SKQD solution of guided_sparse_ground_state_problem_49Q_v1

[willkirby1]

Name

SKQD_for_guided_sparse_ground_state_problem_49Q_v1

Hamiltonian

guided_sparse_ground_state_problem_49Q_v1

Qubits

49

Gates

324 to 1568 two-qubit gates

Energy (Eh)

-85.58662506986455

Low error bound (Eh)

No response

High error bound (Eh)

No response

Method

SKQD

Method proof

https://arxiv.org/abs/2603.03496

Authors

William Kirby, Bibek Pokharel, Javier Robledo Moreno, Kevin C. Smith, Sergey Bravyi, Abhinav Deshpande, Constantinos Evangelinos, Bryce Fuller, James R. Garrison, Ben Jaderberg, Caleb Johnson, Petar Jurcevic, Su-un Lee, Simon Martiel, Mario Motta, Seetharami Seelam, Oles Shtanko, Kevin J. Sung, Minh Tran, Vinay Tripathi, Kazuhiro Seki, Kazuya Shinjo, Han Xu, Lukas Broers, Tomonori Shirakawa, Seiji Yunoki, Kunal Sharma, Antonio Mezzacapo

Institutions

IBM, RIKEN, University of Chicago

Quantum runtime (seconds)

68400

Classical runtime (seconds)

593

Compute resources (quantum)

IBM Heron r3

Compute resources (classical)

Mac Studio, Apple M3 Ultra chip, 32 cores

Notes

This is a synthetic spin Hamiltonian, so energies are not actually in Eh

[willkirby1]

qasm_circuits.zip

[JoeyT1994]

Thanks @willkirby1

Is there a reason this energy is exactly the same as the one in the truncated Arnoldi approach? I.e. did the SKQD really give the exact same energy as the classical one to that many decimal places?

Is there a ground truth here? I.e. what is the actual GS energy of this problem?

[willkirby1]

Yes, both are finding the exact ground state energy. They both do so to classical precision because the final energies are coming from projection and diagonalization on bases containing the ground state support

[matteoacrossi]

What about the DMRG solution in #142? Is that also your submission? The energy is also matching this submission to the last digit, which I find interesting (I would expect some rounding errors or numerical noise since that's not a diagonalization method).

[willkirby1]

Good point, yes that is also from us and we may have inadvertently put the exact energy rather than the actual DMRG solution. The error was on the order of machine precision but I'll make sure we update it with the correct number.

[willkirby1]

OK yes, the DMRG calculation was accurate to the 10th decimal, so its energy should be reported as -85.5866250698. We will update it

[jrm874]

@JoeyT1994 and @matteoacrossi , the DMRG solution has been updated, agreeing up to the 13th decimal point. I believe that additional sweeps may allow us to reach further decimal points, but this solution may be good for now.