Related papers: An Almost-Quadratic Lower Bound for Quantum Formul…
We introduce new semi-algebraic proof systems for Quantified Boolean Formulas (QBF) analogous to the propositional systems Nullstellensatz, Sherali-Adams and Sum-of-Squares. We transfer to this setting techniques both from the QBF…
This memoir contains an overview of the proof of the bounded $L^2$ curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the $L^2$-norm of the…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
We study the close connection between rational functions that approximate a given Boolean function, and quantum algorithms that compute the same function using postselection. We show that the minimal degree of the former equals (up to a…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
Precise measurements of tiny forces and displacements play an important role in science and technology. The precision of recent experiments, while beginning to reach the limits imposed by quantum mechanics, is necessarily spoiled by the…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
This article surveys the state of the art in quantum computer algorithms, including both black-box and non-black-box results. It is infeasible to detail all the known quantum algorithms, so a representative sample is given. This includes a…
This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
We study the power of nonadaptive quantum query algorithms, which are algorithms whose queries to the input do not depend on the result of previous queries. First, we show that any bounded-error nonadaptive quantum query algorithm that…
In a recent paper [2], Chang et al. have proposed studying "Quantum $\mathbb{F}_{un}$": the $q \mapsto 1$ limit of Modal Quantum Theories over finite fields $\mathbb{F}_q$, motivated by the fact that such limit theories can be naturally…
We apply our recent Quantum Approximate Optimization Algorithm to the combinatorial problem of bounded occurrence Max E3LIN2. The input is a set of linear equations each of which contains exactly three boolean variables and each equation…
We use mirror symmetry, quantum geometry and modularity properties of elliptic curves to calculate the refined free energies in the Nekrasov-Shatashvili limit on non-compact toric Calabi-Yau manifolds, based on del Pezzo surfaces. Quantum…
The quantum approximate optimization algorithm (QAOA) and quantum annealing are two of the most popular quantum optimization heuristics. While QAOA is known to be able to approximate quantum annealing, the approximation requires QAOA angles…
Quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set. It has been shown that this is possible for almost all choices of base sets and furthermore that…
We present an algorithm for computing limits of quotients of real analytic functions. The algorithm is based on computation of a bound on the Lojasiewicz exponent and requires the denominator to have an isolated zero at the limit point.
We will try to explore, primarily from the complexity-theoretic point of view, limitations of error-correction and fault-tolerant quantum computation. We consider stochastic models of quantum computation on $n$ qubits subject to noise…
The main result of this paper shows that "test configurations" give new lower bounds on the $L^{2}$ norm of the scalar curvature on a Kahler manifold. This is closely analogous to the analysis of the Yang-Mills functional over Riemann…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…