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Variational quantum algorithms (VQAs) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQAs can maintain…
In this work, we adopt the Gradient Projection Method (GPM) to problems of quantum control. For general $N$-level closed and open quantum systems, we derive the corresponding adjoint systems and gradients of the objective functionals, and…
We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected…
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…
It is shown that quantum walks on one-dimensional arrays of special linear-optical units allow the simulation of discrete-time Hamiltonian systems with distinct topological phases. In particular, a slightly modified version of the…
We present a method for classically simulating quantum circuits based on the tensor contraction model of Markov and Shi (quant-ph/0511069). Using this method we are able to classically simulate the approximate quantum Fourier transform in…
We propose a computational protocol for quantum simulations of Fermionic Hamiltonians on a quantum computer, enabling calculations which were previously not feasible with conventional encoding and ansatses of variational quantum…
We introduce a novel method that simultaneously isolates a quantum computer from decoherence and enables the controlled implementation of computational gates. We demonstrate a quantum computing model that utilizes a qubit's motion to…
Quantum Computing has been evolving in the last years. Although nowadays quantum algorithms performance has shown superior to their classical counterparts, quantum decoherence and additional auxiliary qubits needed for error tolerance…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
We review the staircase algorithm to decompose the exponential of a generalized Pauli matrix and we propose two alternative recursive methods which offer more efficient quantum circuits. The first algorithm we propose, defined as the…
In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. (The theory is constructive in that, operators acting at different times, actually commute.) We first develop an operator version of the…
Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity…
Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has…
In this paper we provide a framework for combining multiple quantum simulation methods, such as Trotter-Suzuki formulas and QDrift into a single Composite channel that builds upon older coalescing ideas for reducing gate counts. The central…
Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm…
We show how techniques from machine learning and optimization can be used to find circuits of photonic quantum computers that perform a desired transformation between input and output states. In the simplest case of a single input state,…
We establish a direct connection between the Feynman-Vernon path integral formalism for open quantum systems and the Wiener path integral used in classical stochastic dynamics. By considering a generalized influence functional in the strong…
The stabilizer formalism is a scheme, generalizing well-known techniques developed by Gottesman [quant-ph/9705052] in the case of qubits, to efficiently simulate a class of transformations ("stabilizer circuits", which include the quantum…
Loop-based boson samplers interfere photons in the time degree of freedom using a sequence of delay lines. Since they require few hardware components while also allowing for long-range entanglement, they are strong candidates for…