Journal
PHYSICAL REVIEW LETTERS
Volume 118, Issue 7, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.118.070503
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Funding
- ANR COMB Project of the French Agence Nationale de la Recherche [ANR-13-BS04-0014]
- DAAD-Campus France Project [35465RJ]
- European Union [704192]
- EPSRC [EP/N003829/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/N003829/1] Funding Source: researchfish
- Marie Curie Actions (MSCA) [704192] Funding Source: Marie Curie Actions (MSCA)
- Agence Nationale de la Recherche (ANR) [ANR-13-BS04-0014] Funding Source: Agence Nationale de la Recherche (ANR)
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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.
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