Related papers: Lecture Notes on Quantum Algorithms
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
We investigate the quantum algorithm of Babbush et al. (arXiv:2303.13012v3) for simulating coupled harmonic oscillators, which promises exponential speedups over classical methods. Focusing on linearly connected oscillator chains, we bridge…
The article is a short opinionated review of the quantum treatment of electromagnetic circuits, with no pretension to exhaustiveness. This review, which is an updated and modernized version of a previous set of Les Houches School lecture…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
These are extended lecture notes of the quantum mechanics course which I am teaching in the Weizmann Institute of Science graduate physics program. They cover the topics listed below. The first four chapter are posted here. Their content is…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
Digital quantum computers provide a computational framework for solving the Schr\"{o}dinger equation for a variety of many-particle systems. Quantum computing algorithms for the quantum simulation of these systems have recently witnessed…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of…
The field of linear optical quantum computation (LOQC) will soon need a repertoire of experimental milestones. We make progress in this direction by describing several experiments based on Grover's algorithm. These experiments range from a…
This tutorial guides a competent programmer through the crafting of a quantum circuit simulator from scratch, even for readers with almost no prior experience in quantum computing. Open source simulators for quantum circuits already exist,…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
Quantum computing is the process of performing calculations using quantum mechanics. This field studies the quantum behavior of certain subatomic particles for subsequent use in performing calculations, as well as for large-scale…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
There exist quantum algorithms that are more efficient than their classical counterparts; such algorithms were invented by Shor in 1994 and then Grover in 1996. A lack of invention since Grover's algorithm has been commonly attributed to…
There are many falsely intuitive introductions to quantum theory and quantum computation in a handwave. There are also numerous documents which teach those subjects in a mathematically sound manner. To my knowledge this paper is the…
A hallmark of the computational campaign in nuclear and particle physics is the lattice-gauge-theory program. It continues to enable theoretical predictions for a range of phenomena in nature from the underlying Standard Model. The…
The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen.…