Bosonic quantum error correction codes in superconducting quantum circuits

Error suppression in multicomponent cat codes with photon subtraction and teleamplification

It is known that multiphoton states can be protected from decoherence due to a passive loss channel by applying noiseless attenuation before and noiseless amplification after the channel. In this work, we propose the combined use of multiphoton subtraction on four-component cat codes and teleamplification to effectively suppress errors under detection and environmental losses. The back-action from multiphoton subtraction modifies the encoded qubit encoded on cat states by suppressing the higher photon numbers, while simultaneously ensuring that the original qubit can be recovered effectively through teleamplification followed by error correction, thus preserving its quantum information. With realistic photon subtraction and teleamplification-based scheme followed by optimal error-correcting maps, one can achieve a worst-case fidelity (over all encoded pure states) of over 93.5% (82% with only noisy teleamplification) at a minimum success probability of about 3.42%, under a 10% environmental-loss rate, 95% detector efficiency and sufficiently large cat states with the coherent-state amplitudes of 2. This sets a promising standard for combating large passive losses in quantum-information tasks in the noisy intermediate-scale quantum (NISQ) era, such as direct quantum communication or the storage of encoded qubits on the photonic platform.

Autonomous Stabilization of Fock States in an Oscillator against Multiphoton Losses

Fock states with a well-defined number of photons in an oscillator have shown a wide range of applications in quantum information science. Nonetheless, their usefulness has been marred by single and multiphoton losses due to unavoidable environment-induced dissipation. Though several dissipation engineering methods have been developed to counteract the leading single-photon-loss error, averting multiple-photon losses remains elusive. Here, we experimentally demonstrate a dissipation engineering method that autonomously stabilizes multiphoton Fock states against losses of multiple photons using a cascaded selective photon-addition operation in a superconducting quantum circuit. Through measuring the photon-number populations and Wigner tomography of the oscillator states, we observe a prolonged preservation of nonclassical Wigner negativities for the stabilized Fock states |N⟩ with N=1, 2, 3 for a duration of about 10 ms. Furthermore, the dissipation engineering method demonstrated here also facilitates the implementation of a nonunitary operation for resetting a binomially encoded logical qubit. These results highlight potential applications in error-correctable quantum information processing against multiple-photon-loss errors.

Artificial intelligence, human cognition, and conscious supremacy

The computational significance of consciousness is an important and potentially more tractable research theme than the hard problem of consciousness, as one could look at the correlation of consciousness and computational capacities through, e.g., algorithmic or complexity analyses. In the literature, consciousness is defined as what it is like to be an agent (i.e., a human or a bat), with phenomenal properties, such as qualia, intentionality, and self-awareness. The absence of these properties would be termed "unconscious." The recent success of large language models (LLMs), such as ChatGPT, has raised new questions about the computational significance of human conscious processing. Although instances from biological systems would typically suggest a robust correlation between intelligence and consciousness, certain states of consciousness seem to exist without manifest existence of intelligence. On the other hand, AI systems seem to exhibit intelligence without consciousness. These instances seem to suggest possible dissociations between consciousness and intelligence in natural and artificial systems. Here, I review some salient ideas about the computational significance of human conscious processes and identify several cognitive domains potentially unique to consciousness, such as flexible attention modulation, robust handling of new contexts, choice and decision making, cognition reflecting a wide spectrum of sensory information in an integrated manner, and finally embodied cognition, which might involve unconscious processes as well. Compared to such cognitive tasks, characterized by flexible and ad hoc judgments and choices, adequately acquired knowledge and skills are typically processed unconsciously in humans, consistent with the view that computation exhibited by LLMs, which are pretrained on a large dataset, could in principle be processed without consciousness, although conversations in humans are typically done consciously, with awareness of auditory qualia as well as the semantics of what are being said. I discuss the theoretically and practically important issue of separating computations, which need to be conducted consciously from those which could be done unconsciously, in areas, such as perception, language, and driving. I propose conscious supremacy as a concept analogous to quantum supremacy, which would help identify computations possibly unique to consciousness in biologically practical time and resource limits. I explore possible mechanisms supporting the hypothetical conscious supremacy. Finally, I discuss the relevance of issues covered here for AI alignment, where computations of AI and humans need to be aligned.

