相关论文: Quantum Formulas: a Lower Bound and Simulation

The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…

We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…

Simon in his FOCS'94 paper was the first to show an exponential gap between classical and quantum computation. The problem he dealt with is now part of a well-studied class of problems, the hidden subgroup problems. We study Simon's problem…

It has been proved that almost all $n$-bit Boolean functions have exact classical query complexity $n$. However, the situation seemed to be very different when we deal with exact quantum query complexity. In this paper, we prove that almost…

Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schr\"odinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately…

We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of…

Starting with an infinite set of non linear Equations for the Li-Keiper coefficients, we first specify a lower bound emerging from the infinite set and give a characterization of it. Then, we propose a possible new upper and lower bound for…

Sign problem in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches…

We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…

We introduce two kinds of quantum algorithms to explore microcanonical and canonical properties of many-body systems. The first one is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a…

Quantum information science currently poses a troubling contradiction. It can be summarized as: (1) To factor efficiently, quantum computers must perform exponentially precise energy estimation. (2) Exponentially precise energy estimation…

Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…

Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have…

A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…

We establish an isomorphism between quantum circuits and a subspace of polyatomic molecules, which suggests that molecules can be used as descriptors of quantum circuits for quantum machine learning. Our numerical results show that the…

In this paper, we investigate an approach to circuit lower bounds via bounded width circuits. The approach consists of two steps: (i) We convert circuits to (deterministic or nondeterministic) bounded width circuits. (ii) We prove lower…

In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum…

We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…

We consider the possibility of encoding m classical bits into much fewer n quantum bits so that an arbitrary bit from the original m bits can be recovered with a good probability, and we show that non-trivial quantum encodings exist that…

Product formulas are one of the main approaches for quantum simulation of the Hamiltonian dynamics of a quantum system. Their implementation cost is computed based on error bounds which are often pessimistic, resulting in overestimating the…