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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Optical d-Level Frequency-Time-Based Cluster States

Michael Kues, Raman Kashyap, Alfonso Carmelo Cino, Sai T. Chu, Brent E. Little, David Moss, Lucia Caspani, William J. Munro, José Azaña, Roberto Morandotti, Christian Reimer, Stefania Sciara, Piotr Roztocki, Mehedi Islam, Luis Romero Cortés, Yanbing Young Zhang, Bennet Fischer, Sébastien Loranger

Published Jun 1, 2019• 0 citations
Publisher

Abstract

Cluster states, a specific class of multi-partite entangled states, are of particular importance for quantum science, as such systems are equivalent to the realization of one-way (or measurement-based) quantum computers [1]. In this scheme, algorithms are implemented through high-fidelity measurements on the parties of the state [2]. While two-level (i.e. qubit) cluster states have been realized so far, increasing the number of particles to boost the computational resource comes at the price of significantly reduced coherence time and detection rates, as well as increased sensitivity to noise, restricting the realization of discrete cluster states to a record of eight qubits. In contrast, the demonstration of d-level (i.e. qudit) cluster states has the potential to i) increase quantum resources without modifying the number of particles; ii) enable the implementation of highly efficient computational protocols; iii) reduce the noise sensitivity of the states. Up till now, the realization of discrete d-level cluster states has not been shown in any quantum platform. We here demonstrate the realization of d-level cluster states, perform d-level one-way quantum processing operations on the states, and show that higher-dimensional forms of cluster states are more noise tolerant than lower dimensional realizations.

DOI
10.1109/cleoe-eqec.2019.8872230

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Cluster states, a specific class of multi-partite entangled states, are of particular importance for quantum science, as such systems are equivalent to the realization of one-way (or measurement-based) quantum computers [1]. In this scheme, algorithms are implemented through high-fidelity measurements on the parties of the state [2]. While two-level (i.e. qubit) cluster states have been realized so far, increasing the number of particles to boost the computational resource comes at the price of significantly reduced coherence time and detection rates, as well as increased sensitivity to noise, restricting the realization of discrete cluster states to a record of eight qubits. In contrast, the demonstration of d-level (i.e. qudit) cluster states has the potential to i) increase quantum resources without modifying the number of particles; ii) enable the implementation of highly efficient computational protocols; iii) reduce the noise sensitivity of the states. Up till now, the realization of discrete d-level cluster states has not been shown in any quantum platform. We here demonstrate the realization of d-level cluster states, perform d-level one-way quantum processing operations on the states, and show that higher-dimensional forms of cluster states are more noise tolerant than lower dimensional realizations.
Large and complex optical quantum states are a key resource for fundamental science and applications such as quantum communications, information processing, and metrology. In this context, cluster states are a particularly important class because they enable the realization of universal quantum computers by means of the so-called `one-way' scheme, where processing operations are performed through measurements on the state. While two-level (i.e. qubit) cluster states have been realized thus far, further boosting this computational resource by increasing the number of particles comes at the price of significantly reduced coherence time and detection rates, as well as increased sensitivity to noise. In contrast, the realization of d-level (with d > 2) cluster states offers the possibility to increase quantum resources without changing the number of particles, enables the implementation of efficient computational protocols, as well as coincides with a reduction in the noise sensitivity of the states. Here, we experimentally realize, characterize, and perform one-way processing operations on three-level, four-partite cluster states formed by two photons in the time and frequency domain. We make use of a unique approach based on integrated photonic chips and optical fiber communications components, enabling scalable, deterministic new functionalities.
One-way quantum computation is a promising scheme for realizing large-scale quantum computation, where computation is done via measurements on a universal multi-mode entangled resource called cluster state. The capability of this method is determined by the size and the dimension of the cluster state; the size is roughly equivalent to the number of input modes times number of operation steps, while the dimension determines universality and fault tolerance of the computation. To achieve universality, two-dimensional cluster state is required. Among many approaches, time-domain multiplexing using optical system [1, 2] is a promising method where quantum state is encoded in a temporal wave packet. Although universality is still lacking, one-million-mode one-dimensional cluster state has been demonstrated with this approach [3].
In this paper, we propose a linear-optical quantum computation scheme that starts from high-dimensionally entangled qudits but performs quantum computation on qubits defined in their subspaces. This approach enables us to increase the success probability of linear-optical fusions from 50%50\%50% to 1−1/d1-1/d1−1/d for qudits of dimension ddd without relying on existing approaches using ancilla photons and quantum codes. In particular, we show that a 2D cluster state of qubits can be generated from 5-qudit 1D cluster states using pairwise fusion gates while preserving their boosted success probability. We numerically demonstrate that this approach can improve the loss tolerance of a percolation-based scheme while keeping the photon number per resource state constant.
Abstract Complex and multi-dimensional cluster states of light are a critical resource for one-way quantum computers. We exploit the frequency, time and polarization domains to generate all-photonic cluster-states in a two-dimensional, 2N qubit, in a 2xN configuration. Cluster states of two dimensions or higher can serve as a resource for universal measurement-based quantum computation, and our approach allows for the realization of measurement-based two-qubit operations in an all-photonic platform. To generate the cluster states, we employ a process in which we construct dual-rail cluster states in time, frequency and polarization, as sequences of dual-color photon pairs encoded in polarization. The demonstrated discrete-variable, multi-photon, 4- and 6-qubit 2xN cluster states are shown to have high lower-bound fidelities of 0.84 and 0.57, respectively. By implementing more frequency bins the cluster state can be extended further, as well as the use of additional photonic degrees of freedom (like spatial modes) for higher dimensional cluster-states.