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We present an algorithm for sparse Hamiltonian simulation whose complexity is optimal (up to log factors) as a function of all parameters of interest. Previous algorithms had optimal or near-optimal scaling in some parameters at the cost of…
Simulating many-body quantum systems is a promising task for quantum computers. However, the depth of most algorithms, such as product formulas, scales with the number of terms in the Hamiltonian, and can therefore be challenging to…
Hamiltonian simulation is a central task in quantum computing, with wide-ranging applications in quantum chemistry, condensed matter physics, and combinatorial optimization. A fundamental challenge lies in approximating the unitary…
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…
The transitionless tracking (TT) algorithm enables the exact tracking of quantum adiabatic dynamics in an arbitrary short time by adding a counterdiabatic Hamiltonian to the original adiabatic Hamiltonian. By applying Husimi's method…
As a milestone for general-purpose computing machines, we demonstrate that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. Moreover, on noisy devices without error correction, we…
Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits. However, they usually lack global convergence guarantees and well-established scaling behavior.…
While quantum simulation is one of the most promising applications of modern quantum devices, accessible simulation times are fundamentally limited by finite coherence times due to omnipresent noise. Based on the ideas of relational…
We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a…
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…
We propose an effective and flexible scheme for reverse engineering of a Hamiltonian by designing the evolution operators to eliminate the terms of Hamiltonian which are hard to be realized in practice. Different from transitionless quantum…
We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations by a factor of up to…
In this paper we discuss how we can design Hamiltonians to implement quantum algorithms, in particular we focus in Deutsch and Grover algorithms. As main result of this paper, we show how Hamiltonian inverse quantum engineering method allow…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
Hamiltonian learning protocols are essential tools to benchmark quantum computers and simulators. Yet rigorous methods for time-dependent Hamiltonians and Lindbladians remain scarce despite their wide use. We close this gap by learning the…
Simulating real-time dynamics under a Hamiltonian is a central goal of quantum information science. While numerous Hamiltonian-simulation quantum algorithms have been proposed, the effects of physical noise have rarely been incorporated…
The main challenges in achieving high-fidelity quantum gates are to reduce the influence of control errors caused by imperfect Hamiltonians and the influence of decoherence caused by environment noise. To overcome control errors, a…
This article proposes a formalism which unifies Hamiltonian simulation techniques from different fields. This formalism leads to a competitive method to construct the Hamiltonian simulation with a comprehensible, simple-to-implement circuit…
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…
The compiling of quantum gates is crucial for the successful quantum algorithm implementations. The environmental noise as well as the bandwidth of control pulses pose a challenge to precise and fast qubit control, especially in a weakly…