Related papers: Higher Order Methods for Simulations on Quantum Co…
We obtain sufficient conditions for the efficient simulation of a continuous variable quantum algorithm or process on a classical computer. The resulting theorem is an extension of the Gottesman-Knill theorem to continuous variable quantum…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
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…
The generating function of a Hamiltonian $H$ is defined as $F(t)=\langle e^{-itH}\rangle$, where $t$ is the time and where the expectation value is taken on a given initial quantum state. This function gives access to the different moments…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Approximation errors must be taken into account when compiling quantum programs into a low-level gate set. We present a methodology that tracks such errors automatically and then optimizes accuracy parameters to guarantee a specified…
Classical simulators play a major role in the development and benchmark of quantum algorithms and practically any software framework for quantum computation provides the option of running the algorithms on simulators. However, the…
Using Suzuki-Trotter decompositions of exponential operators we describe new algorithms for the numerical integration of the equations of motion for classical spin systems. These techniques conserve spin length exactly and, in special…
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…
Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum accelerated simulated…
We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas qubit-based quantum computation is adequate for…
Rational functions are exceptionally powerful tools in scientific computing, yet their abilities to advance quantum algorithms remain largely untapped. In this paper, we introduce effective implementations of rational transformations of a…
As quantum computers of non-trivial size become available in the near future, it is imperative to develop tools to emulate small quantum computers. This allows for validation and debugging of algorithms as well as exploring…
Quantum computing applications in the noisy intermediate-scale quantum (NISQ) era require algorithms that can generate shallower circuits feasible for today's quantum systems. This is particularly challenging for quantum chemistry…
Hybrid classical quantum optimization methods have become an important tool for efficiently solving problems in the current generation of NISQ computers. These methods use an optimization algorithm executed in a classical computer, fed with…
Fault tolerant quantum simulation via the phase estimation algorithm and qubitization has a T-gate count that scales proportionally to the 1-norm of the Hamiltonian, the cost of block encoding the Hamiltonian, and inversely proportionally…
We provide an explicit recursive divide and conquer approach for simulating quantum dynamics and derive a discrete first quantized non-relativistic QED Hamiltonian based on the many-particle Pauli Fierz Hamiltonian. We apply this recursive…
We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end.…
Molecular simulations are widely regarded as leading candidates to demonstrate quantum advantage--defined as the point at which quantum methods surpass classical approaches in either accuracy or scale. Yet the qubit counts and error rates…
The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in…