Related papers: Quantum binary field inversion: improved circuit d…
Quantum simulations of scalar quantum field theories (QFT) provide important benchmarks for demonstrating quantum advantage. We revisit digitization in the occupation basis, which is typically hindered by unfavorable circuit depth scaling.…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
Advancements in gravitational-wave interferometers, particularly the next generation, are poised to profoundly impact gravitational wave astronomy and multimessenger astrophysics. A hybrid quantum algorithm is proposed to carry out quantum…
The study of real-time evolution of lattice quantum field theories using classical computers is known to scale exponentially with the number of lattice sites. Due to a fundamentally different computational strategy, quantum computers hold…
Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit…
In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup \Gamma^0(N), with respect to the usual fundamental domain FN, where N is assumed prime. The cycles Q_1, . . ., Q_n that…
Using the tensor product representation in the density matrix renormalization group, we show that a quantum circuit of Grover's algorithm, which has one-qubit unitary gates, generalized Toffoli gates, and projective measurements, can be…
Optimization of quantum circuits using an efficient compiler is key to its success for NISQ computers. Several 3rd party compilers are evolving to offer improved performance for large quantum circuits. These 3rd parties, or just a certain…
Recently, a polynomial time classical algorithm has been found for learning the shallow representation of a unitary $U$ acting on $n$-qubits, by learning local inversions and then sewing them back together with ancilla qubits and SWAP…
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we describe some simple techniques aimed at performing…
A theoretical spin-based scheme for performing a variety of quantum computations is presented. It makes use of an array of multiple identical computer vectors of phosphorus-doped silicon where the nuclei serve as logical qubits and the…
We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…
Variational quantum algorithms that are used for quantum machine learning rely on the ability to automatically differentiate parametrized quantum circuits with respect to underlying parameters. Here, we propose the rules for differentiating…
The Quantum Fourier Transform (QFT) is a fundamental component of many quantum computing algorithms. In this paper, we present an alternative method for factoring this transformation. Inspired by this approach, we introduce a new quantum…
Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the…
Quantum Information Theory promises to speed up computation so is observed in real quantum computers as proved to its classical counterpart. This revolutionizes every field linked directly or indirectly with computation. Grover algorithm in…
Developing methods to solve nuclear many-body problems with quantum computers is an imperative pursuit within the nuclear physics community. Here, we introduce a quantum algorithm to accurately and precisely compute the ground state of…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
In this paper, we develop a Lie group theoretic approach for parametric representation of unitary matrices. This leads to develop a quantum neural network framework for quantum circuit approximation of multi-qubit unitary gates. Layers of…
In order to understand the bounds of utilization of the Grover's search algorithm for the large unstructured data in presence of the quantum computer noise, we undertake a series of simulations by inflicting various types of noise, modelled…