TY - JOUR

T1 - Continuous-Variable Instantaneous Quantum Computing is Hard to Sample

AU - Douce, T.

AU - Markham, D.

AU - Kashefi, E.

AU - Diamanti, E.

AU - Coudreau, T.

AU - Milman, P.

AU - van Loock, P.

AU - Ferrini, G.

PY - 2017/2/17

Y1 - 2017/2/17

N2 - Instantaneous quantum computing is a subuniversal quantum complexity class, whose circuits have proven to be hard to simulate classically in the discrete-variable realm. We extend this proof to the continuous-variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of postselected circuits. In order to treat postselection in CVs, we consider finitely resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render postselected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.

AB - Instantaneous quantum computing is a subuniversal quantum complexity class, whose circuits have proven to be hard to simulate classically in the discrete-variable realm. We extend this proof to the continuous-variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of postselected circuits. In order to treat postselection in CVs, we consider finitely resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render postselected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.

U2 - 10.1103/PhysRevLett.118.070503

DO - 10.1103/PhysRevLett.118.070503

M3 - Article

VL - 118

SP - 1

EP - 6

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 7-17

M1 - 070503

ER -