Chronological feed of everything captured from Daniel Gottesman.
paper / danielgottesman / Apr 13
Distributive lattices possess pure minimal injective coresolutions if and only if specific antichain modules are perfect, under minimal canonical resolution assumptions. The paper classifies such perfect antichain modules and translates the condition into lattice-theoretic terms for incidence algebras. This resolves an open question by exhibiting Auslander-Gorenstein PI rings lacking pure injective coresolutions.
lattice-theoryhomological-algebraincidence-algebrasinjective-resolutionsperfect-modulesrepresentation-theorydistributive-lattices
“A lattice is distributive if and only if its incidence algebra is Auslander regular.”
paper / danielgottesman / Apr 13
Formulates large-scale tote consolidation in fulfillment centers as MORL to balance speed, resources, and space under constraints. Leverages best-response and no-regret dynamics for principled minimax policy learning in high-dimensional states. Simulations show a single policy satisfying all constraints; introduces framework mitigating error cancellation oscillations for stable solutions.
multi-objective-rlreinforcement-learningwarehouse-optimizationhuman-robot-collaborationlogistics-automationconstrained-rlmorl
“Tote allocation involves trading off processing speed, resource usage, and space utilization under operational constraints.”
paper / danielgottesman / Feb 13
This paper demonstrates fundamental limitations in achieving fault-tolerant implementations of the full Clifford group for quantum codes encoding multiple logical qubits. Through a series of no-go theorems, it
quantum-computationfault-tolerancequantum-error-correctionstabilizer-codesquantum-clifford-groupno-go-theoremquantum-gadgets
“No stabilizer code can implement the full Clifford group transversally on more than one logical qubit.”
paper / danielgottesman / Oct 11
This paper significantly refines the upper bound for $N_0$, the minimum number of qubits required for an eventually universal quantum gate set to achieve universality. The previous bound of $d^8n$ is reduced to $d^4n$, offering a more precise understanding of the qubit scaling required for universal quantum computation. This improved bound has practical implications for the design and analysis of quantum computing systems.
quantum-computingquantum-gatesquantum-systemstheoretical-physicscomputational-complexityquantum-algorithms
“The upper bound for $N_0$ (the minimum number of qubits for an eventually universal gate set) has been improved.”
paper / danielgottesman / Oct 9
A novel method combining quantum-inspired algorithms and quantum information processing dramatically reduces the photon requirement for measuring gravitational microlensing time delays. This advancement enables observations previously impossible due to photon flux and signal coherence constraints. The technique saturates a provable lower bound on photon count, offering significant improvements for both calibrating optical interferometric telescopes and direct mass measurements of microlensing events.
quantum-information-processinggravitational-lensingastrophysicsmicrolensingquantum-algorithmsastronomical-instrumentation
“A new quantum-based method measures astrophysical time delays using exponentially fewer photons than prior methods.”
paper / danielgottesman / Aug 29
The rotation-invariant Hamiltonian problem, a variant of the local Hamiltonian problem with translational and rotational lattice invariance, is proven to be QMA$_{EXP}$-complete. This complexity holds even with arbitrary but fixed lattice dimensions and scaled lattice lengths, extending previous findings for one-dimensional cases and addressing an open question in computational complexity.
quantum-physicscomputational-complexityhamiltonian-problemqma-exp-completequantum-computation
“The rotation-invariant Hamiltonian problem is QMA$_{EXP}$-complete.”
paper / danielgottesman / Aug 13
This paper presents a general framework for fault-tolerant quantum computation encoded in Majorana hardware (nanowires and neutral fermionic atoms), closing a gap where prior schemes were either code-family-specific or incomplete. The authors address the even/odd Majorana code distinction systematically, deriving transversal Clifford gadgets, a Steane-inspired fault-tolerant measurement scheme, and a novel quantum reference frame construction for odd codes that circumvents parity superselection constraints. Notably, they also identify odd Majorana codes with transversal T gates and construct a high-rate quantum LDPC Majorana code, demonstrating that all required primitives for universal fault-tolerant computation are realizable on fermionic hardware.
fault-tolerant-quantum-computingmajorana-codesquantum-error-correctionquantum-ldpc-codestopological-qubitsfermionic-hardwareclifford-gates
“A general, code-family-agnostic fault-tolerant framework for Majorana-based quantum computation covering state preparation, gates, and measurements has been developed.”