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Hamiltonian simulation is a central task in quantum computing, with wide-ranging applications in quantum chemistry, condensed matter physics, and combinatorial optimization. A fundamental challenge lies in approximating the unitary…
Exponentiation of Hamiltonians refers to a mathematical operation to a Hamiltonian operator, typically in the form e^(-i.t.H), where H is the Hamiltonian and t is a time parameter. This operation is fundamental in quantum mechanics,…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…
Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…
Hamiltonian simulation is a fundamental algorithm in quantum computing that has attracted considerable interest owing to its potential to efficiently solve the governing equations of large-scale classical systems. Exponential speedup…
We introduce novel algorithms for the quantum simulation of molecular systems which are asymptotically more efficient than those based on the Trotter-Suzuki decomposition. We present the first application of a recently developed technique…
We describe an improved version of the quantum simulation method based on the implementation of a truncated Taylor series of the evolution operator. The idea is to add an extra step to the previously known algorithm which implements an…
In the last years, we have been witnessing a tremendous push to demonstrate that quantum computers can solve classically intractable problems. This effort, initially focused on the hardware, progressively included the simplification of the…
Quantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum…
Many quantum algorithms, such as adiabatic algorithms (e.g. AQC) and phase randomisation, require simulating Hamiltonian evolution. In addition, the simulation of physical systems is an important objective in its own right. In many cases,…
The most advanced techniques using fault-tolerant quantum computers to estimate the ground-state energy of a chemical Hamiltonian involve compression of the Coulomb operator through tensor factorizations, enabling efficient block-encodings…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
Product formulas can be used to simulate Hamiltonian dynamics on a quantum computer by approximating the exponential of a sum of operators by a product of exponentials of the individual summands. This approach is both straightforward and…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
Finite-dimensional quantum theory serves as the theoretical foundation for quantum information and computation. Mathematically, it is formalized in the category FHilb, comprising all finite-dimensional Hilbert spaces and linear maps between…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating…