Generating quantum computing circuits by distributing approximation errors in a quantum algorithm
Methods for generating quantum computing circuits by distributing approximation errors in a quantum algorithm are described. A method includes decomposing a quantum algorithm into quantum circuits. The method includes using at least one processor, automatically performing a step-wise decomposition of the quantum algorithm until the quantum algorithm is fully decomposed into the quantum circuits, where the automatically performing the step-wise decomposition results in a set of approximation errors and a set of parameters to instantiate at least a subset of the quantum circuits corresponding to the quantum algorithm, such that an overall approximation error caused by the automatically performing the step-wise decomposition is maintained below a specified threshold approximation error.
1. A method for decomposing a quantum algorithm into quantum circuits, the method comprising:
using at least one processor, automatically performing a step-wise decomposition of the quantum algorithm until the quantum algorithm is fully decomposed into the quantum circuits, wherein the automatically performing the step-wise decomposition results in a set of approximation errors and a set of parameters to instantiate at least a subset of the quantum circuits corresponding to the quantum algorithm, such that an overall approximation error caused by the automatically performing the step-wise decomposition is maintained below a specified threshold approximation error.
2. The method of claim 1 , wherein each of the quantum circuits is a gate that can be implemented using a quantum processor.
3. The method of claim 1 , wherein each of the quantum circuits is a fault-tolerant logical gate.
4. The method of claim 1 , wherein each of the quantum circuits is implemented as a protected operation on encoded quantum data.
5. The method of claim 1 further comprising using an optimization problem minimizing a cost metric associated with implementing the quantum circuits while maintaining the overall approximation error below the specified threshold approximation error.
6. The method of claim 5 , wherein the optimization problem encodes a condition to meet the overall approximation error and a condition to minimize the cost metric associated with the quantum circuits.
7. The method of claim 6 , wherein the optimization problem is solved using a heuristic method to select parameters of the quantum circuits.
8. The method of claim 7 , wherein the optimization problem is solved by choosing a random initial assignment of approximation errors and parameters.
9. The method of claim 8 , wherein a solution to the optimization problem is computed using simulated annealing.
10. A method for decomposing a quantum algorithm into quantum circuits, the method comprising:
using at least one processor, automatically performing a step-wise decomposition of the quantum algorithm and distributing an overall approximation error caused by the automatically performing the step-wise decomposition into subroutines until the quantum algorithm is fully decomposed into the quantum circuits; and
using the at least one processor, minimizing a cost metric associated with implementing the quantum circuits while maintaining the overall approximation error below a specified threshold approximation error.
11. The method of claim 10 , wherein each of the quantum circuits is implemented as a protected operation on encoded quantum data.
12. The method of claim 10 , wherein the minimizing the cost metric further comprises solving an optimization problem using a heuristic method to select parameters of the quantum circuits.
13. The method of claim 12 , wherein the optimization problem is solved by choosing a random initial assignment of approximation errors and parameters.
14. A computer-readable medium comprising computer executable instructions for a method comprising:
using at least one processor, automatically performing a step-wise decomposition of the quantum algorithm and distributing an overall approximation error caused by the automatically performing the step-wise decomposition into subroutines until the quantum algorithm is fully decomposed into the quantum circuits, wherein the step-wise decomposition into the subroutines is implemented via a quantum phase estimation (QPE) process; and
using the at least one processor, minimizing a cost metric associated with implementing the quantum circuits while maintaining the overall approximation error below a specified threshold approximation error.
15. The computer-readable medium of claim 14 , wherein the QPE process implements a time evolution of an Ising model in a transverse field.
16. The computer-readable medium of claim 14 , wherein the QPE process is applied to a task of evolving a quantum-mechanical system that is initialized in a given state for a specified total duration of time.
17. The computer-readable medium of claim 16 , wherein the total duration of time is divided into subintervals.
18. The computer-readable medium of claim 17 , wherein the total duration of time is divided into subintervals using Trotter method or Trotter-Suzuki method.
19. The computer-readable medium of claim 17 , wherein the total duration of time is divided into subintervals using a Linear Combination of Unitaries (LCU) method.
20. The computer-readable medium of claim 19 , wherein the LCU method is implemented using state preparation circuits.