Related papers: A Generalized Circuit for the Hamiltonian Dynamics…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a…
We study the Hamilton cycle problem with input a random graph G=G(n,p) in two settings. In the first one, G is given to us in the form of randomly ordered adjacency lists while in the second one we are given the adjacency matrix of G. In…
Quantum simulation is a promising application of future quantum computers. Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. For an accurate product formula approximation,…
Simulation of quantum systems is notoriously challenging for classical computers, while quantum hardware is naturally well-suited for this task. However, the imperfections of contemporary quantum systems poses a considerable challenge in…
Electronic structure simulation is an anticipated application for quantum computers. Due to high-dimensional quantum entanglement in strongly correlated systems, the quantum resources required to perform such simulations are far beyond the…
This paper builds on our earlier proposal for construction of a positive inner product for pseudo-Hermitian Hamiltonians and we give several examples to clarify our method. We show through the example of the harmonic oscillator how our…
The advent of near-term digital quantum computers could offer us an exciting opportunity to investigate quantum many-body phenomena beyond that of classical computing. To make the best use of the hardware available, it is paramount that we…
This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of 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,…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
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…
We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a…
We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a…
We propose a method for constructing $\texttt{PREPARE}$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry by using variational optimization of quantum circuits solely on classical computers. The…
We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…
The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be simulated efficiently on a classical computer. This paper improves that theorem in…
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…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…