Session S47: Superconducting Bosonic Qubits

High-fidelity parametric beamsplitting with a parity-protected converter

Fast, high-fidelity operations between microwave resonators are an important tool for bosonic quantum computation and simulation with superconducting circuits. An attractive approach for implementing these operations is to couple these resonators via a nonlinear converter and actuate parametric processes with RF drives. It can be challenging to make these processes simultaneously fast and high fidelity, since this requires introducing strong drives without activating parasitic processes or introducing additional decoherence channels. We show that in addition to a careful management of drive frequencies and the spectrum of environmental noise, leveraging the inbuilt symmetries of the converter Hamiltonian can suppress unwanted nonlinear interactions, preventing converter-induced decoherence. We demonstrate these principles using a differentially-driven DC-SQUID as our converter, coupled to two high-Q microwave cavities. Using this architecture, we engineer a highly coherent beamsplitter and fast (∼100 ns) swaps between the cavities, limited primarily by their intrinsic single-photon loss. We characterize this beamsplitter in the cavities' joint single-photon subspace, and show that we can detect and post-select photon loss events to achieve a beamsplitter gate fidelity exceeding 99.98%, which to our knowledge far surpasses the current state of the art.   

Dual-rail cavity qubit measurements with erasure detection, Part 1: Design

The dual-rail cavity qubit has recently been proposed for the implementation of an erasure qubit in which the logical information is encoded within the {|01>, |10>} subspace of two superconducting microwave cavities [1]. Here, we focus on the recent experimental realization of a key element of the dual-rail cavity qubit concept: state preparation and measurement (SPAM). State preparation simply amounts to loading a single photon into one of the cavities. In contrast to conventional qubit measurement, the projective logical measurements can result not only in a “0” or “1” outcome, but also can be declared as an “erasure”, which occurs if the cavities have undergone photon loss or if the measurement outcome is ambiguous, indicating an error. By using standard circuit quantum electrodynamics techniques, namely measurements of cavity photon number via a transmon, we demonstrate SPAM fidelities exceeding those in any other qubit platform to date. In part 1 of this two-part talk, we describe the dual-rail cavity qubit hardware, design of our SPAM protocol, and show that repeated measurements of cavity photon number can be used to trade off erasure rates for exceedingly high SPAM fidelities.

[1] Teoh et al., PNAS 120 (41), e2221736120, 2023

[2] Chou et al., arXiv:2307.03169, 2023   

Dual-rail cavity qubit measurements with erasure detection, Part 2: Experiment

The dual-rail cavity qubit has recently been proposed for the implementation of an erasure qubit in which the logical information is encoded within the {|01>, |10>} subspace of two superconducting microwave cavities [1]. Here, we focus on the recent experimental realization of a key element of the dual-rail cavity qubit concept: state preparation and measurement (SPAM) [2]. In part 2 of this two-part talk, we present results of the experimental demonstration of the dual-rail cavity qubit. First, we confirm that the dual-rail cavity qubit can be prepared and measured with high fidelity, showing logical misassignment errors at the 10^{-4}-level and detection efficiency of over 99% of cavity decay events as erasures, in agreement with detailed simulations. Next, we use our measurement to quantify idling errors of our dual-rail cavity qubit, extracting phase error and bit-fip error rates at least 6 and 140 times less frequently than cavity decay errors, respectively. These findings confirm a key predicted error hierarchy of the dual-rail cavity qubit, with most errors detected as erasures and the remaining errors occurring at a much smaller rate. This initial confirmation of this error hierarchy makes the dual-rail cavity qubit a viable candidate for integration into higher-level error correction codes.  

[1] Teoh et al., PNAS 120 (41), e2221736120, 2023

[2] Chou et al., arXiv:2307.03169, 2023   

Erasure Detection for Bosonic Dual-Rail Qubits with a Strong Beamsplitter Interaction (Part 1/2)

A transmon coupled to one of two high-Q cavities can provide universal control of both cavity modes if they are themselves coupled via a tunable beamsplitter. Recent progress has allowed the strength of the beamsplitter interaction between the cavities to exceed the typical strength of the dispersive interaction to the transmon, while preserving high coherences. In this regime, it is possible for the transmon to learn only joint properties of the two cavities, despite their separation in both frequency and space. In particular, the transmon frequency spectrum exhibits number-split peaks that depend on the combined photon number of the two cavities. 

We use this to enact a mid-circuit erasure check for a dual-rail cavity qubit, detecting the joint vacuum state of the two cavities without perturbing the single-photon manifold. This measurement allows us to convert the most-likely qubit error (single photon loss to the vacuum) into erasures, which dramatically ease the task of quantum error correction and lead to higher thresholds in the surface code.

In part 1 of this two-part talk, we explore how a strong beamsplitter drive transforms the transmon spectrum and how this can be used to construct high-fidelity erasure checks.   

