Abstract
Continuous-variable (CV) cluster states are a universal quantum computing platform that has experimentally out-scaled qubit platforms by orders of magnitude. Room-temperature implementation of CV cluster states has been achieved with quantum optics by using multimode squeezed Gaussian states. It has also been proven that fault tolerance thresholds for CV quantum computing can be reached at realistic squeezing levels. In this paper, we show that standard approaches to design and characterize CV cluster states can miss entanglement present in the system. Such hidden entanglement may be used to increase the power of a quantum computer but it can also, if undetected, hinder the successful implementation of a quantum algorithm. By a detailed analysis of the structure of Gaussian states, we derive an algorithm that reveals hidden entanglement in an arbitrary Gaussian state and optimizes its use for one-way quantum computing.
Highlights
Continuous-variable (CV) quantum information [1,2,3] has achieved groundbreaking scalability performance [4,5,6,7,8,9] in the universal, measurement-based, one-way quantum computing (QC) model [10]
We show that hidden entanglement can disrupt quantum computing if unaccounted for in a CV cluster state
We report two mathematical results: (i) we derive a sufficient mathematical criterion to find Gaussian states that have uncorrectable (i.e., “irreducible”) hidden entanglement, which means that not all their imaginary edges can be transferred to real ones under any GLU and that these states cannot be expressed as cluster states; (ii) we derive an analytic algorithm to express a Gaussian state into a valid CV cluster state
Summary
Continuous-variable (CV) quantum information [1,2,3] has achieved groundbreaking scalability performance [4,5,6,7,8,9] in the universal, measurement-based, one-way quantum computing (QC) model [10]. To frame the problem in the most general way, we use the graphical calculus formalism developed by Menicucci et al [20], whose gist is that any pure multimode Gaussian state can be described by a unique graph whose vertices denote the qumodes and whose complex-weighted edges denote the interactions between the qumodes sharing an edge In this formalism, the real parts of the edge weights denote controlled-phase interactions, which are the CV analogs of controlled-Z gates for qubits [21]. It had been assumed that if Gaussian local unitaries (GLUs [24]; which cannot change the entanglement of the state) are applied to make the imaginary edge weights of the graph vanishingly small (e.g., in the limit of infinite squeezing), a valid cluster state is obtained.
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