Unconventional properties of non-Hermitian systems, such as the existence of exceptional points, have recently been suggested as a resource for sensing. The impact of noise and utility in quantum regimes however remains unclear. In this work, we analyze the parametric-sensing properties of linear coupled-mode systems that are described by effective non-Hermitian Hamiltonians. Our analysis fully accounts for noise effects in both classical and quantum regimes, and also fully treats a realistic and optimal measurement protocol based on coherent driving and homodyne detection. Focusing on two-mode devices, we derive fundamental bounds on the signal power and signal-to-noise ratio for any such sensor. We use these to demonstrate that enhanced signal power requires gain, but not necessarily any proximity to an exceptional point. Further, when noise is included, we show that nonreciprocity is a powerful resource for sensing: it allows one to exceed the fundamental bounds constraining any conventional, reciprocal sensor.

Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. Currently, all proposals for the quantum version of machine learning utilize the finite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practical, infinite-dimensional systems. We present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that can lead to exponential speed-ups in situations where classical algorithms scale polynomially. Finally, we also map out an experimental implementation which can be used as a blueprint for future photonic demonstrations.Introduction -We are now in the age of big data [1]. An unprecedented era in history where the storing, managing and manipulation of information is no longer effective using previously techniques. To compensate for this, one important approach in manipulating such large data sets and extracting worthwhile inferences, is by utilizing machine learning techniques. Machine learning [2,3] involves using specially tailored 'learning algorithms' to make important predictions in fields as varied as finance, business, fraud detection, and counter terrorism. Tasks in machine learning can involve either supervised or unsupervised learning and can solve such problems as pattern and speech recognition, classification, and clustering. Interestingly enough, the overwhelming rush of big data in the last decade has also been responsible for the recent advances in the closely related field of artificial intelligence [4].Another important field in information processing which has also seen a significant increase in interest in the last decade is that of quantum computing [5]. Quantum computers are expected to be able to perform certain computations much faster than any classical computer. In fact, quantum algorithms have been developed which are exponentially faster than their classical counterparts [6,7]. Recently, a new subfield within quantum information has emerged combining ideas from quantum computing with artificial intelligence to form quantum machine learning [8].These discrete-variable schemes have observed a performance that scales logarithmically in the vector dimension, such as supervised and unsupervised learning [9], support vector machine [10], cluster assignment [11] and others [12][13][14][15][16][17][18]. Initial proof-of-principle experimental demonstrations have also been performed [19][20][21][22]. It was mentioned in [23], that certain caveats apply to quantum machine learning. However, since then these caveats (relating to sparsity, condition number, epsilon precision, quantum output), have been closed or applications found where they are not a concern, cf. [8,10,18,24].

Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap-tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the 'hardware' problem of engineering quantum-computing-universal interactions, from the 'software' problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.Introduction-In a wide range of quantum computational tasks, the basic quantity of quantum information is a two-level system that can be prepared in an arbitrary superposition state (qubit) [1]. If the quantum system consists of individually addressable energy eigenstates, such as the internal levels in trapped atoms or the polarisation states of electron spins [2], the qubit bases are most trivially represented by two of such states. On the other hand, there are also quantum systems, such as optical modes [3], mechanical oscillators [4], quantised motion of trapped ions [5], and spin ensembles [6,7], that consist of an abundance of evenly-spaced energy levels. In these systems, usually referred to as continuous-variable (CV) systems, addressing a particular energy eigenstate is usually challenging. There is thus no trivial CV representation of a qubit.

