Quantum error correction with dissipatively stabilized squeezed cat qubits

Noise-biased qubits are a promising route toward significantly reducing the hardware overhead associated with quantum error correction. The squeezed cat code, a non-local encoding in phase space based on squeezed coherent states, is an example of a noise-biased (bosonic) qubit with exponential error bias. Here we propose and analyze the error correction performance of a dissipatively stabilized squeezed cat qubit. We find that for moderate squeezing the bit-flip error rate gets significantly reduced in comparison with the ordinary cat qubit while leaving the phase flip rate unchanged. Additionally, we find that the squeezing enables faster and higher-fidelity gates.Comment: updated and accepted versio

Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops

Continuous-variable systems realized in high-coherence microwave cavities are a promising platform for quantum information processing. While strong dynamic nonlinear interactions are desired to implement fast and high-fidelity quantum operations, static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Here we study theoretical models of nonlinear oscillators describing superconducting quantum circuits with asymmetric Josephson-junction loops. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. We support our analytical results by numerical experiments and show that the effective Kerr-type couplings can be canceled by an interplay of higher-order nonlinearities. This can be better understood in a simplified model supporting only cubic and quartic nonlinearities. Our results show that a cubic interaction allows an increase in the effective rates of both linear and nonlinear operations without an increase in the undesired anharmonicity of an oscillator which is crucial for many bosonic encodings

Analog Information Decoding of Bosonic Quantum Low-Density Parity-Check Codes

Quantum error correction is crucial for scalable quantum information-processing applications. Traditional discrete-variable quantum codes that use multiple two-level systems to encode logical information can be hardware intensive. An alternative approach is provided by bosonic codes, which use the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information. Two promising features of bosonic codes are that syndrome measurements are natively analog and that they can be concatenated with discrete-variable codes. In this work, we propose novel decoding methods that explicitly exploit the analog syndrome information obtained from the bosonic qubit readout in a concatenated architecture. Our methods are versatile and can be generally applied to any bosonic code concatenated with a quantum low-density parity-check (QLDPC) code. Furthermore, we introduce the concept of quasi-single shot protocols as a novel approach that significantly reduces the number of repeated syndrome measurements required when decoding under phenomenological noise. To realize the protocol, we present the first implementation of time-domain decoding with the overlapping window method for general QLDPC codes and a novel analog single-shot decoding method. Our results lay the foundation for general decoding algorithms using analog information and demonstrate promising results in the direction of fault-tolerant quantum computation with concatenated bosonic-QLDPC codes

Analog information decoding of bosonic quantum LDPC codes

Quantum error correction is crucial for scalable quantum information processing applications. Traditional discrete-variable quantum codes that use multiple two-level systems to encode logical information can be hardware-intensive. An alternative approach is provided by bosonic codes, which use the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information. Two promising features of bosonic codes are that syndrome measurements are natively analog and that they can be concatenated with discrete-variable codes. In this work, we propose novel decoding methods that explicitly exploit the analog syndrome information obtained from the bosonic qubit readout in a concatenated architecture. Our methods are versatile and can be generally applied to any bosonic code concatenated with a quantum low-density parity-check (QLDPC) code. Furthermore, we introduce the concept of quasi-single-shot protocols as a novel approach that significantly reduces the number of repeated syndrome measurements required when decoding under phenomenological noise. To realize the protocol, we present a first implementation of time-domain decoding with the overlapping window method for general QLDPC codes, and a novel analog single-shot decoding method. Our results lay the foundation for general decoding algorithms using analog information and demonstrate promising results in the direction of fault-tolerant quantum computation with concatenated bosonic-QLDPC codes.Comment: 30 pages, 15 figure

Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits

We provide an explicit construction of a universal gate set for continuous-variable quantum computation with microwave circuits. Such a universal set has been first proposed in quantum-optical setups, but its experimental implementation has remained elusive in that domain due to the difficulties in engineering strong nonlinearities. Here, we show that a realistic microwave architecture allows to overcome this difficulty. As an application, we show that this architecture allows to generate a cubic phase state with an experimentally feasible procedure. This work highlights a practical advantage of microwave circuits with respect to optical systems for the purpose of engineering non-Gaussian states, and opens the quest for continuous-variable algorithms based on a few repetitions of elementary gates from the continuous-variable universal set.Comment: 6+6 pages, 2 figure

Universal control of a bosonic mode via drive-activated native cubic interactions

Linear bosonic modes offer a hardware-efficient alternative for quantum information processing but require access to some nonlinearity for universal control. The lack of nonlinearity in photonics has led to encoded measurement-based quantum computing, which rely on linear operations but requires access to resourceful ('nonlinear') quantum states, such as cubic phase states. In contrast, superconducting microwave circuits offer engineerable nonlinearities but suffer from static Kerr nonlinearity. Here, we demonstrate universal control of a bosonic mode composed of a superconducting nonlinear asymmetric inductive element (SNAIL) resonator, enabled by native nonlinearities in the SNAIL element. We suppress static nonlinearities by operating the SNAIL in the vicinity of its Kerr-free point and dynamically activate nonlinearities up to third order by fast flux pulses. We experimentally realize a universal set of generalized squeezing operations, as well as the cubic phase gate, and exploit them to deterministically prepare a cubic phase state in 60 ns. Our results initiate the experimental field of universal continuous-variables quantum computing.Comment: 11 pages, 6 figures and supplementary material

Investigation of the use of a sensor bracelet for the presymptomatic detection of changes in physiological parameters related to COVID-19: an interim analysis of a prospective cohort study (COVI-GAPP).

