Abstract Beam-splitter operations are an indispensable resource for processing quantum information encoded in bosonic modes. In hybrid quantum systems, however, it can be challenging to implement reliable beam-splitters between two distinct modes due to various experimental imperfections. Without beam-splitters, realizing arbitrary Gaussian operations between bosonic modes can become highly non-trivial or even infeasible. In this work, we develop interference-based protocols for engineering Gaussian operations in multi-mode hybrid bosonic systems without requiring beam-splitters. Specifically, for a given generic multi-mode Gaussian unitary coupler, we demonstrate a universal scheme for constructing Gaussian operations on a desired subset of the modes, requiring only multiple uses of the given coupler interleaved with single-mode Gaussian unitaries. Our results provide efficient construction of operations crucial to quantum information science, and are derived from fundamental physical properties of bosonic systems. The proposed scheme is thus widely applicable to existing platforms and couplers, with the exception of certain edge cases. We introduce a systematic approach to identify and treat these edge cases by utilizing an intrinsically invariant structure associated with our interference-based construction.
Abstract Beam-splitter operations are an indispensable resource for processing quantum information encoded in bosonic modes. In hybrid quantum systems, however, it can be challenging to implement reliable beam-splitters between two distinct modes due to various experimental imperfections. Without beam-splitters, realizing arbitrary Gaussian operations between bosonic modes can become highly non-trivial or even infeasible. In this work, we develop interference-based protocols for engineering Gaussian operations in multi-mode hybrid bosonic systems without requiring beam-splitters. Specifically, for a given generic multi-mode Gaussian unitary coupler, we demonstrate a universal scheme for constructing Gaussian operations on a desired subset of the modes, requiring only multiple uses of the given coupler interleaved with single-mode Gaussian unitaries. Our results provide efficient construction of operations crucial to quantum information science, and are derived from fundamental physical properties of bosonic systems. The proposed scheme is thus widely applicable to existing platforms and couplers, with the exception of certain edge cases. We introduce a systematic approach to identify and treat these edge cases by utilizing an intrinsically invariant structure associated with our interference-based construction.
Beam-splitter operations are widely used to process information encoded in bosonic modes. In hybrid quantum systems, however, it might be challenging to implement a reliable beam-splitter operation between two distinct bosonic modes. Without beam-splitters, some basic operations such as decoupling modes and swapping states between modes can become highly non-trivial or not feasible at all. In this work, we develop novel interference-based protocols for decoupling and swapping selected modes of a multimode bosonic system without requiring beam-splitters. Specifically, for a given generic coupler characterized by a Gaussian unitary process, we show how to decouple a single mode or swap any pair of modes with a constant depth sequence of operations, while maintaining the coupling for the remaining system. These protocols require only multiple uses of the given coupler, interleaved with single-mode Gaussian unitary operations, and thus enable efficient construction of operations crucial to quantum information science, such as high-fidelity quantum transduction. Our results are directly derived from fundamental physical properties of bosonic systems and are therefore broadly applicable to various existing platforms.
Gaussian states, operations, and measurements are central building blocks for continuous-variable quantum information processing which paves the way for abundant applications, especially including network-based quantum computation and communication. To make the most use of the Gaussian processes, it is required to understand and utilize suitable mathematical tools such as the symplectic space, symplectic algebra, and Wigner representation. Applying these mathematical tools to practical quantum scenarios, we developed various schemes for quantum transduction, interference-based bosonic mode permutation and bosonic sensing. We demonstrated that generic coupler characterized by Gaussian unitary process can be transformed into a high-fidelity transducer, assuming the access to infinite squeezing and adaptive feedforward with homodyne measurements. To address the practical limitation of finite squeezing, we explored the interference-based protocols. These protocols let us freely permute bosonic modes only assuming the access to single-mode Gaussian operations and multiple uses of a given multi-mode Gaussian process. Thus, such a scheme not only enables universal decoupling for bosonic systems, which is useful for suppressing undesired coupling between the system and the environment, but also faithful bidirectional single-mode quantum transduction. Moreover, noticing that the Gaussian processes are appropriate theoretical models for optical sensors, we studied the quantum noise theory for optical parameter sensing and its potential in providing great measurement precision enhancement. We also extended the Gaussian theories to discrete variable systems, with several examples such as quantum (gate) teleportation. All the analyses originated from the fundamental quantum commutation relations, and therefore are widely applicable.
