arXiv subjects

Joshua M. Courtney

Publications and source records attributed to Joshua M. Courtney.

13 recordsLinked to original sources

arXiv2026

Simulation of Non-Hermitian Hamiltonians with Bivariate Quantum Signal Processing

We achieve query-optimal quantum simulations of non-Hermitian Hamiltonians $H_{\mathrm{eff}} = H_R + iH_I$, where $H_R$ is Hermitian and $H_I \succeq 0$, using a bivariate extension of quantum signal processing (QSP) with non-commuting signal operators. The algorithm encodes the interaction-picture Dyson series as a polynomial on the bitorus, implemented through a structured multivariable QSP (M-QSP) circuit. A constant-ratio condition guarantees scalar angle-finding for M-QSP circuits with arbitrary non-commuting signal operators. A degree-preserving sum-of-squares spectral factorization permits scalar complementary polynomials in two variables. Angles are deterministically calculated in a classical precomputation step, running in $\mathcal{O}(d_R \cdot d_I)$ classical operations. Operator norms $α_R\,,β_I$ contribute additively with query complexity $\mathcal{O}((α_R + β_I)T + \log(1/\varepsilon)/\log\log(1/\varepsilon))$ matching an information-theoretic lower bound in the separate-oracle model, where $H_R$ and $H_I$ are accessed through independent block encodings. The postselection success probability is $e^{-2β_I T}\|e^{-iH_{\mathrm{eff}}T}|ψ_0\rangle\|^2\cdot (1 - \mathcal{O}(\varepsilon))$, decomposing into a state-dependent factor $\|e^{-iH_{\mathrm{eff}}T}|ψ_0\rangle\|^2$ from the intrinsic barrier and an $e^{-2β_I T}$ overhead from polynomial block-encoding.

quant-ph↗

arXiv2026

Using Tanner Spectral Reduction to Improve Multi-Layer Optical Lattice Routing for Hypergraph-Product and Bivariate Bicycle qLDPC Codes

We characterize the Tanner graph spectrum of hypergraph-product (HGP) / lifted-product (LP) codes and bivariate-bicycle (BB) codes, informing qubit routing for three-dimensional reconfigurable qubit architectures. Syndrome-extraction routing depth on HGP/LP Tanner graphs reduces to a single SVD on the base parity-check matrix, using a spectral ratio $β_\text{HGP} = (1 + β_\text{base})/2$ where $β_\text{base} = σ_2(H)/σ_1(H)$ for the base parity-check matrix, and a diameter identity $D_T = 2 D_\text{base}$ where $D_\text{base}$ is the base Tanner graph diameter. Fourier spectral reduction reveals that the BB Tanner graph spectrum equals the union, over the $l \times m$ grid of characters of $\mathbb{Z}_l \times \mathbb{Z}_m$, of the singular values of a single $2 \times 2$ symbol matrix built from the two defining polynomials. This reduces spectral analysis from an $O((lm)^3)$ diagonalization of the $4lm$-node Tanner graph to $lm$ independent $2 \times 2$ SVDs. These results compose into a multi-layer three-dimensional AOL routing protocol with one-time setup cost $T_\text{Valiant} = O(\log N)$ atom rearrangements amortizable over a memory experiment of $R$ rounds. For a Tanner graph chromatic index $χ'$ and $L_\text{layers}$ stacked AOL planes, the per-syndrome-cycle depth is $\lceil χ'/L_\text{layers} \rceil$ AOL pattern activations with no atom motion, an $8\times$ step-count reduction at $L_\text{layers} \geq χ' = 8$. Contingent on multi-layer AOL hardware, this yields an estimated $\sim50-300\times$ per-cycle wall-clock advantage over a single-layer AOD baseline (degrading to $\sim5-100\times$ under AOD-crosstalk overhead), reducing to equality in the single-layer limit. This paper therefore presents a route toward practical routing improvement for future quantum hardware incorporating multi-layer reconfigurable qubit architectures.

quant-ph↗

arXiv2026

Quantum Algorithm for Open-System Battery Cathodes by Modeling Multiple Strongly Coupled Holstein Polarons with Chain-Mapped Caldeira-Leggett Dynamics

