Session H08: Continuous Variable Quantum Information Processing

Large-Scale Quantum Simulators and Quantum Computers over Continuous Variables: Theory and Experiment

Continuous-variable (CV) quantum computing [1,2] is based on harmonic-oscillator qumodes such as position and momentum, or the two quadrature amplitudes of the quantized electromagnetic field, rather than on qubit- or qudit-based discrete encodings. It is a viable approach for which error correction [3] and fault tolerance [4] have been elucidated. It is particularly well suited to electromagnetic qumodes, which scale up very well as the resonant modes of a single optical cavity, such as that of an optical parametric oscillator, analogously to the classical optical frequency comb of a femtosecond laser. This allows cluster entangled states, which are quantum-computing ``substrates'' [5] in a sense, to be implemented over CV [6] on very large scales [7] as was experimentally demonstrated in the quantum optical frequency comb of a single OPO (60 entangled qumodes, simultaneously accessible) [8]. Note that sequential time-bin implementations are also possible (one million entangled qumodes, accessible two at a time) [9]. This paves the way to realizing interesting testbeds for bosonic, and possibly more general, quantum simulation [10]. In this talk, I will present the fundamentals of scalable CV cluster state generation in quantum optics, experimental realizations on five different continents, and applications to quantum simulation. [1] S. Lloyd and S.L. Braunstein, PRL \textbf{82}, 1784 (1999) [2] S.D. Bartlett, B.C. Sanders, S.L. Braunstein, K. Nemoto, PRL \textbf{88}, 097904 (2002) [3] D. Gottesman, A. Kitaev, and J. Preskill, PRA \textbf{64}, 012310 (2001) [4] N.C. Menicucci, PRL \textbf{112}, 120504 (2014) [5] R. Raussendorf and H.-J. Briegel, PRL \textbf{86}, 5188 (2001) [6] N.C. Menicucci \textit{et al.}, PRL \textbf{97}, 110501 (2006) [7] O. Pfister \textit{et al.}, PRA \textbf{70}, 020302 (2004) [8] M. Chen, N.C. Menicucci, and O. Pfister, PRL \textbf{112}, 120505 (2014) [9] J.-I. Yoshikawa \textit{et al.}, APL Photonics \textbf{1}, 060801 (2016) [10] K. Marshall, R. Pooser, G. Siopsis, and Ch. Weedbrook, PRA \textbf{92}, 063825 (2015)   

Bosonic Codes for Continuous Variable Quantum Information Processing: Theory and Experiment

Continuous variable (CV) quantum information processing requires universal control of the quantum states of harmonic oscillators. It is not a trivial task to carry out arbitrary unitary operations in the high-dimensional joint Hilbert space of these oscillators. Circuit QED uses artificial atoms constructed from Josephson junctions to achieve enormous transition dipole moments and hence strong coupling to microwave photons. The strong-dispersive regime of circuit QED is ideally suited for achieving the kind of universal control required for CV quantum information processing. Recent theoretical and experimental progress in developing and realizing new bosonic codes has allowed us to achieve a long-sought milestone: quantum error correction that reaches and exceeds the breakeven point at which the coherence time of a logical qubit exceeds that of the best physical qubits from which it is constructed. I will also describe other recent experimental progress in execution of new gate operations that entangle logical states in separate cavities. These gates [SWAP, c-SWAP (deterministic Fredkin), and exponential-SWAP] have the remarkable feature that they are universal in the sense that they do not depend on the particular bosonic encoding used to store quantum information in the cavities. These new tools could be the foundation of a modular photonic-based architecture that would be highly advantageous for quantum error correction and fault tolerance.   

Towards Scalability and Fault Tolerance in Continuous-Variable Quantum Computation

Before they can be useful, quantum computers must be made large and robust to noise. I will discuss progress towards both requirements in the context of continuous-variable quantum information, where the data registers are Bosonic modes, such as spatial/temporal modes in quantum optics, or microwave resonator modes in superconducting qubit architectures. I will report on a recent experiment that deterministically generated large-scale quasi-two-dimensional resource states for measurement-based quantum computing [1]. I will also discuss the key challenges to using such states for quantum computation: the effects of limited squeezing and the requirement of a non-Gaussian operation. Fortunately, one can address both issues in one fell swoop: encoded qubits known as Gottesman-Kitaev-Preskill (GKP) states allow for universal quantum computing with a constant squeezing overhead in the entangled resource state, and simultaneously provide the necessary non-Gaussianity for universal quantum computation [2]. \\ References: \\ $[1]$ Time-Domain Multiplexed 2-Dimensional Cluster State: Universal Quantum Computing Platform, Warit Asavanant, Yu Shiozawa, Shota Yokoyama, Baramee Charoensombutamon, Hiroki Emura, Rafael N. Alexander, Shuntaro Takeda, Jun-ichi Yoshikawa, Nicolas C. Menicucci, Hidehiro Yonezawa, Akira Furusawa, arXiv:1903.03918 (2019) \\ $[2]$ All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code, Ben Q. Baragiola, Giacomo Pantaleoni, Rafael N. Alexander, Angela Karanjai, Nicolas C. Menicucci, arXiv:1903.00012 (2019)   

Bosonic Complex Quantum Networks: What, when and why.

In this talk I will present some perspectives on these questions by looking at Hamiltonian models describing complex networks of quantum harmonic oscillators. I will first show that such systems are very useful for investigating the properties of open quantum systems, namely quantum systems interacting with an environment. This framework considers one of the nodes as the open system and the other nodes of the network as part of the environment. I will show that, changing the properties of the network, it is possible to engineer ad hoc open quantum dynamics by modifying the spectral density of the environment. This is particularly relevant in connection to quantum technologies where understanding and modelling environmental noise is crucial to realise robust and scalable commercial quantum devices. With a change in perspective to the complementary view point, the node forming the open quantum system can be seen as a local probe from which one can extract certain properties of the network. Remarkably, we show that global properties can be mapped into the time evolution of the probe hence, measuring the latter one, one can extract them. I will focus in particular on the ability to measure the connectivity of the network by local probing. Finally, I will discuss schemes for efficient and robust energy and entanglement transfer across complex quantum networks. I will argue that, independently of whether or not these systems exist in Nature, the ability to engineer them experimentally has great relevance to both fundamentals of quantum mechanics and applications such as quantum technologies.