Related papers: Constant Factor Analysis of Optimal Quantum Linear…
The solution of linear systems of equations is the basis of many other quantum algorithms, and recent results provided an algorithm with optimal scaling in both the condition number $\kappa$ and the allowable error $\epsilon$ [PRX Quantum…
Recently, several approaches to solving linear systems on a quantum computer have been formulated in terms of the quantum adiabatic theorem for a continuously varying Hamiltonian. Such approaches enabled near-linear scaling in the condition…
Given a linear system of equations $A\boldsymbol{x}=\boldsymbol{b}$, quantum linear system solvers (QLSSs) approximately prepare a quantum state $|\boldsymbol{x}\rangle$ for which the amplitudes are proportional to the solution vector…
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…
We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can readily solve a quantum linear system problem (QLSP) with $\mathcal{O}(\kappa~\text{poly}(\log(\kappa/\epsilon)))$ runtime, where…
The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables,…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
Integer factorization remains a significant challenge for classical computers and is fundamental to the security of RSA encryption. Adiabatic quantum algorithms present a promising solution, yet their practical implementation is limited by…
Adiabatic quantum optimization offers a new method for solving hard optimization problems. In this paper we calculate median adiabatic times (in seconds) determined by the minimum gap during the adiabatic quantum optimization for an NP-hard…
Analog quantum algorithms are formulated in terms of Hamiltonians rather than unitary gates and include quantum adiabatic computing, quantum annealing, and the quantum approximate optimization algorithm (QAOA). These algorithms are…
Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term…
Quantum algorithms for solving the Quantum Linear System (QLS) problem are among the most investigated quantum algorithms of recent times, with potential applications including the solution of computationally intractable differential…
We transform the problem of solving linear system of equations $A\mathbf{x}=\mathbf{b}$ to a problem of finding the right singular vector with singular value zero of an augmented matrix $C$, and present two quantum algorithms for solving…
Finding the solution to linear ordinary differential equations of the form $\partial_t u(t) = -A(t)u(t)$ has been a promising theoretical avenue for \textit{asymptotic} quantum speedups. However, despite the improvements to existing quantum…
Existing quantum discrete adiabatic approaches are hindered by circuit depth that increases linearly with the number of evolution steps, a significant challenge for current quantum hardware with limited coherence times. To address this, we…
In this paper we study the performance of the quantum adiabatic algorithm on random instances of two combinatorial optimization problems, 3-regular 3-XORSAT and 3-regular Max-Cut. The cost functions associated with these two clause-based…
In a previous publication we proposed discrete global optimization as a method to train a strong binary classifier constructed as a thresholded sum over weak classifiers. Our motivation was to cast the training of a classifier into a format…
In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…
Quantum algorithms are prominent in the pursuit of achieving quantum advantage in various computational tasks. However, addressing challenges, such as limited qubit coherence and high error rate in near-term devices, requires extensive…
The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm to solve binary-variable optimization problems. Due to the short circuit depth and its expected robustness to systematic errors, it is one of the…