Cathode lithiation occupies a chemical regime of tightly localized orbitals, narrow bandwidths, and strong electron-lattice coupling. The defining electrochemical observables (open-circuit voltage and differential capacity) are open-system, reservoir-equilibration quantities that closed-Hamiltonian quantum simulation cannot produce, set by exchange with electron, Li$^+$, and phonon baths. We present a fault-tolerant quantum algorithm that recovers them through a unitary chain-mapped Caldeira-Leggett embedding, rendering the baths Trotterizable. The resulting fourth-order Trotter step has a T-gate count polynomial in system size, validating its open-system dynamics against hierarchical equations of motion (HEOM) at strong coupling and the Lindblad limit at weak coupling. For single-carrier olivine LiFePO$_4$, a single voltage anchor on an otherwise DFT-fixed Hamiltonian places the differential-capacity peak within the $\pm5$ mV reproducibility of the experimental plateau. For multi-carrier spinel LiMn$_2$O$_4$, whose $1{:}1$ Mn$^{3+}$/Mn$^{4+}$ filling makes the inter-site Coulomb repulsion dynamically active, the same kernel yields a two-plateau voltage curve with a $125$ mV split, within $17\%$ of the observed $150$ mV. We deliver an end-to-end fault-tolerant resource estimate for such a multi-carrier, three-reservoir observable: $368$ logical qubits and $\sim3\times10^5$ T-gates per step, or $\sim1.7\times10^{12}$ T-gates for a full voltage curve (parallelizable over $\sim10^3$ trajectories), leaving the production-scale dynamical run as a milestone for future hardware. The same kernel reproduces macroscopic quantum coherence, two-band superconductivity, and the Mikheyev-Smirnov-Wolfenstein resonance without modification, placing dynamical battery chemistry and similar Hamiltonians within scope for fault-tolerant quantum simulation.

quant-ph↗

arXiv2026

Permutation Routing on Ramanujan Hypergraphs with Applications to Neutral Atom Quantum Architectures

We consider the routing of neutral atoms on a reconfigurable lattice in terms of hypergraph transformations. We prove the routing number of a Ramanujan $(d,r)$-regular hypergraph on $N$ vertices satisfies $\mathrm{rt}(H) = Θ(\log N)$, where routing is via matchings in the clique expansion graph $G_{\mathrm{cl}}(H)$. Hypergraphs reframe the qubit routing problem by replacing Nenadov's two-sided spectral gap hypothesis with a one-sided condition based on eigenvalue centering. Song--Fan--Miao (SFM) coverings scale for Ramanujan families of every uniformity. A virtual overlay theorem establishes a capacity--depth tradeoff for 3D acousto-optic lens (AOL) architectures, with multi-layer stacking achieving $Θ(\log N)$ routing with $L = O(\log N)$ independent overlay layers. An abelian Alon--Boppana barrier shows that fixed-degree Cayley graphs on $\mathbb{Z}_n^2$ cannot be Ramanujan and affine derandomization on such graphs achieves 15--30% congestion reduction. Towers of $k$-fold Ramanujan coverings yield $\mathrm(H_L) = O(\log N)$ by recursive routing lift. Entanglement-assisted routing by pre-distributed Bell pairs achieves $O(\log N)$ teleportation depth with a stable crossover at $\sim\!4$ routing rounds. Displacement energy analyzes greedy adaptive routing, identifying stalling and a hybrid greedy--Valiant protocol achieving $\sim\!3\times$ speedup at practical scales. Hierarchical multi-scale routing achieves $O(\log^2 N / \log b)$ depth with boundary-only transfers at capacity $k = O(\sqrt{N} \log N)$, and $O(\log N)$ depth with optimal block size $b = Θ(\sqrt{n})$.

quant-ph↗

arXiv2026

Block Permutation Routing on Ramanujan Hypergraphs for Fault-Tolerant Quantum Computing

