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Quantum computing (QC) emulators, which simulate quantum algorithms on classical hardware, are indispensable platforms for testing quantum algorithms before scalable quantum computers become widely available. A critical challenge in QC…
Quantum modular adders are one of the most fundamental yet versatile quantum computation operations. They help implement functions of higher complexity, such as subtraction and multiplication, which are used in applications such as quantum…
Quantum addition circuits are considered being of two types: 1) Toffolli-adder circuits which use only classical reversible gates (CNOT and Toffoli), and 2) QFT-adder circuits based on the quantum Fourier transformation. We present the…
Quantum gates and measurements on quantum hardware are inevitably subject to hardware imperfections that lead to quantum errors. Mitigating such unavoidable errors is crucial to explore the power of quantum hardware better. In this paper,…
We optimize the area and latency of Shor's factoring while simultaneously improving fault tolerance through: (1) balancing the use of ancilla generators, (2) aggressive optimization of error correction, and (3) tuning the core adder…
Quantum computers have the potential to break classical cryptographic systems by efficiently solving problems such as the elliptic curve discrete logarithm problem using Shor's algorithm. While resource estimates for factoring-based…
Quantum computer hardware is predicted to scale over hundreds of thousands of qubits coming online in the next decade. Despite significant theoretical and experimental QEC progress, quantum computer architecture has suffered a significant…
The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route towards a numerical…
Quantum computing has the potential to solve many complex algorithms in the domains of optimization, arithmetics, structural search, financial risk analysis, machine learning, image processing, and others. Quantum circuits built to…
Fault-tolerant quantum computing is a promising tool for simulating molecules and materials, but frequently-considered applications require substantial resources, and the gap between hardware capabilities and requirements remains…
Since Shor's proposition of the method for factoring products of prime numbers using quantum computing, there has been a quest to implement efficient quantum arithmetic algorithms. These algorithms are capable of applying arithmetic…
Quantum-dot Cellular Automata (QCA) is one of the emerging nanotechnologies, promising alternative to CMOS technology due to faster speed, smaller size, lower power consumption, higher scale integration and higher switching frequency. Also,…
We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders,…
Simulation of the Hubbard model is a leading candidate for the first useful applications of a fault-tolerant quantum computer. A recent study of quantum algorithms for early simulations of the Hubbard model [Kivlichan \textit{et al.}…
Considering its relevance in the field of cryptography, integer factorization is a prominent application where Quantum computers are expected to have a substantial impact. Thanks to Shor's algorithm this peculiar problem can be solved in…
Quantum phase estimation~(QPE) is central to numerous quantum algorithms, yet its standard implementation demands an $\calO(m^{2})$-gate quantum Fourier transform~(QFT) on $m$ control qubits-a prohibitive overhead on near-term noisy…
The optimal design of a fault-tolerant quantum computer involves finding an appropriate balance between the burden of large-scale integration of noisy components and the load of improving the reliability of hardware technology. This balance…
Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…
We introduce a truncated addition operation on pairs of N-bit binary numbers that interpolates between ordinary addition mod 2^N and bitwise addition in (Z/2Z)^N. We use truncated addition to analyze hash functions that are built from the…
Physical constraints and engineering challenges, including wafer dimensions, classical control cabling, and refrigeration volumes, impose significant limitations on the scalability of quantum computing units. As a result, a modular quantum…