Related papers: Mitigating algorithmic errors in Hamiltonian simul…
Compilation optimizes quantum algorithms performances on real-world quantum computers. To date, it is performed via classical optimization strategies. We introduce a class of quantum algorithms to perform compilation via quantum computers,…
We consider simulating an $n$-qubit Hamiltonian with nearest-neighbor interactions evolving for time $t$ on a quantum computer. We show that this simulation has gate complexity $(nt)^{1+o(1)}$ using product formulas, a straightforward…
Hamiltonian simulation is one of the most promising candidates for the demonstration of quantum advantage within the next ten years, and several studies have proposed end-to-end resource estimates for executing such algorithms on…
According to the adiabatic theorem of quantum mechanics, a system initially in the ground state of a Hamiltonian remains in the ground state if one slowly changes the Hamiltonian. This can be used in principle to solve hard problems on…
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…
We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a…
Quantum algorithms for simulation of Hamiltonian evolution are often based on product formulae. The fractal methods give a systematic way to find arbitrarily high-order product formulae, but result in a large number of exponentials. On the…
Understanding the intricate quantum spin dynamics of radical pair reactions is crucial for unraveling the underlying nature of chemical processes across diverse scientific domains. In this work, we leverage Trotterization to map coherent…
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
Hamiltonian simulation is one of the most promising applications of quantum computers, and the product formula is one of the most important methods for this purpose. Previous related work has mainly focused on the worst$-$case or…
Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…
Product formula approximations of the time-evolution operator on quantum computers are of great interest due to their simplicity, and good scaling with system size by exploiting commutativity between Hamiltonian terms. However, product…
Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hybrid approach, where Hamiltonians with large amplitude are…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
Quantum error mitigation is an important technique to reduce the impact of noise in quantum computers. With more and more qubits being supported on quantum computers, there are two emerging fundamental challenges. First, the number of shots…
Ever since the discussions about a possible quantum computer arised, quantum simulations have been at the forefront of possible utilities and the task of quantum simulations is one that promises quantum advantage. In recent years,…
Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial…
Quantum computation, a completely different paradigm of computing, benefits from theoretically proven speed-ups for certain problems and opens up the possibility of exactly studying the properties of quantum systems. Yet, because of the…
Hamiltonian simulation represents an important module in a large class of quantum algorithms and simulations such as quantum machine learning, quantum linear algebra methods, and modeling for physics, material science and chemistry. One of…
A fundamental challenge in digital quantum simulation (DQS) is the control of inherent errors. These appear when discretizing the time evolution generated by the Hamiltonian of a quantum many-body system as a sequence of quantum gates,…