Related papers: Schr\"odinger-Heisenberg Variational Quantum Algor…
We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a…
Quantum simulation advantage over classical memory limitations would allow compact quantum circuits to yield insight into intractable quantum many-body problems, but the interrelated obstacles of large circuit depth in quantum time…
The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…
Unitary and non-unitary diagonal operators are fundamental building blocks in quantum algorithms with applications in the resolution of partial differential equations, Hamiltonian simulations, the loading of classical data on quantum…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
Solutions to many-body problem instances often involve an intractable number of degrees of freedom and admit no known approximations in general form. In practice, representing quantum-mechanical states of a given Hamiltonian using available…
Hamiltonian simulation on quantum computers is strongly constrained by gate counts, motivating techniques to reduce circuit depths. While tensor networks are natural competitors to quantum computers, we instead leverage them to support…
In this paper, we construct quantum circuits for the Black-Scholes equations, a cornerstone of financial modeling, based on a quantum algorithm that overcome the cure of high dimensionality. Our approach leverages the Schr\"odingerisation…
Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to…
Neutral atom quantum processors provide a viable route to scalable quantum computing, with recent demonstrations of high-fidelity and parallel gate operations and initial implementation of quantum algorithms using both physical and logical…
The simulation of time evolution of large quantum systems is a classically challenging and in general intractable task, making it a promising application for quantum computation. A Trotter-Suzuki approximation yields an implementation…
The Eastin-Knill theorem states that no quantum error correcting code can have a universal set of transversal gates. For CSS codes that can implement Clifford gates transversally it suffices to provide one additional non-Clifford gate, such…
A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and near-future quantum computers the use of quantum error correction schemes is still out of…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
The performance of quantum gates is often assessed using some form of randomized benchmarking. However, the existing methods become infeasible for more than approximately five qubits. Here we show how to use a simple and customizable class…
According to the Gottesman-Knill theorem, a class of quantum circuits, namely the so-called stabilizer circuits, can be simulated efficiently on a classical computer. We introduce a new algorithm for this task, which is based on the…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
Efficient preparation of arbitrary entangled quantum states is crucial for quantum computation. This is particularly important for noisy intermediate scale quantum simulators relying on variational hybrid quantum-classical algorithms. To…
The Schr\"odingerisation method combined with the autonomozation technique in \cite{cjL23} converts general non-autonomous linear differential equations with non-unitary dynamics into systems of autonomous Schr\"odinger-type equations, via…