Related papers: Trotter Error and Orbital Transformations in Quant…
We study the Trotter approximation for a pair of orbital angular momentum operators, $L_x$ and $L_y$. In particular, we investigate the scaling behavior of the state-dependent Trotter error. We show that for states in the domains of the…
Quantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause…
We derive higher-order error bounds with small prefactors for a general Trotter product formula, generalizing a result of Childs et al. [Phys. Rev. X 11, 011020 (2021)]. We then apply these bounds to the real-time quantum time evolution…
We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and…
Measuring quantum observables by grouping terms that can be rotated to sums of only products of Pauli $\hat z$ operators (Ising form) is proven to be efficient in near term quantum computing algorithms. This approach requires extra unitary…
Solving the electronic structure problem via unitary evolution of the electronic Hamiltonian is one of the promising applications of digital quantum computers. One of the practical strategies to implement the unitary evolution is via…
Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To-date, experimental demonstrations of algorithms such as…
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…
By exploiting the invariance of the molecular Hamiltonian by a unitary transformation of the orbitals it is possible to significantly shorter the depth of the variational circuit in the Variational Quantum Eigensolver (VQE) algorithm by…
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a…
The performance of a quantum error-correction process is determined by the likelihood that a random configuration of errors introduced to the system will lead to the corruption of encoded logical information. In this work we compare two…
We study analytically and numerically the effects of various imperfections in a quantum computation of a simple dynamical model based on the Quantum Wavelet Transform (QWT). The results for fidelity timescales, obtained for a large range of…
Simulating quantum systems is one of the most promising avenues to harness the computational power of quantum computers. However, hardware errors in noisy near-term devices remain a major obstacle for applications. Ideas based on the…
A complex but important challenge in understanding quantum mechanical phenomena is the simulation of quantum many-body dynamics. Although quantum computers offer significant potential to accelerate these simulations, their practical…
Quantum dynamics simulation via Hamilton simulation algorithms is one of the most crucial applications in the quantum computing field. While this task has been relatively considered the target in the fault-tolerance era, the experiment for…
We compare several quantum phase estimation (QPE) protocols intended for early fault-tolerant quantum computers (EFTQCs) in the context of models of their implementations on a surface code architecture. We estimate the logical and physical…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
We present a general framework for promoting first-order pulse sequences in quantum simulation to higher-order sequences that maintain robustness in the presence of finite pulse-width effects. Our approach maps a given first-order pulse…
Quantum simulation is a cornerstone application for quantum computing, yet standard methods face a trade-off between circuit depth and accuracy: Trotterization depth scales with the number of Hamiltonian terms $L$, while sampling-based…
We present an empirical analysis of the scaling of the minimal quantum circuit depth required for a variational quantum simulation (VQS) method to obtain a solution to the time evolution of a quantum system within a predefined error…