相关论文: Quantum Formulas: a Lower Bound and Simulation
We study the computation complexity of Boolean functions in the quantum black box model. In this model our task is to compute a function $f:\{0,1\}\to\{0,1\}$ on an input $x\in\{0,1\}^n$ that can be accessed by querying the black box.…
We present a formulation of quantum circuits where the focus is set on whether a given circuit (made of unitary operators and projective measurements with definite outcomes) does reflect an actually realizable physical experiment. In order…
In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide…
Quantum computers and simulators can potentially outperform classical computers in finding ground states of classical and quantum Hamiltonians. However, if this advantage can persist in the presence of noise without error correction remains…
Nielsen \cite{Nielsen05} recently asked the following question: "What is the minimal size quantum circuit required to exactly implement a specified $% \mathit{n}$-qubit unitary operation $U$, without the use of ancilla qubits?" Nielsen was…
One of the main goals in the study of quantum nonlocality is to determine the maximum violation achieved by quantum correlations in a Bell scenario. However, given a Bell inequality, there is no general algorithm to perform this task. As an…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, using quantum arguments. We prove these lower bounds using a quantum query algorithm for the…
This short note proposes a symbolic approach for representing and reasoning about quantum circuits using complex, vector or matrix-valued Boolean expressions. A major benefit of this approach is that it allows us to directly borrow the…
We prove a lower bound of $\Omega(n^2/\log^2 n)$ on the size of any syntactically multilinear arithmetic circuit computing some explicit multilinear polynomial $f(x_1, \ldots, x_n)$. Our approach expands and improves upon a result of Raz,…
Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable…
We establish connections between the size of circuits and formulas computing monotone Boolean functions and the size of first-order and nonrecursive Datalog rewritings for conjunctive queries over OWL 2 QL ontologies. We use known lower…
The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting…
We give a simple proof of a formula for the minimal time required to simulate a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with fast local unitaries. We also note that a related lower bound holds for arbitrary…
Several upper bounds on the size of quantum codes are derived using the linear programming approach. These bounds are strengthened for the linear quantum codes.
Several researchers, including Leonid Levin, Gerard 't Hooft, and Stephen Wolfram, have argued that quantum mechanics will break down before the factoring of large numbers becomes possible. If this is true, then there should be a natural…
Let X = (x_0,...,x_{n-1})$ be a sequence of n numbers. For \epsilon > 0, we say that x_i is an \epsilon-approximate median if the number of elements strictly less than x_i, and the number of elements strictly greater than x_i are each less…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
The problem of distinguishing between a random function and a random permutation on a domain of size $N$ is important in theoretical cryptography, where the security of many primitives depend on the problem's hardness. We study the quantum…
We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the…