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

Secure function evaluation is a two-party cryptographic primitive where Bob computes a function of Alice's and his respective inputs, and both hope to keep their inputs private from the other party. It has been proven that perfect (or near…

Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates…

Quantum Hamiltonian Computing is a recent approach that uses quantum systems, in particular a single molecule, to perform computational tasks. Within this approach, we present explicit methods to construct logic gates using two different…

This paper introduces a symbolic calculus to evaluate the output signals at the target line(s) of quantum computing subcircuits using controlled negations and controlled-Q gates, where Q represents the k-th root of [0 1; 1 0], the unitary…

We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from…

We introduce a new technique proving formula size lower bounds based on the linear programming bound originally introduced by Karchmer, Kushilevitz and Nisan [11] and the theory of stable set polytope. We apply it to majority functions and…

We investigate fundamental bounds on the curvature of quantum correlation functions in imaginary time. Focusing first on topological phases, we show that quantum geometry can qualitatively modify the imaginary-time decay of correlations,…

Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…

Many quantum algorithms make use of oracles which evaluate classical functions on a superposition of inputs. In order to facilitate implementation, testing, and resource estimation of such algorithms, we present quantum circuits for…

In this paper we discuss an efficient technique that can implement any given Boolean function as a quantum circuit. The method converts a truth table of a Boolean function to the corresponding quantum circuit using a minimal number of…

Quantum computing is greatly advanced in recent years and is expected to transform the computation paradigm in the near future. Quantum circuit simulation plays a key role in the toolchain for the development of quantum hardware and…

As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…

One of the most important quantum algorithms ever discovered is Grover's algorithm for searching an unordered set. We give a new lower bound in the query model which proves that Grover's algorithm is exactly optimal. Similar to existing…

In the Hamiltonian formulation, Quantum Field Theory calculations scale exponentially with spatial volume, making real-time simulations intractable on classical computers and motivating quantum computation approaches. In Hamiltonian…

We prove a lower bound $\Omega\left(\frac{k+l}{k^2l^2}N^{2-\frac{k+l+2}{kl}}\right)$ on the maximal possible weight of a $(k,l)$-free (that is, free of all-ones $k\times l$ submatrices) Boolean circulant $N \times N$ matrix. The bound is…

With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…

A method for computing lower bounds on capacities of 2-dimensional constraints having a symmetric presentation in either the horizontal or the vertical direction is presented. The method is a generalization of the method of Calkin and Wilf…

Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…

The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…

We give a new version of the adversary method for proving lower bounds on quantum query algorithms. The new method is based on analyzing the eigenspace structure of the problem at hand. We use it to prove a new and optimal strong direct…