arXiv subjects

Erik Davis

Publications and source records attributed to Erik Davis.

8 recordsLinked to original sources

arXiv2026

Fast, High-Fidelity Erasure Detection of Dual-Rail Qubits with Symmetrically Coupled Readout

Erasure qubits are a promising platform for implementing hardware-efficient quantum error correction. Realizing the error-correction advantages of this encoding requires frequent mid-circuit erasure checks that are fast, high-fidelity, and scalable. Here, we realize erasure detection with a hardware-efficient circuit consisting of a single readout resonator dispersively and symmetrically coupled to both transmons of a dual-rail qubit. We use this circuit to demonstrate single-shot erasure detection in 384 ns with minimal impact on the dual-rail logical manifold, achieving a residual error per check of $6.0(2) \times 10^{-4}$, with only $8(3) \times 10^{-5}$ induced dephasing per check, and an erasure error per check of $2.54(1)\times 10^{-2}$. The high degree of matched dispersive readout coupling ($\chi$-matching) within the dual-rail qubit code space also allows us to realize a new modality: time-continuous erasure detection performed in parallel with single-qubit gates. Here we achieve a median $7.2 \times 10^{-5}$ error per gate with $< 1 \times 10^{-5}$ error induced by erasure detection. This demonstrates a reduction in erasure detection overhead as well as a crucial ingredient for soft information quantum error correction. Together, these results establish symmetrically coupled dispersive readout as a fast, hardware-efficient, and scalable component for erasure-based quantum error correction using transmon dual-rail qubits.

quant-ph↗

arXiv2025

Hecke $L$-series for Sinha modules

We investigate Goss $L$-functions associated to Anderson $t$-modules defined by Sinha having complex multiplication by Carlitz cyclotomic fields. We show that these $t$-modules are defined over the cyclotomic field and that their $L$-functions are products of Hecke $L$-series for Anderson's Hecke character defined via Coleman functions. Applying identities of Fang and Taelman, we prove that special values of these $L$-functions are expressible in terms of products of values of Thakur's geometric $\Gamma$-function.

math.NT↗

arXiv2025

Heuristics for (ir)reducibility of $p$-rank strata of the moduli space of hyperelliptic curves

Let $\mathcal{H}_g$ denote the moduli space of smooth hyperelliptic curves of genus $g$ in characteristic $p\geq 3$, and let $\mathcal{H}_g^f$ denote the $p$-rank $f$ stratum of $\mathcal{H}_g$ for $0 \leq f \leq g$. Achter and Pries note in their 2011 work that determining the number of irreducible components of $\mathcal{H}_g^f$ would lead to several intriguing corollaries. In this paper, we present a computational approach for estimating the number of irreducible components in various $p$-rank strata. Our strategy involves sampling curves over finite fields and calculating their $p$-ranks. From the data gathered, we conjecture that the non-ordinary locus is geometrically irreducible for all genera $g> 1$. The data also leads us to conjecture that the moduli space $\mathcal{H}^{g-2}_g$ is irreducible and suggests that $\mathcal{H}^f_g$ is irreducible for all $1 \leq f \leq g$. We conclude with a brief discussion on $\mathcal{H}^0_g$.

math.AG↗

arXiv2024

Hardware-efficient quantum error correction via concatenated bosonic qubits

In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead typically associated with error correction motivates the search for more hardware-efficient approaches. Here, using a microfabricated superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance $d=5$. The bosonic cat qubits are passively protected against bit flips using a stabilizing circuit. Cat-qubit phase-flip errors are corrected by the repetition code which uses ancilla transmons for syndrome measurement. We realize a noise-biased CX gate which ensures bit-flip error suppression is maintained during error correction. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold, with logical phase-flip error decreasing with code distance from $d=3$ to $d=5$. Concurrently, the logical bit-flip error is suppressed with increasing cat-qubit mean photon number. The minimum measured logical error per cycle is on average $1.75(2)\%$ for the distance-3 code sections, and $1.65(3)\%$ for the longer distance-5 code, demonstrating the effectiveness of bit-flip error suppression throughout the error correction cycle. These results, where the intrinsic error suppression of the bosonic encodings allows us to use a hardware-efficient outer error correcting code, indicate that concatenated bosonic codes are a compelling paradigm for reaching fault-tolerant quantum computation.

quant-ph↗

arXiv2023

Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons

Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a "dual-rail qubit" consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon $T_1$ errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability $p_\text{erasure} = 2.19(2)\times 10^{-3}$ per gate while the residual errors are $\sim 40$ times lower. We further demonstrate mid-circuit detection of erasure errors while introducing $< 0.1\%$ dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction.

quant-ph↗

arXiv2019

Automated quantum programming via reinforcement learning for combinatorial optimization

We develop a general method for incentive-based programming of hybrid quantum-classical computing systems using reinforcement learning, and apply this to solve combinatorial optimization problems on both simulated and real gate-based quantum computers. Relative to a set of randomly generated problem instances, agents trained through reinforcement learning techniques are capable of producing short quantum programs which generate high quality solutions on both types of quantum resources. We observe generalization to problems outside of the training set, as well as generalization from the simulated quantum resource to the physical quantum resource.

quant-ph↗

arXiv2017

Approximating geodesics via random points

Given a `cost' functional $F$ on paths $γ$ in a domain $D\subset\mathbb{R}^d$, in the form $F(γ) = \int_0^1 f(γ(t),\dotγ(t))dt$, it is of interest to approximate its minimum cost and geodesic paths. Let $X_1,\ldots, X_n$ be points drawn independently from $D$ according to a distribution with a density. Form a random geometric graph on the points where $X_i$ and $X_j$ are connected when $0<|X_i - X_j|<ε$, and the length scale $ε=ε_n$ vanishes at a suitable rate. For a general class of functionals $F$, associated to Finsler and other distances on $D$, using a probabilistic form of Gamma convergence, we show that the minimum costs and geodesic paths, with respect to types of approximating discrete `cost' functionals, built from the random geometric graph, converge almost surely in various senses to those corresponding to the continuum cost $F$, as the number of sample points diverges. In particular, the geodesic path convergence shown appears to be among the first results of its kind.

math.PR↗

arXiv2016

Consistency of modularity clustering on random geometric graphs

We consider a large class of random geometric graphs constructed from samples $\mathcal{X}_n = \{X_1,X_2,\ldots,X_n\}$ of independent, identically distributed observations of an underlying probability measure $ν$ on a bounded domain $D\subset \mathbb{R}^d$. The popular `modularity' clustering method specifies a partition $\mathcal{U}_n$ of the set $\mathcal{X}_n$ as the solution of an optimization problem. In this paper, under conditions on $ν$ and $D$, we derive scaling limits of the modularity clustering on random geometric graphs. Among other results, we show a geometric form of consistency: When the number of clusters is a priori bounded above, the discrete optimal partitions $\mathcal{U}_n$ converge in a certain sense to a continuum partition $\mathcal{U}$ of the underlying domain $D$, characterized as the solution of a type of Kelvin's shape optimization problem.

math.PR↗