We extend the formalism of cluster state quantum secret sharing, as presented in Markham and Sanders [Phys. Rev. A 78, 042309 (2008)] and Keet et al. [Phy. Rev. A 82, 062315 (2010)], to the continuous-variable regime. We show that both classical and quantum information can be shared by distributing continuous-variable cluster states through either public or private channels. We find that the adversary structure is completely denied from the secret if the cluster state is infinitely squeezed, but some secret information would be leaked if a realistic finitely squeezed state is employed. We suggest benchmarks to evaluate the security in the finitely squeezed cases. For the sharing of classical secrets, we borrow techniques from the continuous-variable quantum key distribution to compute the secret sharing rate. For the sharing of quantum states, we estimate the amount of entanglement distilled for teleportation from each cluster state.Comment: v3: Modified abstract and introductio

Optomechanical couplings involve both beam-splitter and two-mode-squeezing types of interactions. While the former underlies the utility of many applications, the latter creates unwanted excitations and is usually detrimental. In this work, we propose a simple but powerful method based on cavity parametric driving to suppress the unwanted excitation that does not require working with a deeply sideband-resolved cavity. Our approach is based on a simple observation: as both the optomechanical two-mode-squeezing interaction and the cavity parametric drive induce squeezing transformations of the relevant photonic bath modes, they can be made to cancel one another. We illustrate how our method can cool a mechanical oscillator below the quantum back-action limit, and significantly suppress the output noise of a sideband-unresolved optomechanical transducer.

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We describe a possible architecture to implement a universal bosonic simulator (UBS) using trapped ions. Single ions are confined in individual traps, and their motional states represent the bosonic modes. Single-mode linear operators, nonlinear phase-shifts, and linear beam splitters can be realized by precisely controlling the trapping potentials. All the processes in a bosonic simulation, except the initialization and the readout, can be conducted beyond the Lamb-Dicke regime. Aspects of our proposal can also be applied to split adiabatically a pair of ions in a single trap.

One of the limitations to the quantum computing capability of a continuous-variable system is determined by our ability to cool it to the ground state, because pure logical states, in which we accurately encode quantum information, are conventionally pure physical states that are constructed from the ground state. In this work, we present an alternative quantum computing formalism that encodes logical quantum information in mixed physical states. We introduce a class of mixed-state protocols that are based on a parity encoding, and propose an implementation of the universal logic gates by using realistic hybrid interactions. When comparing with the conventional pure-state protocols, our formalism could relax the necessity of, and hence the systemic requirements of cooling. Additionally, the mixed-state protocols are inherently resilient to a wider class of noise processes, and reduce the fundamental energy consumption in initialisation. Our work broadens the candidates of continuous-variable quantum computers.Introduction-Quantum computers are expected to outperform classical computers in a wide class of applications such as factoring large numbers, database searching, and simulating quantum systems [1]. The basic logical unit of quantum information is usually a two-level system that can be prepared in an arbitrary superposition state (qubit). A suitable platform for implementing quantum computers should exhibit 'well characterised' physical states for representing the qubit bases |0 L and |1 L [2]. In continuous-variable (CV) quantum systems, such as cavity modes of electromagnetic wave, mechanical oscillators, and spin ensembles [3][4][5][6][7], there is no standard representation of a qubit because each physical degree of freedom (qumode) consists of an abundance of evenlyspaced energy eigenstates. Different CV encodings have been invented to represent a qubit as a superposition of Fock states, coherent states, cat states, superpositions of squeezed states, and else [8][9][10][11][12][13][14][15][16][17][18][19].Despite their differences in detail, all the existing encodings (pure-state encodings) commonly require a pure logical state qubit to be represented by a pure physical state, which is usually prepared from the ground state of a qumode. If the qumode frequency is high, a nearground state with negligible thermal excitation can be obtained by lowering the background temperature [20]. Whereas a low frequency qumode has to be cooled by additional processes, e.g., using feedback controls or coupling to dissipative auxiliary systems [4,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. Despite some remarkable success, ground-state cooling remains challenging for some CV systems due to the lack of appropriate internal structure, absorption heating induced by the cooling laser, and other limitations of apparatus and system. The ability of achieving ground-state cooling is therefore deemed an important criterion for discriminating CV candidates of a quantum computer.Nevertheless, quantum computer...