Autonomous Quantum Error Correction of Gottesman-Kitaev-Preskill States

The Gottesman-Kitaev-Preskill (GKP) code encodes a logical qubit into a bosonic system with resilience against single-photon loss, the predominant error in most bosonic systems. Here we present experimental results demonstrating quantum error correction of GKP states based on reservoir engineering of a superconducting device. Error correction is made fully autonomous through an unconditional reset of an auxiliary transmon qubit. We show that the lifetime of the logical qubit is increased from quantum error correction, therefore reaching the point at which more errors are corrected than generated.

Engineering Arbitrary Hamiltonians in Phase Space

We introduce a general method to engineer arbitrary Hamiltonians in the Floquet phase space of a periodically driven oscillator, based on the noncommutative Fourier transformation technique. We establish the relationship between an arbitrary target Floquet Hamiltonian in phase space and the periodic driving potential in real space. We obtain analytical expressions for the driving potentials in real space that can generate novel Hamiltonians in phase space, e.g., rotational lattices and sharp-boundary wells. Our protocol can be realized in a range of experimental platforms for nonclassical state generation and bosonic quantum computation.

Fragility of the Schrödinger Cat in thermal environments

We describe the decoherence instability of Schrödinger Cat states in the two-site Bose-Hubbard model with an attractive on-site interaction between particles. For N particles with onsite attractive energy U and hopping amplitude between sites t, Cat states exist for [Formula: see text] at zero temperature. However, they are increasingly unstable to small thermal fluctuations as the Cat itself is increasingly well-defined and its components become well-separated. For any given [Formula: see text], the decoherence temperature becomes smaller for large N. The loss of off-diagonal coherence peaks in the equilibrium density matrix is dominated by the thermal admixture of the first excited state of the many-body system with its ground state. Particle number fluctuations, described in the grand canonical ensemble also reduce coherence, but to a lesser degree than thermal fluctuations. The full density matrix of the Schrödinger Cat is obtained by exact numerical diagonalization of the many-body Hamiltonian and a narrow regime in the parameter space of the particle number, temperature, and U/t is identified where small Cat states may survive decoherence in a physical environment.

Dual-rail encoding with superconducting cavities

The design of quantum hardware that reduces and mitigates errors is essential for practical quantum error correction (QEC) and useful quantum computation. To this end, we introduce the circuit-Quantum Electrodynamics (QED) dual-rail qubit in which our physical qubit is encoded in the single-photon subspace, [Formula: see text], of two superconducting microwave cavities. The dominant photon loss errors can be detected and converted into erasure errors, which are in general much easier to correct. In contrast to linear optics, a circuit-QED implementation of the dual-rail code offers unique capabilities. Using just one additional transmon ancilla per dual-rail qubit, we describe how to perform a gate-based set of universal operations that includes state preparation, logical readout, and parametrizable single and two-qubit gates. Moreover, first-order hardware errors in the cavities and the transmon can be detected and converted to erasure errors in all operations, leaving background Pauli errors that are orders of magnitude smaller. Hence, the dual-rail cavity qubit exhibits a favorable hierarchy of error rates and is expected to perform well below the relevant QEC thresholds with today's coherence times.

Significant improvement of fidelity for encoded quantum bell pairs at long and short-distance communication along with generalized circuit

Quantum entanglement is a unique criterion of the quantum realm and an essential tool to secure quantum communication. Ensuring high-fidelity entanglement has always been a challenging task owing to interaction with the hostile channel environment created due to quantum noise and decoherence. Though several methods have been proposed, correcting almost all arbitrary errors is still a gigantic task. As one of the main contributions of this work, a new model for 'large distance communication' has been proposed, which may correct all bit flip errors or other errors quite extensively if proper encoding and subspace measurements are used. To achieve this purpose, at the very first step, the idea of differentiating the 'long-distance communication' and 'short-distance applications' has been introduced. Short-distance is determined by the maximum range of applying unitary control gates by the qubit technology. How the error correcting ability of Quantum codes change for short and long-distance application is investigated in this work, which was not explored in previous literatures as far as we know. At the beginning, we have applied stabilizer formalism and Repetition Code for decoding to distinguish the error correcting ability in long and short distance communication. Particularly for short-distance communication, it has been demonstrated that a 'properly encoded' bell state can identify all the bit flip, or phase flip errors with 100% accuracy theoretically. In contrast, if the bell states are used in long-distance communication, the error-detecting and correcting ability reduces at huge amounts. To increase the fidelity significantly and correct the errors quite extensively for long-distance communication, a new model based on classical communication protocol has been suggested. All the required circuits in these processes have been generalized for arbitrary (even) numbers of ancilla qubits during encoding. Proposed analytical results have also been verified with the Simulation results of IBM QISKIT QASM.

