Quantum Algorithms for Fermionic Quantum Field Theories

Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model, a theory in two spacetime dimensions with quartic interactions. The algorithm introduces new techniques to meet the additional challenges posed by the characteristics of fermionic fields, and its run time is polynomial in the desired precision and the energy. Thus, it constitutes further progress towards an efficient quantum algorithm for simulating the Standard Model of particle physics.Comment: 29 page

Quantum Algorithms for Quantum Field Theories

Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (phi-fourth theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm.Comment: v2: appendix added (15 pages + 25-page appendix

Quantum Computation of Scattering in Scalar Quantum Field Theories

Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally, and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling

Nested Hierarchical Dirichlet Processes

We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according to a document-specific distribution on a shared tree. This alleviates the rigid, single-path formulation of the nCRP, allowing a document to more easily express thematic borrowings as a random effect. We derive a stochastic variational inference algorithm for the model, in addition to a greedy subtree selection method for each document, which allows for efficient inference using massive collections of text documents. We demonstrate our algorithm on 1.8 million documents from The New York Times and 3.3 million documents from Wikipedia.Comment: To appear in IEEE Transactions on Pattern Analysis and Machine Intelligence, Special Issue on Bayesian Nonparametric

BQP-completeness of Scattering in Scalar Quantum Field Theory

Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.Comment: 41 pages, 7 figures. Corrected typo in foote

Thin and lumpy: an experimental investigation of water quality trading

Water quality trading schemes in the United States can predominantly be characterized by low trading volumes. In this paper we utilize laboratory economics experiments to explore the extent to which the technology through which pollution abatement is achieved influences market outcomes. Mirroring the majority of water quality trading markets, the sessions utilize small trading groups composed of six participants. To understand the extent to which abatement technology influences trading behavior, the experimental treatments vary the degree of heterogeneity in initial abatement costs and the potential for long-lived investments in cost-reducing abatement technology.Environmental Economics and Policy,

Polyoxometalate multi-electron-transfer catalytic systems for water splitting

The viable production of solar fuels requires a visible-light-absorbing unit, a H2O (or CO2) reduction catalyst (WRC), and a water oxidation catalyst (WOC) that work in tandem to split water or reduce CO2 with H2O rapidly, selectively, and for long periods of time. Most catalysts and photosensitizers developed to date for these triadic systems are oxidatively, thermally, and/or hydrolytically unstable. Polyoxometalates (POMs) constitute a huge class of complexes with extensively tunable properties that are oxidatively, thermally, and (over wide and adjustable pH ranges) hydrolytically stable. POMs are some of the fastest and most stable WOCs to date under optimal conditions. This Microreview updates the very active POM WOC field; it reports the application of POMs as WRCs and initial self-assembling metal oxide semiconductor–photosensitizer–POM catalyst triad photoanodes. The complexities of investigating these POM systems, including but not limited to the study of POM-hydrated metal-ion–metal-oxide speciation processes, are outlined. The achievements and challenges in POM WOC, WRC, and triad research are outlined