Erasure Detection for Bosonic Dual-Rail Qubits with a Strong Beamsplitter Interaction (Part 2/2)

A transmon coupled to one of two high-Q cavities can provide universal control of both cavity modes if they  are themselves coupled via a tunable beamsplitter. Recent progress has allowed the strength of the beamsplitter interaction between the cavities to exceed the typical strength of the dispersive interaction to the transmon, while preserving high coherences. In this regime, it is possible for the transmon to learn only joint properties of the two cavities, despite their separation in both frequency and space. In particular, the transmon frequency spectrum exhibits number-split peaks that depend on the combined photon number of the two cavities.

 

We use this to enact a mid-circuit erasure check for a dual-rail cavity qubit, detecting the joint vacuum state of the two cavities without perturbing the single-photon manifold. This measurement allows us to convert the most-likely qubit error (single photon loss to the vacuum) into erasures, which dramatically ease the task of quantum error correction and lead to higher thresholds in the surface code.

 

In part 2 of this two-part talk, we benchmark the performance of this mid-circuit erasure check on a dual-rail qubit and demonstrate that it is both high-fidelity and has minimal back action on the code space.   

Demonstrating an erasure-detected entangling gate between dual-rail cavity qubits - part 1

Dual-rail qubits encoded in 3D superconducting cavities are a promising approach for realizing error-detected qubits [1]. Detecting errors on physical qubits allows them to be converted to erasure errors, dramatically easing the task of quantum error correction and improving near-term error-detected algorithms. To this end, it is crucial to be able to detect hardware errors, even when they occur during the qubit operations themselves. This has been achieved for most of the required operations such as state-preparation and measurement [2], single qubit gates [3, 4], and erasure-checks [5].

In part 1 of this talk, we focus on the remaining missing ingredient -- an entangling gate between two dual-rail cavity qubits. Following the proposal in [6], we show how entangling ZZ-gates can be implemented with just a beamsplitter operation between two of the four cavities, and an ancilla transmon that is dispersively coupled to only one of the cavities. We detail the gate operation and show how it can detect the dominant first-order errors in the cavities and transmon, and enables lower gate infidelities that scale as (T_gate/T_coherence)^2 when no errors are flagged.

​​​​​​​[1] Teoh et al., PNAS 120 (41), e2221736120, 2023 

[2] Chou et al., arXiv:2307.03169, 2023 

[3] Lu, Maiti et al., Nat Comm 14, 5767, 2023 

[4] Chapman, de Graaf et al., PRX Quantum 4, 020355, 2023 

[5] Koottandavida, Tsioutsios et al. in prep. 

[6] Tsunoda, Teoh et al., PRX Quantum 4, 020354, 2023    

Demonstrating an erasure-detected entangling gate between dual-rail cavity qubits - part 2

Dual-rail qubits encoded in 3D superconducting cavities are a promising approach for realizing error-detected qubits [1]. Detecting errors on physical qubits allows them to be converted to erasure errors, dramatically easing the task of quantum error correction and improving near-term error-detected algorithms. To this end, it is crucial to be able to detect hardware errors, even when they occur during the qubit operations themselves. This has been achieved for most of the required operations such as state-preparation and measurement [2], single qubit gates [3, 4], and erasure-checks [5].  

In part 2 of this talk, we focus on the implementation of the remaining ingredient, a parametrizable entangling ZZ-gate [6], on our hardware. We describe the gate tune-up procedure and characterize both the error-detected gate fidelity and erasure rate. Our results show the dominant errors occur at the few percent level and are detected with high efficiency, leaving us with highly suppressed gate infidelities when no errors are flagged. These early demonstrations show dual-rail cavity qubits maintain the desired properties of erasure qubits during all necessary qubit operations, including the two-qubit gate. 

[1] Teoh et al., PNAS 120 (41), e2221736120, 2023

[2] Chou et al., arXiv:2307.03169, 2023

[3] Lu, Maiti et al., Nat Comm 14, 5767, 2023

[4] Chapman, de Graaf et al., PRX Quantum 4, 020355, 2023

[5] Koottandavida, Tsioutsios et al. in prep.

[6] Tsunoda, Teoh et al., PRX Quantum 4, 020354, 2023   

Characterizing the coherence in the dual-rail subspace of two superconducting cavities: (Part 1)

Quantum error correction is vital to the realization of fault-tolerant quantum computing since every quantum system used to store and process quantum information is prone to physical errors. Depending on the architecture, some types of errors are more likely than others, leading to an error hierarchy characteristic for each platform. In superconducting cavities, single photon loss is the dominant error channel, while intrinsic dephasing times can exceed energy relaxation timescales by orders of magnitude. To this end, we introduce the dual-rail cavity qubit, where logical information is encoded in the single-photon subspace of two superconducting cavities. With this encoding, leakage out of the computational subspace is detectable and thus convertible into erasure errors. However, since the cavities are intrinsically linear, non-linear auxiliary systems are required for control and logical readout, but these non-linear elements bring with them additional decoherence channels capable of spoiling the error hierarchy.

