC). Quantum computers require error correction, which accounts for 99.9% of the qubit demand and generates heat through information-erasing processes. This heating increases the error rate, necessitating more rounds of error correction. We introduce a dynamical model that characterizes heat generation and dissipation for arrays of qubits weakly coupled to a refrigerator and identify a dynamical phase transition between two operational regimes: a bounded-error phase, where temperature stabilizes and error rates remain below fault-tolerance thresholds, and an unbounded-error phase, where rising temperatures drive error rates beyond sustainable levels, making fault tolerance infeasible. Applying our model to a superconducting qubit system performing Shor's algorithm to factor 2048-bit RSA integers, we find that current experimental parameters place the system in the bounded-error phase. Our results indicate that, while inherent heating can become significant, this thermodynamic constraint should not limit scalable fault tolerance if current hardware capabilities are maintained as systems scale.

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arXiv2024

Addressing misconceptions in university physics: A review and experiences from quantum physics educators

Students often begin physics courses with misconceptions rooted in everyday experience and intuition, which can be resistant to change. While research has identified strategies for addressing misconceptions across physics, it remains unclear whether different domains, like classical and quantum physics, require different approaches. On one hand, quantum concepts are further removed from daily experience, possibly requiring specialized strategies. On the other, all physics must be learned rather than innately understood, and classical physics already contains many counterintuitive ideas, suggesting the same strategies may be equally valid. To explore this question, we first develop a structure to organize the existing literature on addressing misconceptions in physics education. We identify 126 studies, which we group into six categories, three of which include further subcategories. Rather than offering a comprehensive literature review, this scheme provides a structural lens through which to compare how various strategies align. We then take an instructor-centered approach, using our framework to guide interviews with quantum physics instructors. We interview 12 instructors from the University of Waterloo's Institute for Quantum Computing and the Perimeter Institute who have collectively taught over 100 quantum courses. Our findings suggest that quantum physics instructors find strategies similar to those used in classical physics effective for identifying and addressing misconceptions. This highlights the potential to adapt, rather than replace, existing instructional tools to better meet the conceptual challenges of quantum physics. Our work provides practical insights for educators and curriculum designers aiming to support deeper understanding in quantum mechanics.

physics.ed-ph↗

arXiv2024

Noncommuting charges can remove non-stationary quantum many-body dynamics

Studying noncommuting conserved quantities, or 'charges,' has revealed a conceptual puzzle: noncommuting charges hinder thermalization in some ways yet promote it in others. While many quantum systems thermalize according to the Eigenstate Thermalization Hypothesis (ETH), systems with 'dynamical symmetries' violate the ETH and exhibit non-stationary dynamics, preventing them from equilibrating, much less thermalizing. We demonstrate that each pair of dynamical symmetries corresponds to a specific charge. We find that introducing new charges that do not commute with existing ones disrupts these symmetries, thereby eliminating non-stationary dynamics and facilitating thermalization. We illustrate this behavior across various models, including the Hubbard model and Heisenberg spin chains. Our findings demonstrate that noncommuting charges can enhance thermalization by reducing the number of local observables that thermalize according to the ETH.

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arXiv2023

Noncommuting conserved charges in quantum thermodynamics and beyond

Thermodynamic systems typically conserve quantities ("charges") such as energy and particle number. The charges are often assumed implicitly to commute with each other. Yet quantum phenomena such as uncertainty relations rely on observables' failure to commute. How do noncommuting charges affect thermodynamic phenomena? This question, upon arising at the intersection of quantum information theory and thermodynamics, spread recently across many-body physics. Charges' noncommutation has been found to invalidate derivations of the thermal state's form, decrease entropy production, conflict with the eigenstate thermalization hypothesis, and more. This Perspective surveys key results in, opportunities for, and work adjacent to the quantum thermodynamics of noncommuting charges. Open problems include a conceptual puzzle: Evidence suggests that noncommuting charges may hinder thermalization in some ways while enhancing thermalization in others.

