Abstract
The demonstration of quantum speedup, also known as quantum computational supremacy, that is the ability of quantum computers to outperform dramatically their classical counterparts, is an important milestone in the field of quantum computing. While quantum speedup experiments are gradually escaping the regime of classical simulation, they still lack efficient verification protocols and rely on partial validation. Here we derive an efficient protocol for verifying with single-mode Gaussian measurements the output states of a large class of continuous-variable quantum circuits demonstrating quantum speedup, including Boson Sampling experiments, thus enabling a convincing demonstration of quantum speedup with photonic computing. Beyond the quantum speedup milestone, our results also enable the efficient and reliable certification of a large class of intractable continuous-variable multimode quantum states.
Highlights
Quantum information promises many technological applications beyond classical information [1, 2, 3, 4]
The experimental demonstration of quantum speedup involves: (i) a quantum device solving efficiently a sampling task which is provably hard to solve for classical computers under reasonable theoretical assumptions, together with (ii) a verification that the quantum device solved the hard task [7]
The number of measurements needed to estimate with constant precision the output state of a Boson Sampling interferometer with n input photons over m modes with their witnesses scales as Ω(mn+4), under the i.i.d. assumption, while we show that our protocol provides the same precision with O(m2 log m) measurements
Summary
Quantum information promises many technological applications beyond classical information [1, 2, 3, 4]. Any efficient non-interactive verification of current quantum speedup experiments with a verifier restricted to classical computations requires additional cryptographic assumptions [25]. Existing verification protocols with a classical verifier based on total variation distance either rely on little-studied assumptions [12, 26, 27], or induce an overhead for the prover [24, 28, 29] which prevents a near-term use for an experimental demonstration of quantum speedup. Weaker but more resource-efficient methods of verification with a classical verifier, which are sometimes referred to as validation [30], consist in performing a partial verification where only specific properties of the experimental probability distribution are tested, rather than closeness in total variation distance to the ideal distribution. There is no efficient verification protocol using single-mode Gaussian state preparation nor single-mode Gaussian measurements for Boson Sampling with input single photons: current methods used for the validation of Boson sampling are either not scalable or only provide partial certificates on the tested probability distribution [30, 52, 53, 54, 55, 56, 57]
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