Related papers: Error Interference in Quantum Simulation
Simulating quantum dynamics beyond the reach of classical computers is one of the main envisioned applications of quantum computers. The most promising quantum algorithms to this end in the near-term are the simplest, which use the Trotter…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…
Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term. Many state-of-the-art error mitigation schemes use knowledge of the errors in the quantum processor, which opens…
Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using…
The quantum circuit model is the de-facto way of designing quantum algorithms. Yet any level of abstraction away from the underlying hardware incurs overhead. In the era of near-term, noisy, intermediate-scale quantum (NISQ) hardware with…
When estimating the eigenvalues of a given observable, even fault-tolerant quantum computers will be subject to errors, namely algorithmic errors. These stem from approximations in the algorithms implementing the unitary passed to phase…
Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault tolerant schemes. Recently, error mitigation has been…
Understanding the dynamics of quantum systems is crucial in many areas of physics, but simulating many-body systems presents significant challenges due to the large Hilbert space to navigate and the exponential growth of computational…
From celestial mechanics to quantum theory of atoms and molecules, perturbation theory has played a central role in natural sciences. Particularly in quantum mechanics, the amount of information needed for specifying the state of a…
Quantum computers use the quantum interference of different computational paths to enhance correct outcomes and suppress erroneous outcomes of computations. A common pattern underpinning quantum algorithms can be identified when quantum…
Quantum entanglement is an essential feature of many-body systems that impacts both quantum information processing and fundamental physics. The growth of entanglement is a major challenge for classical simulation methods. In this work, we…
In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those…
Quantum simulation is a promising way toward practical quantum advantage, but noise in current quantum hardware poses a significant obstacle. We prove that not only the physical error but also the algorithmic error in a single Trotter step…
Recent experimental breakthroughs have signalled the imminent arrival of the early fault-tolerant era. However, for a considerable period in the foreseeable future, relying solely on quantum error correction for full error suppression will…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
Quantum computers can efficiently simulate many-body systems. As a widely used Hamiltonian simulation tool, the Trotter-Suzuki scheme splits the evolution into the number of Trotter steps $N$ and approximates the evolution of each step by a…
Efficient error estimates for the Trotter product formula are central in quantum computing, mathematical physics, and numerical simulations. However, the Trotter error's dependency on the input state and its application to unbounded…
Trotter approximation in conjunction with Quantum Phase Estimation can be used to extract eigen-energies of a many-body Hamiltonian on a quantum computer. There were several ways proposed to assess the quality of this approximation based on…
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently proposed interference measure. We…
This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random…