Related papers: A linear time quantum algorithm for 3SAT using irr…
We show how one can use certain deterministic algorithms for higher-value constraint satisfaction problems (CSPs) to speed up deterministic local search for 3-SAT. This way, we improve the deterministic worst-case running time for 3-SAT to…
We describe the experimental implementation of a recently proposed quantum algorithm involving quantum entanglement at the level of two qubits using NMR. The algorithm solves a generalisation of the Deutsch problem and distinguishes between…
A legend tells that once Loschmidt asked Boltzmann on what happens to his statistical theory if one inverts the velocities of all particles, so that, due to the reversibility of Newton's equations, they return from the equilibrium to a…
The NOT operation is a reversible transformation acting on a 1-bit logical state, and should be achievable in a physically reversible manner at no energetic cost. We experimentally demonstrate a bit-flip protocol based on the momentum of an…
We review and investigate the general theory of thermodynamics of computation, and derive the fundamental inequalities that set the lower bounds of the work requirement and the heat emission during a computation. These inequalities…
Solving linear systems of equations is a frequently encountered problem in machine learning and optimisation. Given a matrix $A$ and a vector $\mathbf b$ the task is to find the vector $\mathbf x$ such that $A \mathbf x = \mathbf b$. We…
Numerical solutions to Newton's equations of motion for chaotic self gravitating systems of more than 2 bodies are often regarded to be irreversible. This is due to the exponential growth of errors introduced by the integration scheme and…
We explore the possibility of adding complex absorbing potential at the boundaries when solving the one-dimensional real-time Schr\"odinger evolution on a grid using a quantum computer with a fully quantum algorithm described on a $n$ qubit…
The erasure of a bit of information encoded in a physical system is an irreversible operation bound to dissipate an amount of energy $Q = k_\text{B} T\ln 2$. As a result, work $W \geq Q$ has to be applied to the physical system to restore…
We prove the equivalence among symmetricity, time reversibility, and zero entropy production of the stationary solutions of linear stochastic differential equations. A sufficient and necessary reversibility condition expressed in terms of…
This paper proposes a general quantum algorithm that can be applied to any classical computer program. Each computational step is written using reversible operators, but the operators remain classical in that the qubits take on values of…
Solving systems of linear equations is a fundamental problem, but it can be computationally intensive for classical algorithms in high dimensions. Existing quantum algorithms can achieve exponential speedups for the quantum linear system…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via Quantum Linear System Algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require…
Quantum computing promises to solve problems previously deemed infeasible. However, high error rates necessitate quantum error correction for practical applications. Seminal experiments with zoned neutral atom architectures have shown…
Quantum error correcting codes can be cast in a way which is strikingly similar to a quantum heat engine undergoing an Otto cycle. In this paper we strengthen this connection further by carrying out a complete assessment of the…
We establish the potential of continuous-variable Gaussian states of linear dynamical systems for machine learning tasks. Specifically, we consider reservoir computing, an efficient framework for online time series processing. As a…
We present a variational algorithm for fault tolerant quantum computing to solve a system of linear equations which directly maximises the parameters of the target fidelity. This so-called measurement test algorithm can be applied to any…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
The structural phase transitions and computational complexity of random 3-SAT instances are traditionally described using thermodynamic analogies from statistical physics, such as Replica Symmetry Breaking and energy landscapes. While…