Related papers: Quantum Circuit for Calculating Symmetrized Functi…
This paper is a gentle but rigorous introduction to quantum computing intended for discrete mathematicians. Starting from a small set of assumptions on the behavior of quantum computing devices, we analyze their main characteristics,…
The Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced…
This work tests the performance of Grover's search circuits on some IBM superconducting quantum devices in case of the size of search space $N=2^4$ and $N=2^5$. Ideally, we expect to get an outcome probability distribution that is clearly…
In a recently developed approximation technique for quantum field theory the standard one-loop result is used as a seed for a recursive formula that gives a sequence of improved Gaussian approximations for the generating functional. In this…
Grover's search algorithm was originally proposed for circuit-based quantum computers. A crucial part of it is to query an oracle -- a black-box unitary operation. Generation of this oracle is formally beyond the original algorithm design.…
The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically…
An active area of investigation in the search for quantum advantage is Quantum Machine Learning. Quantum Machine Learning, and Parameterized Quantum Circuits in a hybrid quantum-classical setup in particular, could bring advancements in…
Quantum oracles are widely adopted in problems, like query oracle in Grover's algorithm, cipher in quantum cryptanalytic and data encoder in quantum machine learning. Notably, the bit-flip oracle, capable of flipping the state based on a…
Many quantum algorithms for attacking symmetric cryptography involve the rank problem of quantum linear equations. In this paper, we first propose two quantum algorithms for solving quantum linear systems of equations with coherent…
The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…
Alternative mathematical explorations in quantum computing can be of great scientific interest, especially if they come with penetrating physical insights. In this paper, we present a critical revisitation of our geometric (Clifford)…
Quantum computing is emerging as an important (but radical) technology that might take us beyond Moore's law for certain applications. Today, in parallel with improving quantum computers, computer scientists are relying heavily on quantum…
Logic entailment is essential to reasoning, but entailment checking has the worst-case complexity of an exponential of the variable size. With recent development, quantum computing when mature may allow an effective approach for various…
Random quantum circuits take an input quantum state and randomize it. This is a task with a growing number of identified uses in quantum information processing. We suggest a scheme to implement random circuits in a weighted graph state. The…
We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…
Grover recently presented the fixed-point search algorithm. In this letter, we study the fixed-point search algorithm obtained by replacing equal phase shifts of $\pi /3$ by different phase shifts.
The quantum walk is a quantum counterpart of the classical random walk. On the other hand, the absolute zeta function can be considered as a zeta function over F_1. This paper presents a connection between the quantum walk and the absolute…
In this paper we develop and compare different real-time methods to calculate spectral functions. These are classical-statistical simulations, the Gaussian state approximation (GSA), and the functional renormalization group (FRG) formulated…
The query model (or black-box model) has attracted much attention from the communities of both classical and quantum computing. Usually, quantum advantages are revealed by presenting a quantum algorithm that has a better query complexity…
Procedures are given below to construct symmetric and anti-symmetric quantum functions. If hidden in an oracle, such functions can be identified exactly, without iterative interrogation. This is another example of quantum search. The…