Searcharxiv⌕ Search

arXiv subjects

Parsa Bonderson

Publications and source records attributed to Parsa Bonderson.

At least 19 recordsLinked to original sources
arXiv2025

Excising dead components in the surface code using minimally invasive alterations: A performance study

The physical implementation of a large-scale error-corrected quantum processor will necessarily need to mitigate the presence of defective (thereby "dead") physical components in its operation, for example, identified during bring-up of the device or detected in the middle of a computation. In the context of solid-state qubits, the quantum error correcting protocol operating in the presence of dead components should ideally (i) use the same native operation set as that without dead components, (ii) maximize salvaging of functional components, and (iii) use a consistent global operating schedule which optimizes logical qubit performance and is compatible with the control requirements of the system. The scheme proposed by Grans-Samuelsson et al. [Quantum 8, 1429 (2024)] satisfies all three of these criteria: it effectively excises (cuts out) dead components from the surface code using minimally invasive alterations (MIA). We conduct extensive numerical simulations of this proposal for the pairwise-measurement-based surface code protocol in the presence of dead components under circuit-level noise. To that end, we also describe techniques to automatically construct performant check (detector) bases directly from circuits without manual circuit annotation, which may be of independent interest. Both the MIA scheme and this automated check basis computation can be readily used with measurement-based as well as CNOT-based circuits, and the results presented here demonstrate state-of-the-art performance.

quant-ph↗
arXiv2025

Roadmap to fault tolerant quantum computation using topological qubit arrays

We describe a concrete device roadmap towards a fault-tolerant quantum computing architecture based on noise-resilient, topologically protected Majorana-based qubits. Our roadmap encompasses four generations of devices: a single-qubit device that enables a measurement-based qubit benchmarking protocol; a two-qubit device that uses measurement-based braiding to perform single-qubit Clifford operations; an eight-qubit device that can be used to show an improvement of a two-qubit operation when performed on logical qubits rather than directly on physical qubits; and a topological qubit array supporting lattice surgery demonstrations on two logical qubits. Devices that enable this path require a superconductor-semiconductor heterostructure that supports a topological phase, quantum dots and coupling between those quantum dots that can create the appropriate loops for interferometric measurements, and a microwave readout system that can perform fast, low-error single-shot measurements. We describe the key design components of these qubit devices, along with the associated protocols for demonstrations of single-qubit benchmarking, Clifford gate execution, quantum error detection, and quantum error correction, which differ greatly from those in more conventional qubits. Finally, we comment on implications and advantages of this architecture for utility-scale quantum computation.

quant-ph↗
arXiv2024

Fault-tolerant quantum computation with a neutral atom processor

Quantum computing experiments are transitioning from running on physical qubits to using encoded, logical qubits. Fault-tolerant computation can identify and correct errors, and has the potential to enable the dramatically reduced logical error rates required for valuable algorithms. However, it requires flexible control of high-fidelity operations performed on large numbers of qubits. We demonstrate fault-tolerant quantum computation on a quantum processor with 256 qubits, each an individual neutral Ytterbium atom. The operations are designed so that key error sources convert to atom loss, which can be detected by imaging. Full connectivity is enabled by atom movement. We demonstrate the entanglement of 24 logical qubits encoded into 48 atoms, at once catching errors and correcting for, on average 1.8, lost atoms. We also implement the Bernstein-Vazirani algorithm with up to 28 logical qubits encoded into 112 atoms, showing better-than-physical error rates. In both cases, "erasure conversion," changing errors into a form that can be detected independently from qubit state, improves circuit performance. These results begin to clear a path for achieving scientific quantum advantage with a programmable neutral atom quantum processor.