Approximate Autonomous Quantum Error Correction with Reinforcement Learning

Autonomous quantum error correction (AQEC) protects logical qubits by engineered dissipation and thus circumvents the necessity of frequent, error-prone measurement-feedback loops. Bosonic code spaces, where single-photon loss represents the dominant source of error, are promising candidates for AQEC due to their flexibility and controllability. While existing proposals have demonstrated the in-principle feasibility of AQEC with bosonic code spaces, these schemes are typically based on the exact implementation of the Knill-Laflamme conditions and thus require the realization of Hamiltonian distances d≥2. Implementing such Hamiltonian distances requires multiple nonlinear interactions and control fields, rendering these schemes experimentally challenging. Here, we propose a bosonic code for approximate AQEC by relaxing the Knill-Laflamme conditions. Using reinforcement learning (RL), we identify the optimal bosonic set of code words (denoted here by RL code), which, surprisingly, is composed of the Fock states |2⟩ and |4⟩. As we show, the RL code, despite its approximate nature, successfully suppresses single-photon loss, reducing it to an effective dephasing process that well surpasses the break-even threshold. It may thus provide a valuable building block toward full error protection. The error-correcting Hamiltonian, which includes ancilla systems that emulate the engineered dissipation, is entirely based on the Hamiltonian distance d=1, significantly reducing model complexity. Single-qubit gates are implemented in the RL code with a maximum distance d_{g}=2.

Beating the break-even point with a discrete-variable-encoded logical qubit

Quantum error correction (QEC) aims to protect logical qubits from noises by using the redundancy of a large Hilbert space, which allows errors to be detected and corrected in real time1. In most QEC codes2-8, a logical qubit is encoded in some discrete variables, for example photon numbers, so that the encoded quantum information can be unambiguously extracted after processing. Over the past decade, repetitive QEC has been demonstrated with various discrete-variable-encoded scenarios9-17. However, extending the lifetimes of thus-encoded logical qubits beyond the best available physical qubit still remains elusive, which represents a break-even point for judging the practical usefulness of QEC. Here we demonstrate a QEC procedure in a circuit quantum electrodynamics architecture18, where the logical qubit is binomially encoded in photon-number states of a microwave cavity8, dispersively coupled to an auxiliary superconducting qubit. By applying a pulse featuring a tailored frequency comb to the auxiliary qubit, we can repetitively extract the error syndrome with high fidelity and perform error correction with feedback control accordingly, thereby exceeding the break-even point by about 16% lifetime enhancement. Our work illustrates the potential of hardware-efficient discrete-variable encodings for fault-tolerant quantum computation19.

Contextuality and Wigner Negativity Are Equivalent for Continuous-Variable Quantum Measurements

Quantum computers promise considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting-a promising paradigm for the realization of universal, scalable, and fault-tolerant quantum computing-contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard models of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way toward practical demonstrations of continuous-variable contextuality and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.

Quantum-enhanced radiometry via approximate quantum error correction

Quantum sensing based on exotic quantum states is appealing for practical metrology applications and fundamental studies. However, these quantum states are vulnerable to noise and the resulting quantum enhancement is weakened in practice. Here, we experimentally demonstrate a quantum-enhanced sensing scheme with a bosonic probe, by exploring the large Hilbert space of the bosonic mode and developing both the approximate quantum error correction and the quantum jump tracking approaches. In a practical radiometry scenario, we attain a 5.3 dB enhancement of sensitivity, which reaches 9.1 × 10⁻⁴ Hz^−1/2 when measuring the excitation population of a receiver mode. Our results demonstrate the potential of quantum sensing with near-term quantum technologies, not only shedding new light on the quantum advantage of sensing, but also stimulating further efforts on bosonic quantum technologies.

Exotic quantum states can be advantageous for sensing, but are very fragile, so that some form of quantum error correction is needed. Here, the authors show how approximate QEC helps overcoming decoherence due to noise when measuring the excitation population of a receiver mode in a superconducting circuit.

Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding

Quantum resource theories are a powerful framework for characterizing and quantifying relevant quantum phenomena and identifying processes that optimize their use for different tasks. Here, we define a resource measure for magic, the sought-after property in most fault-tolerant quantum computers. In contrast to previous literature, our formulation is based on bosonic codes, well-studied tools in continuous-variable quantum computation. Particularly, we use the Gottesman-Kitaev-Preskill code to represent multiqubit states and consider the resource theory for the Wigner negativity. Our techniques are useful in finding resource lower bounds for different applications as state conversion and gate synthesis. The analytical expression of our magic measure allows us to extend current analysis limited to small dimensions, easily addressing systems of up to 12 qubits.

