Squeezed light enhances readout SNR in multilevel systems.

A widely used method for measuring qubits faces a fundamental challenge: qubit decay during the measurement itself, alongside limitations in signal-to-noise ratio. Researchers are now applying squeezed-light states to overcome these issues, a technique driven by the need for both speed and fidelity in quantum readout protocols. This approach encodes qubit information into a squeezed cavity, preventing state-dependent rotation and ensuring enhanced signal, and now extends to multilevel systems for advanced quantum information processing.

Dispersive Readout Limitations in Qubit Fidelity

Dispersive readout, a prevalent technique for measuring qubits in circuit quantum electrodynamics and optomechanical systems, contends with inherent limitations stemming from qubit-state decay during measurement and finite signal-to-noise ratios in single-shot readings. These challenges restrict the ultimate fidelity achievable with this widely implemented method, demanding innovative solutions to maintain qubit coherence throughout the readout process. The performance of conventional dispersive readout relies on increasing both the encoding level and the number of measurements, a strategy that significantly strains coherence time and ultimately limits readout speed.

A 2018 approach used statistical averaging across multiple independent measurements to suppress the impact of single-shot errors and qubit relaxation, improving readout fidelity. However, this improvement necessitated increased encoding levels and measurement counts. This trade-off between fidelity and speed prompted exploration of alternative methods, including the application of squeezed-light states to enhance performance.

The experimental setup, as illustrated in accompanying diagrams, involves reading the state of a microwave cavity mode via its dispersive coupling to a logical qubit, which is then measured through its coupling to a readout cavity. A key aspect of the protocol is the simultaneous application of both intracavity squeezing, a two-photon drive with specific amplitude, frequency and phase, and external squeezing, using a squeezed vacuum reservoir with a defined squeezing parameter and reference phase.

This dual-squeezing technique allows for precise control over the quantum state of the readout cavity, minimizing noise and maximizing the signal that reveals the qubit’s state. The theoretical analysis reveals that the exponentially suppressed readout time (τ_s) and measurement error (δ_s) are critical to achieving the observed fidelity enhancement. By minimizing these factors, the protocol significantly reduces the disturbance to the qubit during measurement, preserving its quantum information for longer periods.

The team’s work builds upon existing techniques for qubit readout, offering a pathway toward achieving the high-fidelity measurements necessary for complex quantum computations. Maintaining these parameters within optimal ranges is essential for maximizing the enhancement in dispersive coupling and signal-to-noise ratio. This approach represents a step towards realizing practical quantum computation by addressing a fundamental limitation in qubit readout. The ability to perform fast, high-fidelity measurements is essential for scaling up quantum systems and performing complex algorithms.

Qin et al.’s Dual-Squeezing Enhances Readout SNR

Extending the benefits of dual-squeezing techniques to multilevel quantum systems offers a pathway to faster, more accurate readout of bosonic qubits, according to work detailed in the journal. The researchers demonstrate an exponential enhancement of the signal-to-noise ratio in a three-level system, a result they then generalized to systems with any number of levels, showing that the signal distinguishing adjacent energy levels also benefits from exponential improvement.

This advancement addresses a critical limitation in bosonic qubit readout, where encoding logical qubits in multiphoton Fock states demands greater fault tolerance. The team’s calculations reveal that the dual-squeezing framework, employing both externally injected squeezing and intracavity squeezing, achieves a more efficient enhancement in dispersive readout than previously possible. This is particularly important because dispersive coupling strength and measurement signal-to-noise ratio between any adjacent energy levels both experience similar exponential gains.

The study focuses on a process where a bosonic qubit is mapped onto an ancilla, then read out, with the duration of this initial readout termed τ. The researchers evaluated their protocol under two extreme conditions, κτ approaching zero and κτ approaching infinity, using both majority voting and maximum likelihood estimation (MLE) as classification strategies at encoding levels L and their optimal thresholds m. Results, depicted in accompanying figures, demonstrate that the squeezing-enhanced protocol consistently outperforms its non-squeezed counterpart.

The work builds on the concept of quantum nondemolition (QND) measurement, where the measurement process avoids disturbing the qubit, allowing for consistent repeated measurements. States |nm〉 map to the ancilla excited state, with decays and excitations occurring only between adjacent bosonic Fock states, each mapped to a unique ancilla state. This precise mapping is important for accurate readout and minimizing errors. The researchers emphasize that this method is not limited to specific qubit architectures and can be adapted to various bosonic qubit implementations, further broadening its potential impact.

Squeezed-Light Reduces Measurement Time and Error

The ability to rapidly and accurately determine a qubit’s state is now bolstered by a technique that simultaneously amplifies the signal and minimizes noise. The new protocol uses intracavity and externally applied squeezed light to enhance the dispersive coupling strength, a critical factor in readout speed. The improvement stems from a constructive interplay between these two squeezing mechanisms; intracavity squeezing amplifies the interaction between light and the qubit, while external squeezing reshapes the noise impacting the signal.

By carefully controlling the phase of the external squeezing, researchers can effectively cancel added noise, resulting in a stronger, clearer signal. Mathematical modeling of the process demonstrates the exponential enhancement of the signal-to-noise ratio.

Numerical simulations confirm this enhancement even as the measurement time approaches a limit dictated by the cavity properties. Qin et al. demonstrated that by concurrently employing both injected external squeezing and intracavity squeezing, it is possible to achieve an exponential improvement in the readout SNR for arbitrary measurement times. The resulting SNR scales as $e^{2}r$ for short-time measurements, where r is the squeezing parameter.

Beyond two-level architectures, however, multilevel systems are of profound importance in modern quantum information processing, particularly for bosonic encoding that uses the infinite-dimensional Hilbert space of a harmonic oscillator to construct logical qubits. Therefore, extending the dual-squeezing enhancement mechanism to multilevel architectures provides a promising way for fast, high-fidelity readout of multilevel bosonic qubits.

Robust Bosonic Qubit Readout via Ancilla Mapping

A new protocol addresses these challenges by mapping the bosonic qubit onto an ancilla, then repeatedly measuring that ancilla, a process refined through the application of squeezed light states. This technique allows for a significant reduction in the time required for each individual measurement, circumventing the typical trade-off between speed and fidelity. The approach builds upon earlier work in 2018 establishing a robust readout method relying on statistical averaging from multiple measurements, but avoids its demand for increased encoding levels and measurement counts.

The core of this advancement lies in a dual-squeezing configuration that simultaneously boosts the strength of dispersive coupling and minimizes measurement noise. This is important for complex quantum systems where multiple energy levels must be accurately distinguished. This improvement is achieved even when using lower encoding levels and requiring fewer measurement repetitions, a significant advantage for practical implementation.

The researchers specifically considered two scenarios when evaluating the protocol’s performance: one accounting only for bosonic mode relaxation, and another incorporating both relaxation and heating. The second case introduces a threshold state |m〉, defining the boundary between states mapped to the ancilla ground or excited state. For a multilevel ancilla, each Fock state is mapped to a unique auxiliary state, further refining the readout process.

The performance of the readout is quantified by the readout fidelity, calculated as the probability of correctly determining the initial state of the bosonic qubit given the outcome of the second-level readout. This reduction in time is particularly important for maintaining qubit coherence, as longer measurement times increase the likelihood of decoherence and errors.

This is a departure from previous methods that relied on increasing both encoding levels and the number of measurements to achieve similar results. The team’s work demonstrates a path toward building more robust and efficient quantum systems.

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