Related papers: Parallel Quantum Algorithm for Hamiltonian Simulat…
Parallelization is a major challenge in quantum algorithms due to physical constraints like no-cloning. This is vividly illustrated by the conjecture of Moore and Nilsson from their seminal work on quantum circuit complexity [MN01,…
The construction of quantum circuits to simulate Hamiltonian evolution is central to many quantum algorithms. State-of-the-art circuits are based on oracles whose implementation is often omitted, and the complexity of the algorithm is…
As quantum technology advances, quantum simulation becomes increasingly promising, with significant implications for quantum many-body physics and quantum chemistry. Despite being one of the most accessible simulation methods, the product…
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,…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
Large-scale variational quantum algorithms are widely recognized as a potential pathway to achieve practical quantum advantages. However, the presence of quantum noise might suppress and undermine these advantages, which blurs the…
Analog quantum simulation is widely considered a step on the path to fault tolerant quantum computation. If based on current noisy hardware, the accuracy of an analog simulator will degrade after just a few time steps, especially when…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
An important aspect that strongly impacts the experimental feasibility of quantum circuits is the ratio of gate times and typical error time scales. Algorithms with circuit depths that significantly exceed the error time scales will result…
Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing by replacing sequences of one- and two-qubit gates with a unitary transformation generated…
The quantum kernel method has attracted considerable attention in the field of quantum machine learning. However, exploring the applicability of quantum kernels in more realistic settings has been hindered by the number of physical qubits…
Incorporating higher-order interactions in information processing enables us to build more accurate models, gain deeper insights into complex systems, and address real-world challenges more effectively. However, existing methods, such as…
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
Quantum computers can in principle simulate quantum physics exponentially faster than their classical counterparts, but some technical hurdles remain. Here we consider methods to make proposed chemical simulation algorithms computationally…
Larger multi-qubit quantum gates allow shallower, more efficient quantum circuits, which could decrease the prohibitive effect of noise on algorithms for noisy intermediate-scale quantum (NISQ) devices and fault-tolerant error correction…
Building on recent advances in quantum algorithms which measure and reuse qubits and in efficient classical simulation leveraging projective measurements, we extend these frameworks to real-time dynamics of quantum many-body systems…
Quantum algorithms often use quantum RAMs (QRAM) for accessing information stored in a database-like manner. QRAMs have to be fast, resource efficient and fault-tolerant. The latter is often influenced by access speeds, because shorter…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…