Ancilla-free continuous-variable SWAP test

Abstract

We propose a continuous-variable (CV) SWAP test that requires no ancilla register, thereby generalizing the ancilla-free SWAP test for qubits. In this ancilla-free CV SWAP test, the computational basis measurement is replaced by photon number-resolving measurement, and we calculate an upper bound on the error of the overlap estimate obtained from a finite Fock cutoff in the detector. As an example, we show that estimation of the overlap of pure, centered, single-mode Gaussian states of energy $E$ and squeezed in opposite quadratures can be obtained to error $\epsilon$ using photon statistics below a Fock basis cutoff $O(E\ln {\epsilon }^{-1})$. This cutoff is greatly reduced to $E+O(\sqrt{E}\ln {\epsilon }^{-1})$ when the states have rapidly decaying Fock tails, such as coherent states. We show how the ancilla-free CV SWAP test can be extended to many modes and applied to quantum algorithms such as variational compiling and entanglement spectroscopy in the CV setting. For the latter we also provide a new algorithm which does not have an analog in qubit systems. The ancilla-free CV SWAP test is implemented on Xanadu's 8-mode photonic processor in order to estimate the vacuum probability of a two-mode squeezed state.

18 pages, 4 figures

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Cited by in corpus (6)

• Swap Test-based Characterization of Quantum Processes in Universal Quantum Computers
• Efficient detection of nonclassicality using moments of the Wigner function
• Equivalent noise properties of scalable continuous-variable cluster states
• Out-of-distribution generalisation for learning quantum channels with low-energy coherent states
• Strategies for variational quantum compiling of a zero-phase beamsplitter on the Xanadu X8 processor
• The Role of Symmetry in Generalized Hong-Ou-Mandel Interference and Quantum Metrology