Related papers: Synthesizing Quantum Circuits for Simple Periodic …
Topological quantum computation has been extensively studied due to its robustness against decoherence. A conventional way to realize it is by adiabatic operations---it requires relatively long time to accomplish so that the speed of…
In this paper we discuss the problem of performing elementary finite field arithmetic on a quantum computer. Of particular interest, is the controlled-multiplication operation, which is the only group-specific operation in Shor's algorithms…
Classical simulations of quantum circuits are essential for verifying and benchmarking quantum algorithms, particularly for large circuits, where computational demands increase exponentially with the number of qubits. Among available…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
We generalize quantum circuits for the Toffoli gate presented by Selinger and Jones for functionally controlled NOT gates, i.e., $X$ gates controlled by arbitrary $n$-variable Boolean functions. Our constructions target the gate set…
MQuantum algorithms of matrix operations are of great significance in many fields in science and technology. In this paper, by leveraging multi-qubit Toffoli gates and basic single-qubit operations, the quantum algorithms of matrix…
Shor's factoring algorithm (SFA), by its ability to efficiently factor large numbers, has the potential to undermine contemporary encryption. At its heart is a process called order finding, which quantum mechanics lets us perform…
Quantum algorithms often benefit from the ability to execute multi-qubit (>2) gates. To date such multi-qubit gates are typically decomposed into single- and two-qubit gates, particularly in superconducting qubit architectures. The ability…
Quantum computing has transformative computational power to make classically intractable computing feasible. As the algorithms that achieve practical quantum advantage are beyond manual tuning, quantum circuit optimization has become…
Topological quantum error correction codes are extremely practical, typically requiring only a 2-D lattice of qubits with tunable nearest neighbor interactions yet tolerating high physical error rates p. It is computationally expensive to…
We develop the first constructive algorithms for compiling single-qubit unitary gates into circuits over the universal $V$ basis. The $V$ basis is an alternative universal basis to the more commonly studied $\{H,T\}$ basis. We propose two…
One-way functions are central to classical cryptography. They are both necessary for the existence of non-trivial classical cryptosystems, and sufficient to realize meaningful primitives including commitments, pseudorandom generators and…
Optimal synthesis of reversible functions is a non-trivial problem. One of the major limiting factors in computing such circuits is the sheer number of reversible functions. Even restricting synthesis to 4-bit reversible functions results…
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm…
One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose…
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…
We present QFAST, a quantum synthesis tool designed to produce short circuits and to scale well in practice. Our contributions are: 1) a novel representation of circuits able to encode placement and topology; 2) a hierarchical approach with…
We study functional graphs generated by quadratic polynomials over prime fields. We introduce efficient algorithms for methodical computations and provide the values of various direct and cumulative statistical parameters of interest. These…
The quantum circuit model allows gates between any pair of qubits yet physical instantiations allow only limited interactions. We address this problem by providing an interaction graph together with an efficient method for compiling quantum…
A method for synthesizing quantum gates is presented based on interpolation methods applied to operators in Hilbert space. Starting from the diagonal forms of specific generating seed operators with non-degenerate eigenvalue spectrum one…