Analyzing the Quantum Annealing Approach for Solving Linear Least Squares Problems

Box algorithm for the solution of differential equations on a quantum annealer

“…This restriction makes the representation of solutions of double precision similar to a classical computer extremely expensive. In ( [18,19]), the problem of minimizing ||Ax − b|| in the least squares sense was posed by encoding physical qubits to represent rational numbers using a radix 2 representation. This format requires a significant number of physical qubits and connections to represent positive rational numbers and an additional qubit to represent the sign of the number ( [18]).…”

“…In ( [18,19]), the problem of minimizing ||Ax − b|| in the least squares sense was posed by encoding physical qubits to represent rational numbers using a radix 2 representation. This format requires a significant number of physical qubits and connections to represent positive rational numbers and an additional qubit to represent the sign of the number ( [18]). In comparison, the box algorithm searches within a small discrete set of up/down qubit values with each element of the set mapped to a double precision value, thereby eliminating the need for additional qubits to achieve higher precision.…”

Hybrid classical-quantum linear solver using Noisy Intermediate-Scale Quantum machines

“…Interestingly, the Harrow-Hassidim-Lloyd (HHL) quantum algorithm [4][5][6][7][8][9][10][11][12][13], which is based on the quantum circuit model [14], takes only O(log(N )) to solve a sparse N × N system of linear equations, while for dense systems it requires O( √ N log(N )) [11]. Linear solvers and experimental realizations that use quantum annealing and adiabatic quantum computing machines [15][16][17] are also reported [18][19][20]. Most recently, methods [21,22] inspired by adiabatic quantum computing are proposed to be implemented on circuit-based quantum computers.…”