Since the early days of quantum information science, diverse strategies have been proposed to encode qubits and implement quantum gates across various physical platforms. Modes and bosonic states offer a flexible framework for quantum information processing, from single-photon optics to superconducting circuits, combining massless and massive particles. Universal gate sets have been established for specific encodings—such as those based on Fock states or the field’s quadratures. However, a general framework clarifying how different bosonic resources—such as mode structure, particle-number statistics, Gaussian and non-Gaussian states and operations—combine to enable universality and potential quantum advantage irrespectively of the encoding remains lacking. A main difficulty lies in the coexistence of distinct paradigms that appear to combine loosely in bosonic quantum information: discrete-variable schemes—where information is encoded in qubits or effective finite-dimensional systems—and continuous-variable schemes—which rely on infinite-dimensional Hilbert spaces associated with the field’s quadratures. Despite the success of each approach, they remain seemingly incompatible in many aspects—in particular in terms of physical resource analysis for universality—due to their underlying mathematical differences. In this work, we apply a superselection-rule-compliant framework for bosonic quantum information that unifies these paradigms. This representation explicitly incorporates the phase reference and enforces total particle number conservation, allowing for a consistent treatment of bosonic quantum information protocols and resources across both discrete and continuous regimes. We derive necessary and sufficient conditions expressed in terms of Gaussian and non-Gaussian resources for universality that apply to any encoding, without resorting to specific mappings. Our results show that continuous variable encodings are not fundamentally distinct from discrete ones, but rather emerge as subspaces within a general bosonic structure. Importantly, in such a widely studied framework, non-Gaussian properties of bosonic states and operations can be washed out, providing evidence that the continuous variables regime is not the most suitable to fully assess the quantum properties of bosons.
Controlling the quantum interface between two bosonic modes is essential in countless implementations of quantum information processing. However, full controllability is rarely achieved in most platforms due to specific physical limitations. In this work, we completely characterize the linear two-mode interfaces under the most pessimistic restriction that only single-mode operation is available. When arbitrary Gaussian single-mode operations can be applied to both modes, we find that every interface can be characterized by an invariant transmission strength. Moreover, in the practical situation that squeezing is restricted in one of the modes, we discover two additional quantities, irreducible squeezing and irreducible shearing, that are invariant under the allowable controls. By using this characterization, we develop systematic strategies to engineer an arbitrary linear interface through cascading multiple fixed component interfaces. Without squeezing restriction, our protocol is optimal and requires at most three component interfaces. Under the squeezing constraint, our protocol can be extended to engineer also the additional invariants by using no more than two more rounds of cascade. We also propose the remote squeezing scheme to tackle the squeezing restriction through interfacing with an active auxiliary mode. Published by the American Physical Society 2024
Fault-tolerant quantum computation with bosonic qubits often necessitates the use of noisy discrete-variable ancillae. In this work, we establish a comprehensive and practical fault-tolerance framework for such a hybrid system and synthesize it with fault-tolerant protocols by combining bosonic quantum error correction (QEC) and advanced quantum control techniques. We introduce essential building blocks of error-corrected gadgets by leveraging ancilla-assisted bosonic operations using a generalized variant of path-independent quantum control. Using these building blocks, we construct a universal set of error-corrected gadgets that tolerate a single-photon loss and an arbitrary ancilla fault for four-legged cat qubits. Notably, our construction requires only dispersive coupling between bosonic modes and ancillae, as well as beam-splitter coupling between bosonic modes, both of which have been experimentally demonstrated with strong strengths and high accuracy. Moreover, each error-corrected bosonic qubit is comprised of only a single bosonic mode and a three-level ancilla, featuring the hardware efficiency of bosonic QEC in the full fault-tolerant setting. We numerically demonstrate the feasibility of our schemes using current experimental parameters in the circuit-QED platform. Finally, we present a hardware-efficient architecture for fault-tolerant quantum computing by concatenating the four-legged cat qubits with an outer qubit code utilizing only beam-splitter couplings. Our estimates suggest that the overall noise threshold can be reached using existing hardware. These developed fault-tolerant schemes extend beyond their applicability to four-legged cat qubits and can be adapted for other rotation-symmetrical codes, offering a promising avenue toward scalable and robust quantum computation with bosonic qubits. Published by the American Physical Society 2024
A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.