stoquastic

English

Etymology

Blend of stochastic +‎ quantum

Pronunciation

• IPA^(key): /stəˈkwæstɪk/

  Rhymes: -æstɪk

Adjective

stoquastic (not comparable)

1. (mathematics) Of a Hermitian matrix, having real non-positive off-diagonal elements. These matrices have elements of quantum mechanics and classical theory of stochastic matrices. For non-technical purposes ‘stoquastic’ is equivalent to “avoiding the sign problem”.^[1]
   • 2015, Ian Kivlichan, “On the complexity of stoquastic Hamiltonians,” publication not named (termpaper?), 11 December 2015

     Stoquastic Hamiltonians, those for which all off-diagonal matrix elements in the standard basis are real and non-positive, are common in the physical world.

   • 2016, Edward Farhi, Aram W Harrow, “Quantum Supremacy through the Quantum Approximate Optimization Algorithm”, in arXiv‎:

     We contrast this with the case of sampling from the output of a quantum computer running the Quantum Adiabatic Algorithm (QADI) with the restriction that the Hamiltonian that governs the evolution is gapped and stoquastic.

   • 2016, R. Barends et al., “Digitized adiabatic quantum computing with a superconducting circuit”, in Nature, 534, 222-226, 9 June 2016:

     As stoquastic problems we use frustrated Ising Hamiltonians, having random local X and Z fields, and random σ_zσ_z couplings.

Derived terms

• stoquastic Hamiltonian

References

1. Sergey Bravyi: “Monte Carlo Simulation Of Stoquastic Hamiltonians.” Quantum Information & Computation, volume 15, issue 13&14, October 2015, pp. 1122–1140. Page 1123.