quant-ph↗
arXiv2024

A fault-tolerant pairwise measurement-based code on eight qubits

We construct a pairwise measurement-based code on eight qubits that is error correcting for circuit noise, with fault distance 3. The code can be implemented on a subset of a rectangular array of qubits with nearest neighbor connectivity of pairwise Pauli measurements, with a syndrome extraction circuit of depth 28. We describe fault-tolerant logical operations on patches of this eight-qubit code that generate the full Clifford group. We estimate the performance under circuit noise both during logical idle and during a logical two-qubit measurement. We estimate the pseudo-threshold to be between $10^{-5}$ and $2\times 10^{-4}$, depending on the amount of noise on idle physical qubits. The use of post-selection in addition to error correction (correcting all degree one faults and rejecting a subset of the higher degree faults) can improve the pseudo-threshold by up to an order of magnitude.

quant-ph↗
arXiv2024

Improved Pairwise Measurement-Based Surface Code

We devise a new realization of the surface code on a rectangular lattice of qubits utilizing single-qubit and nearest-neighbor two-qubit Pauli measurements and three auxiliary qubits per plaquette. This realization gains substantial advantages over prior pairwise measurement-based realizations of the surface code. It has a short operation period of 4 steps and our performance analysis for a standard circuit noise model yields a high fault-tolerance threshold of approximately $0.66\% $. The syndrome extraction circuits avoid bidirectional hook errors, so we can achieve full code distance by choosing appropriate boundary conditions. We also construct variants of the syndrome extraction circuits that entirely prevent hook errors, at the cost of larger circuit depth. This achieves full distance regardless of boundary conditions, with only a modest decrease in the threshold. Furthermore, we propose an efficient strategy for dealing with dead components (qubits and measurements) in our surface code realization, which can be adopted more generally for other surface code realizations. This new surface code realization is highly optimized for Majorana-based hardware, accounting for constraints imposed by layouts and the implementation of measurements, making it competitive with the recently proposed Floquet codes.

quant-ph↗
arXiv2023

G-crossed Modularity of Symmetry-Enriched Topological Phases

The universal properties of (2 + 1)D topological phases of matter enriched by a symmetry group G are described by G-crossed extensions of unitary modular tensor categories (UMTCs). While the fusion and braiding properties of quasiparticles associated with the topological order are described by a UMTC, the G-crossed extensions further capture the properties of the symmetry action, fractionalization, and defects arising from the interplay of the symmetry with the topological order. We describe the relation between the G-crossed UMTC and the topological state spaces on general surfaces that may include symmetry defect branch lines and boundaries that carry topological charge. We define operators in terms of the G-crossed UMTC data that represent the mapping class transformations for such states on a torus with one boundary, and show that these operators provide projective representations of the mapping class groups. This allows us to represent the mapping class group on general surfaces and ensures a consistent description of the corresponding symmetry-enriched topological phases on general surfaces. Our analysis also enables us to prove that a faithful G-crossed extension of a UMTC is necessarily G-crossed modular.

cond-mat.str-el↗
arXiv2022

Torsorial actions on G-crossed braided tensor categories

We develop a method for generating the complete set of basic data under the torsorial actions of $H^2_{[ρ]}(G,\mathcal{A})$ and $H^3(G,\text{U}(1))$ on a $G$-crossed braided tensor category $\mathcal{C}_G^\times$, where $\mathcal{A}$ is the set of invertible simple objects in the braided tensor category $\mathcal{C}$. When $\mathcal{C}$ is a modular tensor category, the $H^2_{[ρ]}(G,\mathcal{A})$ and $H^3(G,\text{U}(1))$ torsorial action gives a complete generation of possible $G$-crossed extensions, and hence provides a classification. This torsorial classification can be (partially) collapsed by relabeling equivalences that appear when computing the set of $G$-crossed braided extensions of $\mathcal{C}$. The torsor method presented here reduces these redundancies by systematizing relabelings by $\mathcal{A}$-valued $1$-cochains. We also use our methods to compute the composition rule of these torsor functors.

math.QA↗
arXiv2022

Characterization and Classification of Fermionic Symmetry Enriched Topological Phases