In this talk, we examine an implementation of a cavity dual-rail qubit and provide an overview of auxiliary sources of dephasing, as well as methods by which we can suppress these channels. We then implement these techniques to peel back the curtain of photon loss and extrinsic dephasing, revealing improved measurements for coherence in the dual-rail subspace.   

Characterizing the coherence in the dual-rail subspace of two superconducting cavities (Part 2)

Quantum error correction is vital to the realization of fault-tolerant quantum computing since every quantum system used to store and process quantum information is prone to physical errors. Depending on the architecture, some types of errors are more likely than others, leading to an error hierarchy characteristic for each platform. In superconducting cavities, single photon loss is the dominant error channel, while intrinsic dephasing times can exceed energy relaxation timescales by orders of magnitude. To this end, we introduce the dual-rail cavity qubit, where logical information is encoded in the single-photon subspace of two superconducting cavities. With this encoding, leakage out of the computational subspace is detectable and thus convertible into erasure errors. However, since the cavities are intrinsically linear, non-linear auxiliary systems are required for control and logical readout, but these non-linear elements bring with them additional decoherence channels capable of spoiling the error hierarchy.

In this talk, we present the mechanisms of decoherence in the dual-rail subspace intrinsic to the cavities, and how errors in the auxiliary systems can propagate into the logical subspace. Thanks to the high level of control over the system, we can check for errors in the individual hardware components and mitigate error propagation. We compare the prediction of our error model to measurements performed on a single dual-rail cavity qubit.     

Dual-rail encoding in a fixed-frequency multimode transmon qubit with ancilla-free erasure error-detection

Amplitude damping errors are a dominant source of error in high performance quantum processors. A promising approach in error-detection are “erasure qubits”, where amplitude damping errors are converted into detectable leakage outside of the computational subspace. Dual-rail encoding has been demonstrated in superconducting quantum devices to show extended coherence above that of the constituent elements, however, these architectures can require the use of an ancillary qubit to perform the erasure error detection. Hardware efficiency is a crucial requirement, should these erasure qubits be used in quantum processors or error-correcting codes.

Here we present a dual-rail encoding within a single fixed-frequency superconducting multimode transmon qubit. The three island, two junction device comprises two strongly coupled transmonlike modes with a detuning of 1.5 GHz. We perform all-microwave control of the logical states using a single capacitively coupled coaxial control line. A resonator on the opposing side of the substrate allows for the dispersive readout of the multimode state of the device, with an error-detected logical state assignment fidelity of above 99%. In addition, we are able to perform a weak error-detection measurement using the same resonator with minimal dephasing of the logical state, enabling mid-circuit error detection operations. Finally, we report logical coherence metrics, and discuss its relationship to noise and decoherence in transmon qubits.   

Achieving Negative Dispersive Shift Matching for Fault Tolerant Error Mapping in Pair Coherent States.

The stabilization of Bosonic qubits in microwave cavities is a promising step towards implementing quantum error correction codes. The pair cat code, which utilizes a two mode entangled state, assures significant advantages over the previously implemented one-mode cat code for autonomous quantum error correction schemes [1]. A pair coherent state (PCS) forms the basis of this pair cat code where the error syndrome can be measured from the photon number difference (PND) between the two modes [2]. Measuring the PND of the system can be made first order fault tolerant by achieving negative matching of the dispersive shift values for the two storage modes. We achieve this by utilizing a fluxonium qubit, with a local flux application to avoid storage lifetime degradation, as an ancilla due to the large anharmonicity. This allows practical use of the straddling regime of the qubit spectrum to produce negative chi matching on the two modes.

[1] V. V. Albert et al., Quantum Sci. Technol. 4, 035007 (2019).

[2] J. M. Gertler et al., PRX Quantum 4, 020319 (2023).   

QRAM architectures using 3D superconducting cavities

Quantum random access memory (QRAM) is a common architecture resource for algorithms with many proposed applications, including quantum chemistry, windowed quantum arithmetic, unstructured search, machine learning, and quantum cryptography.  We propose two bucket-brigade QRAM architectures based on high-coherence superconducting resonators, which differ in their realizations of the conditional-routing operations. In the first, we directly construct controlled-$mathsf{SWAP}$ ($mathsf{CSWAP}$) operations, while in the second we utilize the properties of giant-unidirectional emitters (GUEs). For both architectures we analyze single-rail and dual-rail implementations of a bosonic qubit. In the single-rail encoding we can detect first-order ancilla errors, while the dual-rail encoding additionally allows for the detection of photon losses. For parameter regimes of interest the post-selected infidelity of a QRAM query in a dual-rail architecture is nearly an order of magnitude below that of a corresponding query in a single-rail architecture, suggesting that dual-rail encodings are particularly attractive as architectures for QRAM devices in the era before fault tolerance.