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arXiv2023

Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits

Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a "spin-sharpening transition." On one side is a phase in which the measurements can efficiently identify the system's total spin quantum number; on the other side is a phase in which measurements cannot.

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arXiv2022

Non-Abelian symmetry can increase entanglement entropy

The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and may enhance finite-size deviations from eigenstate thermalization. Bridging quantum thermodynamics to many-body physics, we quantify the effects of charges' noncommutation -- of a symmetry's non-Abelian nature -- on Page curves. First, we construct two models that are closely analogous but differ in whether their charges commute. We show analytically and numerically that the noncommuting-charge case has more entanglement. Hence charges' noncommutation can promote entanglement.

quant-ph↗

arXiv2021

How to build Hamiltonians that transport noncommuting charges in quantum thermodynamics

Noncommuting conserved quantities have recently launched a subfield of quantum thermodynamics. In conventional thermodynamics, a system of interest and an environment exchange quantities -- energy, particles, electric charge, etc. -- that are globally conserved and are represented by Hermitian operators. These operators were implicitly assumed to commute with each other, until a few years ago. Freeing the operators to fail to commute has enabled many theoretical discoveries -- about reference frames, entropy production, resource-theory models, etc. Little work has bridged these results from abstract theory to experimental reality. This paper provides a methodology for building this bridge systematically: We present a prescription for constructing Hamiltonians that conserve noncommuting quantities globally while transporting the quantities locally. The Hamiltonians can couple arbitrarily many subsystems together and can be integrable or nonintegrable. Our Hamiltonians may be realized physically with superconducting qudits, with ultracold atoms, and with trapped ions.

quant-ph↗

arXiv2021

Detecting violations of macrorealism when the original Leggett-Garg inequalities are satisfied

Macroscopic realism (MR) is the notion that a time-evolving system possesses definite properties, irrespective of past or future measurements. Quantum mechanical theories can, however, produce violations of MR. Most research to date has focused on a single set of conditions for MR, the Leggett-Garg inequalities (LGIs), and on a single data set, the "standard data set", which consists of single-time averages and second-order correlators of a dichotomic variable Q for three times. However, if such conditions are all satisfied, then where is the quantum behaviour? In this paper, we provide an answer to this question by considering expanded data sets obtained from finer-grained measurements and MR conditions on those sets. We consider three different situations in which there are violations of MR that go undetected by the standard LGIs. First, we explore higher-order LGIs on a data set involving third- and fourth-order correlators, using a spin-1/2 and spin-1 system. Second, we explore the pentagon inequalities (PIs) and a data set consisting of all possible averages and second-order correlators for measurements of Q at five times. Third, we explore the LGIs for a trichotomic variable and measurements made with a trichotomic operator to, again, identify violations for a spin-1 system beyond those seen with a single dichotomic variable. We also explore the regimes in which combinations of two and three-time LGIs can be satisfied and violated in a spin-1 system, extending recent work. We discuss the possible experimental implementation of all the above results.

quant-ph↗

arXiv2018

A unification of the coding theory and OAQEC perspective on hybrid codes

There is an advantage in simultaneously transmitting both classical and quantum information over a quantum channel compared to sending independent transmissions. The successful implementation of simultaneous transmissions of quantum and classical information will require the development of hybrid quantum-classical error-correcting codes, known as hybrid codes. The characterization of hybrid codes has been performed from a coding theory perspective and an operator algebra quantum error correction (OAQEC) perspective. First, we demonstrate that these two perspectives are equivalent and that the coding theory characterization is a specific case of the OAQEC model. Second, we include a generalization of the quantum Hamming bound for hybrid error-correcting codes. We discover a necessary condition for developing non-trivial hybrid codes -- they must be degenerate. Finally, we construct an example of a non-trivial degenerate 4-qubit hybrid code.

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