Related papers: A Classical-Quantum Adder with Constant Workspace …
The question of finding a lower bound on the number of Toffoli gates in a classical reversible circuit is addressed. A method based on quantum information concepts is proposed. The method involves solely concepts from quantum information -…
Windowed arithmetic [Gidney, 2019] is a technique for reducing the cost of quantum arithmetic circuits with space--time tradeoffs using memory queries to precomputed tables. It can reduce the asymptotic cost of modular exponentiation from…
Physical implementation of scalable quantum architectures faces an immense challenge in form of fragile quantum states. To overcome it, quantum architectures with fault tolerance is desirable. This is achieved currently by using surface…
We study the achievements of quantum circuits comprised of several one- and two-qubit gates. Quantum process matrices are determined for the basic one- and two-qubit gate operations and concatenated to yield the process matrix of the…
Algorithms for quantum information processing are usually decomposed into sequences of quantum gate operations, most often realized with single- and two- qubit gates[1]. While such operations constitute a universal set for quantum…
Three-qubit quantum gates are key ingredients for quantum error correction and quantum information processing. We generate quantum-control procedures to design three types of three-qubit gates, namely Toffoli, Controlled-Not-Not and Fredkin…
Quantum addition based on the quantum Fourier transform can be an integral part of a quantum circuit and proved to be more efficient than the existing classical ripple carry adder. Our study includes identifying the quantum resource…
Quantum formulas, defined by Yao [FOCS '93], are the quantum analogs of classical formulas, i.e., classical circuits in which all gates have fanout one. We show that any read-once quantum formula over a gate set that contains all…
Qutrit (or ternary) structures arise naturally in many quantum systems, particularly in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and quantum arithmetics. Our main result is the derivation of…
The von Neumann architecture for a classical computer comprises a central processing unit and a memory holding instructions and data. We demonstrate a quantum central processing unit that exchanges data with a quantum random-access memory…
Quantum-enhanced auxiliary field quantum Monte Carlo (QC-AFQMC) uses output from a quantum computer to increase the accuracy of its classical counterpart. The algorithm requires the estimation of overlaps between walker states and a trial…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
Universal quantum entangling gates are a crucial building block in the large-scale quantum computation and quantum communication, and it is an important task to find simple ways to implement them. Here an effective quantum circuit for the…
In this work, we revisit prefix sums through the lens of linear algebra. We describe an identity that decomposes triangular all-ones matrices as a sum of two Kronecker products, and apply it to design recursive prefix sum algorithms and…
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 propose a scheme to achieve quantum computation with neutral atoms whose interactions are catalyzed by single photons. Conditional quantum gates, including an $N$-atom Toffoli gate and nonlocal gates on remote atoms, are obtained through…
Implementing quantum algorithms on realistic hardware requires translating high-level global operations into sequences of native elementary gates, a process known as quantum compiling. Physical limitations, such as constraints in…
Universal quantum gates and quantum error correction~(QEC) lie in the heart of quantum information science. Large-scale quantum computing depends on a universal set of quantum gates, in which some gates may be easily carried out, while…
Quantum algorithms are a promising framework for unfolding the causal configurations of multiloop Feynman diagrams, which is equivalent to querying the \textit{directed acyclic graph} (DAG) configurations of undirected graphs in graph…
Efficient constructions for quantum logic are essential since quantum computation is experimentally challenging. This thesis develops quantum logic synthesis as a paradigm for reducing the resource overhead in fault-tolerant quantum…