We analyze permutation routing of rigid blocks representing surface code patches of $d_C^2$ atoms on a reconfigurable lattice with hypergraph transformations. For a hypergraph $H$, code distance $d_C$, $s=d_C^2$, number of blocks $N_L$, and guard distance $g$, we show the block routing number $\mathrm{rt}_B(H, s, g) = Θ(d_C \log N_L)$. A spectral analysis of the quotient graph $Q(G_{\mathrm{cl}}(H), B)$ (blocks as supervertices) shows that the spectral ratio $β_Q < 1$ is preserved in the high-connectivity regime. Negative association of block permutations and congestion bounds are used for random intermediate configurations. Serialization establishes that each quotient routing phase requires $O(d_C)$ physical sub-steps due to the block footprint width. A lower bound $\mathrm{rt}_B = Ω(d_C \log N_L)$ follows from combining the spectral lower bound on quotient phases with the traversal cost per phase. We include error model analysis grounded in recent experimental results, syndrome extraction protocols (stop-and-correct, rolling active fault-tolerant (AFT) measurement, and adaptive deformation), and integration with lattice surgery compilation via the Litinski protocol. Composition with the correlated-decoding scheme reduces syndrome-extraction overhead from $O(d_C)$ to $O(1)$ per correction window, leaving routing as the leading-order contributor to the integrated $O(d_C \log N_L)$ depth. Spectral inheritance is organized in a hierarchy: exact (Haemers interlacing on equitable partitions), perturbative (Weyl bounds for near-equitable partitions, a practically relevant case for surface-code patches), and universal (higher-order Cheeger). Methods extend directly to QCCD trapped-ion architectures under the same regime condition, with junction crossings replacing AOD transports as the elementary single-hop translation.

quant-ph↗

arXiv2026

Optimal Bounds, Barriers, and Extensions for Non-Hermitian Bivariate Quantum Signal Processing

Multivariate quantum signal processing (M-QSP) has recently been shown to be applicable for non-Hermitian Hamiltonian simulation, opening several problems regarding the optimization landscape, angle-finding, and constant-factor analysis. We resolve several of these problems here. We find the anti-Hermitian query complexity $d_I = Θ(\betaI T + \log(1/\varepsilon)/\log\log(1/\varepsilon))$ to be tight, established via Chebyshev coefficient bounds, modified Bessel function asymptotics, and Lambert~$W$ inversion. Fast-forwarding to $d_I = \mathcal{O}(\sqrt{\betaI T})$ is impossible in the bivariate polynomial model, though a linear state-dependent improvement to $d_I = \mathcal{O} β_{\mathrm{eff}} T + \log(1/\varepsilon)/\log\log(1/\varepsilon))$ is achievable. The optimization landscape of M-QSP admits spurious local minima, but a warm-start basin guarantee ensures the two-stage algorithm converges. CRC-exploiting block peeling reduces angle-finding from $\mathcal{O}(d^3)$ to $\mathcal{O}(d^2)$ classical operations, and optimized error allocation yields a leading constant of approximately~$2$ relative to the information-theoretic lower bound. A constant-ratio condition extends to non-identical signal operators, enabling time-dependent non-Hermitian simulation with query complexity $\mathcal{O}(\int_0^T(\alphaR(s) + \betaI(s))\,ds + \log(1/\varepsilon)/\log\log(1/\varepsilon))$. Block-encoding overhead $e^{-2\betaI T}$ holds across all function classes within the walk-operator oracle model, and dilational methods (Schrödingerization) achieve the walk-operator barrier. A precisely characterized direct-access construction achieves the intrinsic barrier $e^{-2ωT}$ (with $ω< \betaI$ for non-commuting Hamiltonians) on a restricted domain, though extension to the full bitorus remains open.

quant-ph↗

arXiv2026

Variationally Compressing Quantum Circuits to Approximate Nonadiabatic Molecular Quantum Dynamics

Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably approximating deep circuits representing potential landscapes becomes crucial for simulating real quantum systems. Variationally approximating unitaries allows for shallower circuits and accuracy tunable to hardware fidelity, so long as the observable quantities are preserved. We show the variational compression of Trotter terms preserve reaction rate coefficients via classical emulation of a hybrid quantum-classical optimization method, as well as fast-forwarded adiabatic dynamics on quantum hardware. Compressed circuits can be incorporated with product-formula-based time evolution to approximate dynamics of a particle in two coupled harmonic potentials, allowing tunability when removing high-cost qubit interactions. Approximate rate coefficients are recovered after substituting terms in a nonadiabatic dynamic process, giving proof-of-principle for observable preservation under variational optimization. Attention is paid to minimizing qubit and gate-count resources.

quant-ph↗

arXiv2015

Predictions Wrong Again on Dead Zone Area -- Gulf of Mexico Gaining Resistance to Nutrient Loading

