Related papers: A random compiler for fast Hamiltonian simulation
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing…
Trotter decomposition provides a simple approach to simulating open quantum systems by decomposing the Lindbladian into a sum of individual terms. While it is established that Trotter errors in Hamiltonian simulation depend on nested…
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators $H=\sum_k A_k$, for…
Bounding the cost of classically simulating the outcomes of universal quantum circuits to additive error $\delta$ is often called weak simulation and is a direct way to determine when they confer a quantum advantage. Weak simulation of the…
A quantum unitary gate is realized in this paper by perturbing a free charged particle in a one-dimensional box with a time- and position-varying electric field. The perturbed Hamiltonian is composed of a free particle Hamiltonian plus a…
In fault-tolerant quantum computing, the cost of calculating Hamiltonian eigenvalues using the quantum phase estimation algorithm is proportional to the constant scaling the Hamiltonian matrix block-encoded in a unitary circuit. We present…
Demonstrating a quantum computational speedup is a crucial milestone for near-term quantum technology. Recently, quantum simulation architectures have been proposed that have the potential to show such a quantum advantage, based on commonly…
We present a quantum computational framework using Hamiltonian Truncation (HT) for simulating real-time scattering processes in $(1+1)$-dimensional scalar $\phi^4$ theory. Unlike traditional lattice discretisation methods, HT approximates…
Determining the Hamiltonian of a quantum system is essential for understanding its dynamics and validating its behavior. Hamiltonian learning provides a data-driven approach to reconstruct the generator of the dynamics from measurements on…
In quantum computing, the efficient optimization of Pauli string decompositions is a crucial aspect for the compilation of quantum circuits for many applications, such as chemistry simulations and quantum machine learning. In this paper, we…
The fabrication, utilisation, and efficiency of quantum technologies rely on a good understanding of quantum thermodynamic properties. Many-body systems are often used as hardware for these quantum devices, but interactions between…
Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-$\frac{1}{2}$ systems. Here, we instead consider…
We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…
Quantum simulations of lattice gauge theories offer the potential to directly study the non-perturbative dynamics of quantum chromodynamics, but naive analyses suggest that they require large computational resources. Large $N_c$ expansions…
We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged…
We consider a class of random quantum circuits where at each step a gate from a universal set is applied to a random pair of qubits, and determine how quickly averages of arbitrary finite-degree polynomials in the matrix elements of the…
The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…
Large-scale classical simulation of quantum computers is crucial for benchmarking quantum algorithms, establishing boundaries of quantum advantage and exploring heuristic quantum algorithms. We present a full-state vector simulation…