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Quantum Hamiltonian simulation is one of the most promising applications of quantum computing and forms the basis for many quantum algorithms. Benchmarking them is an important gauge of progress in quantum computing technology. We present a…
Extensions of average Hamiltonian theory to quantum computation permit the design of arbitrary Hamiltonians, allowing rotations throughout a large Hilbert space. In this way, the kinematics and dynamics of any quantum system may be…
Non-autonomous dynamical systems appear in a very wide range of interesting applications, both in classical and quantum dynamics, where in the latter case it corresponds to having a time-dependent Hamiltonian. However, the quantum…
With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical…
Quantum computing architectures are on the verge of scalability, a key requirement for the implementation of a universal quantum computer. The next stage in this quest is the realization of quantum error correction codes, which will…
Many methods solve Poisson equations by using grid techniques which discretize the problem in each dimension. Most of these algorithms are subject to the curse of dimensionality, so that they need exponential runtime. In the paper "Quantum…
Recent advances in the field of adiabatic quantum computing and the closely related field of quantum annealers has centered around using more advanced and novel Hamiltonian representations to solve optimization problems. One of these…
We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly…
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…
A custom-built and precisely controlled quantum system may offer access to a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analog quantum simulator…
Quantum computation and quantum simulation require a versatile gate set to optimize circuit compilation for practical applications. However, existing platforms are often limited to specific gate types or rely on parametric couplers to…
Approximation based on perturbation theory is the foundation for most of the quantitative predictions of quantum mechanics, whether in quantum many-body physics, chemistry, quantum field theory or other domains. Quantum computing provides…
Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum…
Quantum computing is an exciting field that uses quantum principles, such as quantum superposition and entanglement, to tackle complex computational problems. Superconducting quantum circuits, based on Josephson junctions, is one of the…
Quantum simulation provides a powerful route for exploring many-body phenomena beyond the capabilities of classical computation. Existing approaches typically proceed in the forward direction: a model Hamiltonian is specified, implemented…
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…
Fundamental questions in chemistry and physics may never be answered due to the exponential complexity of the underlying quantum phenomena. A desire to overcome this challenge has sparked a new industry of quantum technologies with the…
In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator…
Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental…
Quantum signal processing provides an optimal procedure for simulating Hamiltonian evolution on a quantum computer using calls to a block encoding of the Hamiltonian. In many situations it is possible to control between forward and reverse…