We examine the interplay of symmetry and topological order in $2+1$ dimensional fermionic topological phases of matter. We define fermionic topological symmetries acting on the emergent topological effective theory described using braided tensor category theory. Connecting this to the ${\cal G}^{\rm f}$ fermionic symmetry of the microscopic physical system, we characterize and classify symmetry fractionalization in fermionic topological phases. We find that the physical fermion provides constraints that result in a tiered structure of obstructions and classification of fractionalization with respect to the physical fermions, the quasiparticles, and the vortices. The fractionalization of the (bosonic) symmetry $G= {\cal G}^{\rm f}/\mathbb{Z}_2^{\rm f}$ on the physical fermions is essentially the central extension of $G$ by the $\mathbb{Z}_2^{\rm f}$ fermion parity conservation that yields the fermionic symmetry ${\cal G}^{\rm f}$. We develop an algebraic theory of ${\cal G}^{\rm f}$ symmetry defects for fermionic topological phases using $G$-crossed braided tensor category theory. This formalism allows us to fully characterize and classify $2+1$ dimensional fermionic symmetry enriched topological phases with on-site unitary fermionic symmetry group ${\cal G}^{\rm f}$. We first apply this formalism to extract the minimal data specifying a general fermionic symmetry protected topological phase, and demonstrate that such phases with fixed ${\cal G}^{\rm f}$ form a group under fermionic stacking. Then we analyze general fermionic symmetry enriched topological phases and find their classification is given torsorially by the classification of the symmetry fractionalization of quasiparticles combined with the classification of fermionic symmetry protected topological phases. We illustrate our results by detailing a number of examples, including all the invertible fermionic topological phases.

cond-mat.str-el↗
arXiv2021

Measuring Topological Order

The topological order of a (2+1)D topological phase of matter is characterized by its chiral central charge and a unitary modular tensor category that describes the universal fusion and braiding properties of its anyonic quasiparticles. I discuss the topologically invariant quantities associated with these and identify ones that are useful for determining the topological order. I propose a variety of physical experiments that probe these quantities and detail the relation of the measured data to the topological invariants.

cond-mat.str-el↗
arXiv2020

Optimizing Clifford gate generation for measurement-only topological quantum computation with Majorana zero modes

One of the main challenges for quantum computation is that while the number of gates required to perform a non-trivial quantum computation may be very large, decoherence and errors in realistic quantum architectures limit the number of physical gate operations that can be performed coherently. Therefore, an optimal mapping of the quantum algorithm into the physically available set of operations is of crucial importance. We examine this problem for a measurement-only topological quantum computer based on Majorana zero modes, where gates are performed through sequences of measurements. Such a scheme has been proposed as a practical, scalable approach to process quantum information in an array of topological qubits built using Majorana zero modes. Building on previous work that has shown that multi-qubit Clifford gates can be enacted in a topologically protected fashion in such qubit networks, we discuss methods to obtain the optimal measurement sequence for a given Clifford gate under the constraints imposed by the physical architecture, such as layout and the relative difficulty of implementing different types of measurements. Our methods also provide tools for comparative analysis of different architectures and strategies, given experimental characterizations of particular aspects of the systems under consideration. As a further non-trivial demonstration, we discuss an implementation of the surface code in Majorana-based topological qubits. We use the techniques developed here to obtain an optimized measurement sequence that implements the stabilizer measurements using only fermionic parity measurements on nearest-neighbor topological qubit islands.

quant-ph↗
arXiv2019

On Realizing Modular Data

We use zesting and symmetry gauging of modular tensor categories to analyze some previously unrealized modular data obtained by Grossman and Izumi. In one case we find all realizations and in the other we determine the form of possible realizations; in both cases all realizations can be obtained from quantum groups at roots of unity.