Mississippi River nutrient loads and water stratification on the Louisiana-Texas shelf contribute to an annually recurring, short-lived hypoxic bottom layer in areas of the northern Gulf of Mexico comprising less than 2% of the total Gulf of Mexico bottom area. This paper observes that the NOAA and LUMCON have now published errant predictions of possible record size areas of temporary bottom water hypoxia ("dead zones") three times since 2005, in 2008, 2011, and 2013 and that the LUMCON predictions of the area of hypoxic bottom water average 31% higher than the actual measured hypoxic areas from 2006 to 2014. These systematically high predictions depend on the assumption that the susceptibility of the Gulf of Mexico to forming hypoxic areas in response to nutrient loading has been relatively constant since 2001, though the susceptibility has been occasionally adjusted upward in different models. It has been previously suggested that tropical storms in a given year that occur on the Louisiana-Texas shelf between the peak nutrient loading in spring and formation of the hypoxic zone in summer can mitigate the size of the hypoxic zone that year through mixing of stratified well oxygenated lighter and warmer surface layers and oxygen depleted heavier and cooler bottom layers. This paper suggests several reasons why the Louisiana-Texas shelf may be systematically growing less susceptible to a given level of nutrient loading over time so that predictions based on the measured area of temporary bottom water hypoxia prior to 2006 tend to be too big in recent years.

q-bio.QM↗

arXiv2013

Comments on "Analysis of permanent magnets as elasmobranch bycatch reduction devices in hook-and-line and longline trials"

A recent study (Fish. Bull. 109:394-401 (2011)) purportedly tests two hypotheses: 1. that the capture of elasmobranchs would be reduced with hooks containing magnets in comparison with control hooks in hook-and-line and longline studies. 2. that the presence of permanent magnets on hooks would not alter teleost capture because teleosts lack the ampullary organ. Review of this paper shows some inconsistencies in the data supporting the first hypothesis and insufficient data and poor experimental design to adequately test the second hypothesis. Further, since several orders of teleosts are known to possess ampullary organs and demonstrate electroreception, grouping all teleosts in a study design or data analysis of magnetic hook catch rates is not warranted. Adequate tests of the hypothesis that permanent magnets or magnetized hooks do not alter teleost capture requires a more careful study design and much larger sample sizes than O'Connell et al. (Fish. Bull. 109:394-401 (2011)).

q-bio.PE↗

arXiv2013

National Oceanic and Atmospheric Administration Publishes Misleading Information on Gulf of Mexico "Dead Zone"

Mississippi River nutrient loads and water stratification on the Louisiana-Texas shelf contribute to an annually recurring, short-lived hypoxic bottom layer in areas of the northern Gulf of Mexico comprising less than 2% of the total Gulf of Mexico bottom area. Many publications demonstrate increases in biomass and fisheries production attributed to nutrient loading from river plumes. Decreases in fisheries production when nutrient loads are decreased are also well documented. However, the National Oceanic and Atmospheric Administration (NOAA) persists in describing the area adjacent to the Mississippi River discharge as a "dead zone" and predicting dire consequences if nutrient loads are not reduced. In reality, these areas teem with aquatic life and provide 70-80% of the Gulf of Mexico fishery production. On June 18, 2013, NOAA published a misleading figure purporting to show the "dead zone" in an article predicting a possible record dead zone area for 2013 (http://www.noaanews.noaa.gov/stories2013/20130618_deadzone.html). This area is not a region of hypoxic bottom water at all nor is it related directly to 2013 predicted hypoxia. This figure appeared as early as 2004 in a National Aeronautics and Space Administration (NASA) article (http://www.nasa.gov/vision/earth/environment/dead_zone.html) as a satellite image where the red area represents turbidity and is much larger than the short-lived areas of hypoxic bottom water documented in actual NOAA measurements. Thus, it is misleading for NOAA to characterize the red area in that image as a "dead zone." The NOAA has also published other misleading and exaggerated descriptions of the consequences of nutrient loading.

