Related papers: Average-case Speedup for Product Formulas
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
Trotterization is a standard approach for simulating quantum time evolution on quantum computers, where the Hamiltonian is split into local terms and each term is applied in sequence. The order of these terms affects the fidelity of the…
Unitary operations are the building blocks of quantum programs. Our task is to design effcient or optimal implementations of these unitary operations by employing the intrinsic physical resources of a given n-qubit system. The most common…
One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc, in order to accelerate the process of discovery. It is important to ask: Can this be achieved…
A fundamental challenge in digital quantum simulation (DQS) is the control of inherent errors. These appear when discretizing the time evolution generated by the Hamiltonian of a quantum many-body system as a sequence of quantum gates,…
We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the…
A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.
Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-$\frac{1}{2}$ systems. Here, we instead consider…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
Hamiltonian formulations of lattice field theories provide access to real-time dynamics, but their simulation is difficult to implement efficiently. Trotter-Suzuki decompositions are at the center of time evolution computation, either on…
A multi-product formula (MPF) is a promising approach for Hamiltonian simulation efficiently both in the system size $N$ and the inverse allowable error $1/\varepsilon$ by combining Trotterization and the linear combination of unitaries…
Simulating the time-evolution of a Hamiltonian is one of the most promising applications of quantum computers. Multi-Product Formulas (MPFs) are well suited to replace standard product formulas since they scale better with respect to time…
Fault-tolerant quantum computing is a promising tool for simulating molecules and materials, but frequently-considered applications require substantial resources, and the gap between hardware capabilities and requirements remains…
Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using…
The factorized form of the unitary coupled cluster ansatz is a popular state preparation ansatz for electronic structure calculations of molecules on quantum computers. It often is viewed as an approximation (based on the Trotter product…
Simulation of materials is one of the most promising applications of quantum computers. On near-term hardware the crucial constraint on these simulations is circuit depth. Many quantum simulation algorithms rely on a layer of unitary…
We develop a numerical method based on matrix product states for simulating quantum many-body systems at finite temperatures without importance sampling and evaluate its performance in spin 1/2 systems. Our method is an extension of the…
Conventional approaches to fault-tolerant quantum computing realize logical circuits gate-by-gate, synthesizing each gate independently on one or more code blocks. This incurs excess overhead and doesn't leverage common structures in…
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…
Efficient simulation of many-body quantum systems is central to advances in physics, chemistry, and quantum computing, with a key question being whether the simulation cost scales polynomially with the system size. In this work, we analyze…