Phase estimation with randomized hamiltonians
Existing methods for dynamical simulation of physical systems use either a deterministic or random selection of terms in the Hamiltonian. In this application, example approaches are disclosed where the Hamiltonian terms are randomized and the precision of the randomly drawn approximation is adapted as the required precision in phase estimation increases. This reduces both the number of quantum gates needed and in some cases reduces the number of quantum bits used in the simulation.
1. A method of operating a quantum computing
device, comprising:
inputting a Hamiltonian to be computed by the quantum
computing device;
reducing a number of Hamiltonian terms in the Hamiltonian using randomization within a phase estimation algorithm; and
outputting a quantum circuit description for the Hamiltonian with the reduced number of Hamiltonian terms.
2. The method of claim 1 , wherein the method is performed by a classical computer.
3. The method of claim 1 , wherein the reducing comprises:
selecting one or more random Hamiltonian terms based on an importance function;
reweighting the selected random Hamiltonian terms based on an importance of each of the selected random Hamiltonian terms;
generate the quantum circuit description using the reweighted random terms.
4. The method of claim 3 , further comprising:
implementing, in the quantum computing device, a quantum circuit as described by the quantum circuit description;
measuring a quantum state of the quantum circuit.
5. The method of claim 4 , further comprising re-performing the method of claim 4 based on results from the measuring.
6. The method of claim 5 , herein the re-performing is performed based on an iterative process.
7. The method of claim 6 , wherein the iterative process comprises:
computing a desired precision value for the Hamiltonian;
computing a standard deviation for the Hamiltonian based on results from the implementing and measuring; and
comparing the desired precision value to the standard deviation.
8. The method of claim 1 , further comprising changing an order of the Hamiltonian terms based on the reducing.
9. The method of claim 1 , further comprising:
applying importance functions to terms of the Hamiltonian in a ground state; and
selecting one or more random Hamiltonian terms based at least in part on the importance functions.
10. The method of claim 1 , further comprising:
using importance sampling based on a variational approximation to a groundstate.
11. The method of claim 1 , further comprising:
using adaptive Bayesian methods to quantify a precision needed for the Hamiltonian given an estimate of the current uncertainty in an eigenvalue.
12. One or more computer-readable media storing computer-executable instructions, which when executed by a computer cause the computer to perform a method, the method comprising:
inputting a Hamiltonian to be computed by a quantum computer device;
reducing a number of Hamiltonian terms in the Hamiltonian using randomization within a phase estimation algorithm; and
outputting a quantum circuit description for the Hamiltonian with the reduced number of Hamiltonian terms.
13. The one or more computer-readable media of claim 12 , wherein the method further comprises:
selecting one or more random Hamiltonian terms based on an importance function;
reweighting the selected random Hamiltonian terms based on an importance of each of the selected random Hamiltonian terms; and
generating the quantum circuit description using the reweighted random terms.
14. The one or more computer-readable media of claim 13 , wherein the method further comprises:
causing a quantum circuit as described by the quantum circuit description to be implemented by the quantum computing device; and
measuring a quantum state of the quantum circuit.
15. The one or more computer-readable media of claim 14 , wherein the method further comprises:
computing a desired precision value for the Hamiltonian;
computing a standard deviation for the Hamiltonian based on results from the implementing and measuring;
comparing the desired precision value to the standard deviation; and
re-performing the reducing based on a result of the comparing.
16. A system, comprising:
a quantum computing system; and
a classical computing system configured to communicate with and control the quantum computing system, the classical computing system being further configured to:
input a Hamiltonian to be computed by the quantum computing system;
reduce a number of Hamiltonian terms in the Hamiltonian using randomization within an iterative phase estimation algorithm; and
output a quantum circuit description for the Hamiltonian with the reduced number of Hamiltonian terms.
17. The system of claim 16 , wherein the classical computing system is further configured to:
select one or more random Hamiltonian terms based on an importance function;
reweight the selected random Hamiltonian terms based on an importance of each of the selected random Hamiltonian terms; and
generate the quantum circuit description using the reweighted random terms.
18. The system of claim 17 , wherein the classical computing system is further configured to:
cause a quantum circuit as described by the quantum circuit description to be implemented by the quantum computing device; and
measure a quantum state of the quantum circuit.
19. The system of claim 18 , wherein the classical computing system is further configured to:
compute a desired precision value for the Hamiltonian;
compute a standard deviation for the Hamiltonian based on results from the implementing and measuring;
compare the desired precision value to the standard deviation; and
re-perform the reducing based on a result of the comparing.
20. The system of claim 16 , wherein the classical computing system is further configured to omit one or more unnecessary qubits based on the reduced number of Hamiltonian terms.