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Optica

Hypercubic cluster states in the phase-modulated quantum optical frequency comb

Xuan Zhu, Chun-Hung Chang, Carlos González-Arciniegas, Avi Pe’er, Jacob Higgins, Olivier Pfister

Published Jan 26, 2021• 34 citations
Publisher

Abstract

We propose and fully analyze the simplest technique to date (to our knowledge) for generating light-based universal quantum computing resources, namely, 2D, 3D, and n -hypercubic cluster states in general. The technique uses two standard optical components: first, a single optical parametric oscillator pumped below threshold by a monochromatic field, which generates Einstein–Podolsky–Rosen entangled states, a.k.a. two-mode squeezed states, over the quantum optical frequency comb; second, phase modulation at frequencies that are multiples of the comb spacing (via RF or optical means). The compactness of this technique paves the way to implementing quantum computing on chip using quantum nanophotonics.

DOI
10.1364/optica.411713

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We propose and fully analyze the simplest technique to date (to our knowledge) for generating light-based universal quantum computing resources, namely, 2D, 3D, and n -hypercubic cluster states in general. The technique uses two standard optical components: first, a single optical parametric oscillator pumped below threshold by a monochromatic field, which generates Einstein–Podolsky–Rosen entangled states, a.k.a. two-mode squeezed states, over the quantum optical frequency comb; second, phase modulation at frequencies that are multiples of the comb spacing (via RF or optical means). The compactness of this technique paves the way to implementing quantum computing on chip using quantum nanophotonics.
In the one-way model of quantum computing, quantum algorithms are implemented using only measurements on an entangled initial state. Much of the hard work is done upfront when creating this universal resource, known as a cluster state, on which the measurements are made. Here we detail a new proposal for a scalable method of creating cluster states using only a single multimode optical parametric oscillator (OPO). The method generates a continuous-variable cluster state that is universal for quantum computation and encoded in the quadratures of the optical frequency comb of the OPO. This work expands on the presentation in Menicucci, Flammia and Pfister (2008 Phys. Rev. Lett. 101 , 130501).
One-way quantum computing allows any quantum algorithm to be implemented easily using just measurements. The difficult part is creating the universal resource, a cluster state, on which the measurements are made. We propose a scalable method that uses a single, multimode optical parametric oscillator (OPO). The method is very efficient and generates a continuous-variable cluster state, universal for quantum computation, with quantum information encoded in the quadratures of the optical frequency comb of the OPO.
Cluster states with higher-dimensional lattices that cannot be physically embedded in three-dimensional space have important theoretical interest in quantum computation and quantum simulation of topologically ordered condensed-matter systems. We present a simple, scalable, top-down method of entangling the quantum optical frequency comb into hypercubic-lattice continuous-variable cluster states of a size of about 104{10}^{4}104 quantum field modes, using existing technology. A hypercubic lattice of dimension DDD (linear, square, cubic, hypercubic, etc.) requires but DDD optical parametric oscillators with bichromatic pumps whose frequency splittings alone determine the lattice dimensionality and the number of copies of the state.
The quantum optical frequency comb (QOFC) of a single optical parametric oscillator (OPO) is a scalable platform for quantum information as a generator of large size cluster states. We show that the phase modulation of the QOFCs emitted by an OPO is a powerful graph engineering technique that can increase the topological dimension of the generated cluster state, from zero (independent EPR pairs) to one (linear cluster state), and from one to two (square-lattice cluster state), thereby allowing the creation and tailoring of universal quantum computing resources. This concept is highly compatible with integrated photonics.
Quantum computing promises exponential speedup for particular computational tasks, such as integer factoring, which bears importance for encryption technology, and quantum simulation, which holds vast scientific potential. Comparing with the traditional circuit-based quantum computers, one-way quantum computers are experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. In this thesis, I first review the fundamental theory of one-way quantum computing and its experimental implementation using the quantum optical frequency comb. After that, I present two novel schemes for generating ultra-scalable cluster states with rich structures that can be used for universal quantum computing.