Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) 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.

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 φ 4 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.

We derive factorization theorems for Λ QCD /m b power corrections to inclusive B-decays in the endpoint region, where m 2 X ∼ m b Λ QCD . In B → X u ℓν our results are for the full triply differential rate. A complete enumeration of Λ QCD /m b corrections is given. We point out the presence of new Λ QCD /m b -suppressed shape functions, which arise at tree level with a 4π-enhanced coefficient, and show that these previously neglected terms induce an additional significant uncertainty for current inclusive methods of measuring |V ub | that depend on the endpoint region of phase space.

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 $\phi^4$ 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.

We point out that in inclusive B → Xsℓ + ℓ − decay an angular decomposition provides a third (q 2 dependent) observable sensitive to a different combination of Wilson coefficients than the rate and the forward-backward asymmetry. Since a precise measurement of q 2 dependence requires large data sets, it is important to consider the data integrated over regions of q 2 . We develop a strategy to extract all measurable Wilson coefficients in B → Xsℓ + ℓ − from a few simple integrated rates in the low q 2 region. A similar decomposition in B → K * ℓ + ℓ − , together with the B → K * γ rate, also provides a determination of the Wilson coefficients, without reliance on form factor models and without having to measure the zero of the forward-backward asymmetry.

Dedicated to Professor Richard Askey on the occasion of his 65th birthday.Abstract. We study combinatorial aspects of q-weighted, length-L Forrester-Baxter paths,, and p and p ′ are co-prime.We obtain a bijection between P p,p ′ a,b,c (L) and partitions with certain prescribed hook differences. Thereby, we obtain a new description of the q-weights of P p,p ′ a,b,c (L). Using the new weights, and defining s 0 and r 0 to be the smallest non-negative integers for which |ps 0 − p ′ r 0 | = 1, we restrict the discussion to P p,p ′ s 0

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 φ 4 theory coupled to classical spacetime-dependent sources.

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