Related papers: Quantum binary field multiplication with subquadra…
Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor's algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary…
The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete…
Mutually unbiased bases (MUBs) play a crucial role in numerous applications within quantum information science, such as quantum state tomography, error correction, entanglement detection, and quantum cryptography. Utilizing \(2^n + 1\) MUB…
Numerous scientific developments in this NISQ-era (Noisy Intermediate Scale Quantum) have raised the importance for quantum algorithms relative to their conventional counterparts due to its asymptotic advantage. For resource estimates in…
We prove that constant-depth quantum circuits are more powerful than their classical counterparts. To this end we introduce a non-oracular version of the Bernstein-Vazirani problem which we call the 2D Hidden Linear Function problem. An…
In some quantum algorithms, arithmetic operations are of utmost importance for resource estimation. In binary quantum systems, some efficient implementation of arithmetic operations like, addition/subtraction, multiplication/division,…
The problem of finding efficient decompositions of multi-qubit gates is of importance for quantum computing, especially, in application to existing noisy intermediate-scale quantum devices, whose resources are substantially limited. Here we…
Quantum image processing is one of the promising fields of quantum information. The complexity overhead to design circuits to represent quantum images is a significant problem. So, we proposed a new method to minimize the total number…
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…
We propose a new quantum circuit for the quantum search problem. The quantum circuit is superior to Grover's algorithm in some realistic cases. The reasons for the superiority are in short as follows: In the quantum circuit proposed in this…
Efficient quantum arithmetic circuits are commonly found in numerous quantum algorithms of practical significance. Till date, the logarithmic-depth quantum adders includes a constant coefficient k >= 2 while achieving the Toffoli-Depth of…
Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, by F\"{u}rer, shows that two $n$-bit numbers can be multiplied via a boolean circuit of size $O(n \lg…
A Toffoli gate ($C^{n}$-NOT gate) is regarded as an important unitary gate in quantum computation, and is simulated by a quantum circuit composed of $C^{2}$-NOT gates. This paper presents a quantum circuit with a new configuration of…
The matrices that can be exactly represented by a circuit over the Toffoli-Hadamard gate set are the orthogonal matrices of the form $M/ \sqrt{2}{}^k$, where $M$ is an integer matrix and $k$ is a nonnegative integer. The exact synthesis…
Quantum computation is conventionally performed using quantum operations acting on two-level quantum bits, or qubits. Qubits in modern quantum computers suffer from inevitable detrimental interactions with the environment that cause errors…
Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible…
This study presents a quantum circuit for estimating the pi value using arithmetic circuits and by quantum amplitude estimation. We review two types of quantum multipliers and propose quantum squaring circuits based on the multiplier as…
We introduce a fault-tolerant construction to implement a composite quantum operation of four overlapping Toffoli gates. The same construction can produce two independent Toffoli gates. This result lowers resource overheads in designs for…
We present two new constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T =…
Most of the work on implementing arithmetic on a quantum computer has borrowed from results in classical reversible computing (e.g. [VBE95], [BBF02], [DKR04]). These quantum networks are inherently classical, as they can be implemented with…