OBJECTIVES We investigated machinelearningbased identification of presymptomatic COVID-19 and detection of infection-related changes in physiology using a wearable device. DESIGN Interim analysis of a prospective cohort study. SETTING, PARTICIPANTS AND INTERVENTIONS Participants from a national cohort study in Liechtenstein were included. Nightly they wore the Ava-bracelet that measured respiratory rate (RR), heart rate (HR), HR variability (HRV), wrist-skin temperature (WST) and skin perfusion. SARS-CoV-2 infection was diagnosed by molecular and/or serological assays. RESULTS A total of 1.5 million hours of physiological data were recorded from 1163 participants (mean age 44±5.5 years). COVID-19 was confirmed in 127 participants of which, 66 (52%) had worn their device from baseline to symptom onset (SO) and were included in this analysis. Multi-level modelling revealed significant changes in five (RR, HR, HRV, HRV ratio and WST) device-measured physiological parameters during the incubation, presymptomatic, symptomatic and recovery periods of COVID-19 compared with baseline. The training set represented an 8-day long instance extracted from day 10 to day 2 before SO. The training set consisted of 40 days measurements from 66 participants. Based on a random split, the test set included 30% of participants and 70% were selected for the training set. The developed long short-term memory (LSTM) based recurrent neural network (RNN) algorithm had a recall (sensitivity) of 0.73 in the training set and 0.68 in the testing set when detecting COVID-19 up to 2 days prior to SO. CONCLUSION Wearable sensor technology can enable COVID-19 detection during the presymptomatic period. Our proposed RNN algorithm identified 68% of COVID-19 positive participants 2 days prior to SO and will be further trained and validated in a randomised, single-blinded, two-period, two-sequence crossover trial. Trial registration number ISRCTN51255782; Pre-results

Sex-specific differences in physiological parameters related to SARS-CoV-2 infections among a national cohort (COVI-GAPP study)

Considering sex as a biological variable in modern digital health solutions, we investigated sex-specific differences in the trajectory of four physiological parameters across a COVID-19 infection. A wearable medical device measured breathing rate, heart rate, heart rate variability, and wrist skin temperature in 1163 participants (mean age = 44.1 years, standard deviation [SD] = 5.6; 667 [57%] females). Participants reported daily symptoms and con-founders in a complementary app. A machine learning algorithm retrospectively ingested daily biophysical parameters to detect COVID-19 infections. COVID-19 serology samples were collected from all participants at baseline and follow-up. We analysed potential sex-specific differences in physiology and antibody titres using multilevel modelling and t-tests. Over 1.5 million hours of physiological data were recorded. During the symptomatic period of infection, men demonstrated larger increases in skin temperature, breathing rate, and heart rate as well as larger decreases in heart rate variability than women. The COVID-19 infection detection algorithm performed similarly well for men and women. Our study belongs to the first research to provide evidence for differential physiological responses to COVID-19 between females and males, highlighting the potential of wearable technology to inform future precision medicine approaches

Quantum error correction with dissipatively stabilized squeezed-cat qubits

Noise-biased qubits are a promising route toward significantly reducing the hardware overhead associated with quantum error correction. The squeezed-cat code, a nonlocal encoding in phase space based on squeezed coherent states, is an example of a noise-biased (bosonic) qubit with exponential error bias. Here we propose and analyze the error correction performance of a dissipatively stabilized squeezed-cat qubit. We find that for moderate squeezing the bit-flip error rate gets significantly reduced in comparison with the ordinary cat qubit while leaving the phase-flip rate unchanged. Additionally, we find that the squeezing enables faster and higher-fidelity gates

Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements

Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware overhead required for fault-tolerant quantum information processing. A broad class of bosonic codes, namely rotation-symmetric codes, can be characterized by their phase-space rotation symmetry. However, their performance has been examined to date only within an idealistic noise model. Here, we further analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. To this end, we numerically compute the average gate fidelity, including measurement errors into the noise model of the data qubit. Focusing on physical measurement models, we assess the performance of heterodyne and adaptive homodyne detection in comparison to the previously studied canonical phase measurement. This setting allows us to shed light on the role of different currently available measurement schemes when decoding the encoded information. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential. In addition, we perform a detailed analysis of Gottesman-Kitaev-Preskill (GKP) codes using a similar error-correction circuit that allows us to analyze the effect of realistic measurement models on different codes. In comparison to RSB codes, we find for GKP codes an even greater reduction in performance together with a vulnerability to photon-number dephasing. Our results show that highly efficient measurement protocols constitute a crucial building block towards error-corrected quantum information processing with bosonic continuous-variable systems.Comment: revised & accepted versio