Erratum: Phase-space-simulation method for quantum computation with magic states on qubits [Phys. Rev. A 101 , 012350 (2020)]

Hidden Variable Model for Universal Quantum Computation with Magic States on Qubits

“…Negativity in a Wigner function is, from a quantum optics perspective, considered a sign of genuine quantumness. Complementing this, previous work on the role of finite-dimensional Wigner functions in quantum computation [8][9][10][11][12][13][14][15] has established positivity of the Wigner function W ρ of the initial magic state ρ as an indicator of classicality. That is, if the Wigner function is positive then there is no quantum computational speedup.…”

“…The earlier works establish that Wigner function positivity is an indicator of classicality; and the present work does not oppose this. In fact, the generalized phase point operators identified in the multi-qubit setting of [11] are special cases of the phase point operators discussed here; see the Supplementary Material, Section I. And thus, the present approach provides a broader and yet conceptually simpler framework for the classical simulation of quantum computation by sampling, subsuming the earlier ones as special cases.…”

“…Note though that this restriction does not affect the universality of quantum computation with magic states! To conclude, we comment on the relation of the present work to its direct precursors [8][9][10][11][12], which examine the role of Wigner functions for quantum computation with magic states. The earlier works establish that Wigner function positivity is an indicator of classicality; and the present work does not oppose this.…”

“…The prevailing view on the above one-qubit example is that it is an exception, and for multiple qubits negativity will inevitably creep into any quasiprobability function of any computationally useful quantum state, rendering classical simulation inefficient [5]. This hypothesis is informed by the study of Wigner functions in finitedimensional state spaces, which establishes Wigner function negativity as a necessary computational resource, i.e., there can be no quantum speedup without negativity, [8][9][10][11][12][13][14][15]. A quantum optics notion of quantumnessnegativity of Wigner functions-and a computational notion-hardness of classical simulation-thus align.…”

“…The process closely resembles classical simulation of QCM by sampling from the Wigner function of the initial magic state [8], [11]. That simulation method requires the initial Wigner function to be positive, restricting the range of applicability.…”