Ancilla-free continuous-variable SWAP test

Journal Article · Thu Sep 08 00:00:00 EDT 2022 · Quantum

DOI:https://doi.org/10.22331/q-2022-09-08-800· OSTI ID:1887149

Volkoff, Tyler James ^[1]; Subasi, Yigit ^[1]

---

1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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 ϵ using photon statistics below a Fock basis cutoff O(Elnϵ^–1). This cutoff is greatly reduced to E + O(√ Elnϵ^–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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1887149
• Report Number(s): LA-UR-22-21141
• Journal Information: Quantum, Journal Name: Quantum Vol. 6; ISSN 2521-327X
• Publisher: Quantum Science Open Community
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
continuous variables
linear optics
quantum algorithms
quantum computation