Stabilizing a Bosonic Qubit Using Colored Dissipation

Protected qubits such as the 0-π qubit, and bosonic qubits including cat qubits and Gottesman-Kitaev-Preskill (GKP) qubits offer advantages for fault tolerance. Some of these protected qubits (e.g., 0-π qubit and Kerr-cat qubit) are stabilized by Hamiltonians which have (near-)degenerate ground state manifolds with large energy gaps to the excited state manifolds. Without dissipative stabilization mechanisms the performance of such energy-gap-protected qubits can be limited by leakage to excited states. Here, we propose a scheme for dissipatively stabilizing an energy-gap-protected qubit using colored (i.e., frequency-selective) dissipation without inducing errors in the ground state manifold. Concretely we apply our colored dissipation technique to Kerr-cat qubits and propose colored Kerr-cat qubits which are protected by an engineered colored single-photon loss. When applied to the Kerr-cat qubits our scheme significantly suppresses leakage-induced bit-flip errors (which we show are a limiting error mechanism) while only using linear interactions. Beyond the benefits to the Kerr-cat qubit we also show that our frequency-selective loss technique can be applied to a broader class of protected qubits.

Digital System Design for Quantum Error Correction Codes

Quantum computing is a computer development technology that uses quantum mechanics to perform the operations of data and information. It is an advanced technology, yet the quantum channel is used to transmit the quantum information which is sensitive to the environment interaction. Quantum error correction is a hybrid between quantum mechanics and the classical theory of error-correcting codes that are concerned with the fundamental problem of communication, and/or information storage, in the presence of noise. The interruption made by the interaction makes transmission error during the quantum channel qubit. Hence, a quantum error correction code is needed to protect the qubit from errors that can be caused by decoherence and other quantum noise. In this paper, the digital system design of the quantum error correction code is discussed. Three designs used qubit codes, and nine-qubit codes were explained. The systems were designed and configured for encoding and decoding nine-qubit error correction codes. For comparison, a modified circuit is also designed by adding Hadamard gates.

Quantum control of bosonic modes with superconducting circuits

Bosonic modes have wide applications in various quantum technologies, such as optical photons for quantum communication, magnons in spin ensembles for quantum information storage and mechanical modes for reversible microwave-to-optical quantum transduction. There is emerging interest in utilizing bosonic modes for quantum information processing, with circuit quantum electrodynamics (circuit QED) as one of the leading architectures. Quantum information can be encoded into subspaces of a bosonic superconducting cavity mode with long coherence time. However, standard Gaussian operations (e.g., beam splitting and two-mode squeezing) are insufficient for universal quantum computing. The major challenge is to introduce additional nonlinear control beyond Gaussian operations without adding significant bosonic loss or decoherence. Here we review recent advances in universal control of a single bosonic code with superconducting circuits, including unitary control, quantum feedback control, driven-dissipative control and holonomic dissipative control. Various approaches to entangling different bosonic modes are also discussed.

Generating Long-Lived Macroscopically Distinct Superposition States in Atomic Ensembles

We propose to create and stabilize long-lived macroscopic quantum superposition states in atomic ensembles. We show that using a fully quantum parametric amplifier can cause the simultaneous decay of two atoms and, in turn, create stabilized atomic Schrödinger cat states. Remarkably, even with modest parameters these intracavity atomic cat states can have an extremely long lifetime, up to 4 orders of magnitude longer than that of intracavity photonic cat states under the same parameter conditions, reaching tens of milliseconds. This lifetime of atomic cat states is ultimately limited to several seconds by extremely weak spin relaxation and thermal noise. Our work opens up a new way toward the long-standing goal of generating large-size and long-lived cat states, with immediate interests both in fundamental studies and noise-immune quantum technologies.

Continuous-Variable Assisted Thermal Quantum Simulation

Simulation of a quantum many-body system at finite temperatures is crucially important but quite challenging. Here we present an experimentally feasible quantum algorithm assisted with continuous variable for simulating quantum systems at finite temperatures. Our algorithm has a time complexity scaling polynomially with the inverse temperature and the desired accuracy. We demonstrate the quantum algorithm by simulating a finite temperature phase diagram of the quantum Ising and Kitaev models. It is found that the important crossover phase diagram of the Kitaev ring can be accurately simulated by a quantum computer with only a few qubits and thus the algorithm may be implementable on current quantum processors. We further propose a protocol with superconducting or trapped ion quantum computers.