Related papers: Simulating Quantum Computations with Tutte Polynom…
Efficient classical simulation of noisy intermediate-scale quantum (NISQ) circuits has been a topic of intense study over the past few years. The majority of results on efficient simulation assume that the circuits undergo some variant of…
Computing topological invariants of 3-manifolds is generally intractable, yet specialized algebraic structures can enable efficient algorithms. For Witten-Reshetikhin-Turaev (WRT) invariants of torus bundles, we exploit the non-commutative…
We propose an efficient classical algorithm to estimate the Neural Tangent Kernel (NTK) associated with a broad class of quantum neural networks. These networks consist of arbitrary unitary operators belonging to the Clifford group…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
The Pauli matrices are a set of three 2x2 complex Hermitian, unitary matrices. In this article, we investigate the relationships between certain roots of the Pauli matrices and how gates implementing those roots are used in quantum…
We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…
Primitive polynomials over finite fields are crucial for various domains of computer science, including classical pseudo-random number generation, coding theory and post-quantum cryptography. Nevertheless, the pursuit of an efficient…
Quantum computers promise to revolutionize our ability to simulate molecules, and cloud-based hardware is becoming increasingly accessible to a wide body of researchers. Algorithms such as Quantum Phase Estimation and the Variational…
Several quantum and classical Monte Carlo algorithms for Betti Number Estimation (BNE) on clique complexes have recently been proposed, though it is unclear how their performances compare. We review these algorithms, emphasising their…
The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…
Randomized protocols are procedures that incorporate probabilistic choices during their execution and they play a central role in quantum algorithms, spanning Hamiltonian simulation, noise mitigation, and measurement tasks. In practical…
We propose a new class of quantum computing algorithms which generalize many standard ones. The goal of our algorithms is to estimate probability distributions. Such estimates are useful in, for example, applications of Decision Theory and…
We present a quantum-classical hybrid random power method that approximates a ground state of a Hamiltonian. The quantum part of our method computes a fixed number of elements of a Hamiltonian-matrix polynomial via quantum polynomial…
A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group B n for every $n \ge 2$. If we view such an operator as a quantum-computational gate, then topological…
The stabiliser formalism plays a central role in quantum computing, error correction, and fault tolerance. Conversions between and verifications of different specifications of stabiliser states and Clifford gates are important components of…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
We present a method to model a discretized time evolution of probabilistic networks on gate-based quantum computers. We consider networks of nodes, where each node can be in one of two states: good or failed. In each time step,…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
We propose to perform amplitude estimation with the help of constant-depth quantum circuits that variationally approximate states during amplitude amplification. In the context of Monte Carlo (MC) integration, we numerically show that…