Related papers: A Quadratic Lower Bound for Simulation
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
One of the main aims in the field of quantum simulation is to achieve a quantum speedup, often referred to as "quantum computational supremacy", referring to the experimental realization of a quantum device that computationally outperforms…
Sample complexity bounds are a common performance metric in the Reinforcement Learning literature. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\gamma)$, where $\gamma…
Various fundamental phenomena of strongly-correlated quantum systems such as high-$T_c$ superconductivity, the fractional quantum-Hall effect, and quark confinement are still awaiting a universally accepted explanation. The main obstacle is…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
Scheduling with testing is a recent online problem within the framework of explorable uncertainty motivated by environments where some preliminary action can influence the duration of a task. Jobs have an unknown processing time that can be…
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…
The analysis of computer models can be aided by the construction of surrogate models, or emulators, that statistically model the numerical computer model. Increasingly, computer models are becoming stochastic, yielding different outputs…
Quantum circuit simulation is paramount to the verification and optimization of quantum algorithms, and considerable research efforts have been made towards efficient simulators. While circuits often contain high-level gates such as oracles…
This paper serves as a bridge between quantum computing and analogical modeling (a general theory for predicting categories of behavior in varying contexts). Since its formulation in the early 1980s, analogical modeling has been…
Applicative bisimulation is a coinductive technique to check program equivalence in higher-order functional languages. It is known to be sound, and sometimes complete, with respect to context equivalence. In this paper we show that…
We give a converging semidefinite programming hierarchy of outer approximations for the set of quantum correlations of fixed dimension and derive analytical bounds on the convergence speed of the hierarchy. In particular, we give a…
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
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…
What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer and Cirac [Phys. Rev. Lett. 88 (2002) 237902] have obtained a set of powerful results characterizing the time-optimal…
We propose a way of reasoning about minimal and maximal values of the weights of transitions in a weighted transition system (WTS). This perspective induces a notion of bisimulation that is coarser than the classic bisimulation: it relates…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
In this paper we study an extension of the Polynomial Calculus proof system where we can introduce new variables and take a square root. We prove that an instance of the subset-sum principle, the binary value principle, requires refutations…