q-bio.PE↗

arXiv2013

Nutrient Loading Increases Red Snapper Production in the Gulf of Mexico

A large, annually recurring region of hypoxia in the northern Gulf of Mexico has been attributed to water stratification and nutrient loading of nitrogen and phosphorus delivered by the Mississippi and Atchafalaya rivers. This nutrient loading increased nearly 300% since 1950, primarily due to increased use of agricultural fertilizers. Over this same time period, the red snapper (Lutjanus campechanus) population in the Gulf of Mexico has shifted strongly from being dominated by the eastern Gulf of Mexico to being dominated by the northern and western Gulf of Mexico, with the bulk of the current population in the same regions with significant nutrient loading from the Mississippi and Atchafalaya rivers and in or near areas with development of mid-summer hypoxic zones. The population decline of red snapper in the eastern Gulf is almost certainly attributable to overfishing, but the cause of the population increase in the northern and western Gulf is subject to broad debate, with the impact of artificial reefs (primarily oil platforms which have incr eased greatly since the 1960s) being the most contentious point. Nutrient loading has been shown to positively impact secondary production of fish in many marine systems. The present paper offers the hypothesis that increased nutrient loading has contributed significantly to increased red snapper population in the northern and western Gulf of Mexico. Nutrient loading may be working in synergy with the abundant oil platforms both increasing primary production and providing structure encouraging red snapper to feed throughout the water column.

q-bio.PE↗

arXiv2013

Do Rainbow Trout and Their Hybrids Outcompete Cutthroat Trout in a Lentic Ecosystem?

Much has been written about introduced rainbow trout interbreeding and outcompeting native cutthroat trout. However, specific mechanisms have not been thoroughly explored, and most data is limited to lotic ecosystems. Samples of Snake River cutthroat trout (Oncorhynchus clarkii bouvieri), the rainbow-cutthroat hybrid, the cutbow trout (Onchorhynchus mykiss x clarkii), and rainbow trout (Oncorhynchus mykiss), were obtained from a lentic ecosystem (Eleven Mile Reservoir, Colorado) by creel surveys conducted from May to October, 2012. The total length and weight of each fish was measured and the relative condition factor of each fish was computed using expected weight from weight-length relationships from the Colorado Division of Parks and Wildlife (CDPW). Data from the CDPW collected from 2003-2010 in the same lentic ecosystem were used to compute relative condition factors for additional comparison, as was independent creel survey data from 2011. Cutthroat trout were plump: the mean relative condition factor of the cutthroat trout was 112.0% (+/- 1.0%). Cutbow hybrid trout were close to the expected weights with a mean relative condition factor of 99.8% (+/- 0.6%). Rainbow trout were thinner with a mean relative condition factor of 96.4% (+/- 1.4%). Comparing mean relative condition factors of CDPW data from earlier years and plotting the 2012 data relative to percentile curves also shows the same trend of cutthroat trout being plumper than expected and rainbow trout being thinner than the cutthroat trout, with the hybrid cutbow trout in between. This data supports the hypothesis that rainbow trout do not outcompete cutthroat trout in lentic ecosystems. Comparison with data from three other Colorado reservoirs also shows that cutthroat trout tend to be more plump than rainbow trout and their hybrids in sympatric lentic ecosystems.

q-bio.PE↗

arXiv2013

Estimating Interaction Strengths with Correlations in Annual Relative Weight: Interspecific Competition and Predation in Fishes, Pueblo Reservoir, Colorado

Quantifying interaction strength between species is of interest in food web studies for understanding population dynamics. Theory has run ahead of experiment in solving equations describing ecological systems (the Lotka-Volterra equations, for example). Modeling approaches depend upon quantitative knowledge of interaction strengths among species, yet there are few methods available for estimating strengths of interactions between species, especially in the field. Competition and predation in fishes is traditionally studied with a variety of methods, most requiring extensive sampling to determine stock densities or extensive stomach content or isotope analysis. Average relative weight of fish species in an ecosystem can usually be accurately determined with much smaller sample sizes than required for accurate determination of stock densities. Correlations of mean annual relative weights may be used to test hypotheses and establish interaction strengths regarding competition and predation among fishes. The trends are sufficiently suggestive to use a strong positive correlation as supporting evidence of competition and possibly indicative of the magnitude of competition if other evidence such as analysis of stomach contents is also present. Likewise, a strong negative correlation might be interpreted as relevant when forming a hypothesis of predation and as supporting evidence of the magnitude of predation if other evidence is also present. In systems where regular weight and length survey data are available, this method can suggest the likely strength of competitive and predatory relationships and may be more cost effective than stomach content or isotope analysis.

q-bio.PE↗