Related papers: Fast quantum integer multiplication with zero anci…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
Multi-controlled gates are fundamental components in the design of quantum algorithms, where efficient decompositions of these operators can enhance algorithm performance. The best asymptotic decomposition of an n-controlled X gate with one…
A crucial subroutine in quantum computing is to load the classical data of $N$ complex numbers into the amplitude of a superposed $n=\lceil \log_2N\rceil$-qubit state. It has been proven that any algorithm universally implementing this…
We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base 2, base 3, or…
An efficient technique of computing on encrypted data allows a client with limited capability to perform complex operations on a remote fault-tolerant server without leaking anything about the input or output. Quantum computing provides…
We construct a quantum algorithm that creates the Laughlin state for an arbitrary number of particles $n$ in the case of filling fraction one. This quantum circuit is efficient since it only uses $n(n-1)/2$ local qudit gates and its depth…
Variational quantum algorithms have emerged as a cornerstone of contemporary quantum algorithms research. Practical implementations of these algorithms, despite offering certain levels of robustness against systematic errors, show a decline…
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however…
We present a novel and efficient in terms of circuit depth design for Shor's quantum factorization algorithm. The circuit effectively utilizes a diverse set of adders based on the quantum Fourier transform (QFT) Draper's adders to build…
We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…
We propose a method for implementation of an universal set of one- and two-quantum-bit gates for quantum computation in the system of two coupled electrons with constant non-diagonal exchange interaction. Suppression of the exchange…
We present an efficient addition circuit, borrowing techniques from the classical carry-lookahead arithmetic circuit. Our quantum carry-lookahead (QCLA) adder accepts two n-bit numbers and adds them in O(log n) depth using O(n) ancillary…
Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian…
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…
We explore a method for automatically recompiling a quantum circuit A into a target circuit B, with the goal that both circuits have the same action on a specific input i.e. B|in> = A|in>. This is of particular relevance to hybrid, NISQ-era…
We present a constructive method to create quantum circuits that implement oracles $|x\rangle|y\rangle|0\rangle^k \mapsto |x\rangle|y \oplus f(x)\rangle|0\rangle^k$ for $n$-variable Boolean functions $f$ with low $T$-count. In our method…
This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form of an efficient classical algorithm for compiling an arbitrary single-qubit gate into a sequence of gates from a fixed and finite set. The algorithm can be…
Elliptic curves over finite fields GF(2^n) play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with affine or projective coordinates. In this…
Near-term quantum computers are limited by the decoherence of qubits to only being able to run low-depth quantum circuits with acceptable fidelity. This severely restricts what quantum algorithms can be compiled and implemented on such…
Recently, the development of quantum chips has made great progress-- the number of qubits is increasing and the fidelity is getting higher. However, qubits of these chips are not always fully connected, which sets additional barriers for…