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Quantum models of computation are widely believed to be more powerful than classical ones. Efforts center on proving that, for a given problem, quantum algorithms are more resource efficient than any classical one. All this, however,…
Simulating quantum algorithms with classical resources generally requires exponential resources. However, heuristic classical approaches are often very efficient in approximately simulating special circuit structures, for example with…
Stochastic models are highly relevant tools in science, engineering, and society. Recent work suggests emerging quantum computing technologies can substantially decrease the memory requirements for simulating stochastic models. Here we show…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
Recent advances in quantum hardware motivate the development of algorithmic frameworks that integrate quantum sampling with classical inference. This work introduces a segmentation-based regression method tailored to quantum neural networks…
What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…
Quantum hardware continues to advance, yet finding new quantum algorithms - quantum software - remains a challenge, with classically trained computer programmers having little intuition of how computational tasks may be performed in the…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the…
Quantum computers must meet extremely stringent qualitative and quantitative requirements on their qubits in order to solve real-life problems. Quantum circuit fragmentation techniques divide a large quantum circuit into a number of…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
Quantum mechanics has led not only to new physical theories, but also a new understanding of information and computation. Quantum information began by yielding new methods for achieving classical tasks such as factoring and key distribution…
Shor's algorithm for integer factorization offers an exponential speedup over classical methods but remains impractical on Noisy Intermediate Scale Quantum (NISQ) hardware due to the need for many coherent qubits and very deep circuits.…
State-of-the-art classical optimization solvers set a high bar for quantum computers to deliver utility in this domain. Here, we introduce a quantum preconditioning approach based on the quantum approximate optimization algorithm. It…