math.QA↗
arXiv2019

Symmetry Fractionalization, Defects, and Gauging of Topological Phases

We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the \it topological symmetry \rm group, which characterizes the symmetry of the emergent topological quantum numbers of a topological phase, and we describe its relation with the microscopic symmetry of the underlying physical system. We derive a general framework to characterize and classify symmetry fractionalization in topological phases, including phases that are non-Abelian and symmetries that permute the quasiparticle types and/or are anti-unitary. We develop a theory of extrinsic defects (fluxes) associated with elements of the symmetry group, which provides a general classification of symmetry-enriched topological phases derived from a topological phase of matter $\mathcal{C}$ with symmetry group $G$. The algebraic theory of the defects, known as a $G$-crossed braided tensor category $\mathcal{C}_{G}^{\times}$, allows one to compute many properties, such as the number of topologically distinct types of defects associated with each group element, their fusion rules, quantum dimensions, zero modes, braiding exchange transformations, a generalized Verlinde formula for the defects, and modular transformations of the $G$-crossed extensions of topological phases. We also examine the promotion of the global symmetry to a local gauge invariance, wherein the extrinsic $G$-defects are turned into deconfined quasiparticle excitations, which results in a different topological phase $(\mathcal{C}_{G}^{\times})^{G}$. A number of instructive and/or physically relevant examples are studied in detail.

cond-mat.str-el↗
arXiv2018

On invariants of Modular categories beyond modular data

We study novel invariants of modular categories that are beyond the modular data, with an eye towards a simple set of complete invariants for modular categories. Our focus is on the $W$-matrix--the quantum invariant of a colored framed Whitehead link from the associated TQFT of a modular category. We prove that the $W$-matrix and the set of punctured $S$-matrices are strictly beyond the modular data $(S,T)$. Whether or not the triple $(S,T,W)$ constitutes a complete invariant of modular categories remains an open question.

math.QA↗
arXiv2017

Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface

The Lieb-Schultz-Mattis theorem and its higher dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must either have a continuum of low energy excitations, spontaneously break some symmetries, or exhibit topological order with anyonic excitations. We establish a connection between these constraints and a remarkably similar set of constraints at the surface of a 3D interacting topological insulator. This, combined with recent work on symmetry-enriched topological phases (SETs) with on-site unitary symmetries, enables us to develop a framework for understanding the structure of SETs with both translational and on-site unitary symmetries, including the effective theory of symmetry defects. This framework places stringent constraints on the possible types of symmetry fractionalization that can occur in 2D systems whose unit cell contains fractional spin, fractional charge, or a projective representation of the symmetry group. As a concrete application, we determine when a topological phase must possess a "spinon" excitation, even in cases when spin rotational invariance is broken down to a discrete subgroup by the crystal structure. We also describe the phenomena of "anyonic spin-orbit coupling", which may arise from the interplay of translational and on-site symmetries. These include the possibility of on-site symmetry defect branch lines carrying topological charge per unit length and lattice dislocations inducing on-site symmetry protected degeneracies.

cond-mat.str-el↗
arXiv2017

Anyonic Entanglement and Topological Entanglement Entropy

We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a general method of deriving the universal topological contributions to the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. We analyze a number of examples in detail. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy.

quant-ph↗
arXiv2017

Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes

We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological $T$-junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.

cond-mat.mes-hall↗
arXiv2017

Congruence Subgroups and Super-Modular Categories

A super-modular category is a unitary pre-modular category with Müger center equivalent to the symmetric unitary category of super-vector spaces. Super-modular categories are important alternatives to modular categories as any unitary pre-modular category is the equivariantization of a either a modular or super-modular category. Physically, super-modular categories describe universal properties of quasiparticles in fermionic topological phases of matter. In general one does not have a representation of the modular group $\mathrm{SL}(2,\mathbb{Z})$ associated to a super-modular category, but it is possible to obtain a representation of the (index 3) $θ$-subgroup: $Γ_θ<\mathrm{SL}(2,\mathbb{Z})$. We study the image of this representation and conjecture a super-modular analogue of the Ng-Schauenburg Congruence Subgroup Theorem for modular categories, namely that the kernel of the $Γ_θ$ representation is a congruence subgroup. We prove this conjecture for any super-modular category that is a subcategory of modular category of twice its dimension, i.e. admitting a minimal modular extension. Conjecturally, every super-modular category admits (precisely 16) minimal modular extensions and, therefore, our conjecture would be a consequence.

math.QA↗