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Building a large-scale quantum computer requires effective strategies to correct errors that inevitably arise in physical quantum systems 1 . Quantum error-correction codes 2 present a way to reach this goal by encoding logical information redundantly into many physical qubits. A key challenge in implementing such codes is accurately decoding noisy syndrome information extracted from redundancy checks to obtain the correct encoded logical information. Here we develop a recurrent, transformer-based neural network that learns to decode the surface code, the leading quantum error-correction code 3 . Our decoder outperforms other state-of-the-art decoders on real-world data from Google’s Sycamore quantum processor for distance-3 and distance-5 surface codes 4 . On distances up to 11, the decoder maintains its advantage on simulated data with realistic noise including cross-talk and leakage, utilizing soft readouts and leakage information. After training on approximate synthetic data, the decoder adapts to the more complex, but unknown, underlying error distribution by training on a limited budget of experimental samples. Our work illustrates the ability of machine learning to go beyond human-designed algorithms by learning from data directly, highlighting machine learning as a strong contender for decoding in quantum computers. A recurrent, transformer-based neural network, called AlphaQubit, learns high-accuracy error decoding to suppress the errors that occur in quantum systems, opening the prospect of using neural-network decoders for real quantum hardware.

Quantum information science uses the distinguishing features of quantum mechanics for novel information processing tasks, ranging from metrology to computation. This manuscript explores multiple topics in this field. We discuss implementations of hybrid quantum systems composed of trapped ions and superconducting circuits, protocols for detecting signatures of entanglement in small and many-body systems, and a proposal for ground state preparation in quantum Hamiltonian simulators.

Quantum error correcting codes typically do not account for quantum state transitions - leakage - out of the computational subspace. Since these errors can last for multiple detection rounds they can significantly contribute to logical errors. It is therefore important to understand how to numerically model them efficiently. Fully quantum simulations of leakage require more levels per leaked qubit, which substantially limits the system sizes that may be simulated. To address this, we introduce a Subspace Twirling Approximation (STA) on quantum channels that preserves the incoherence between the computational and leakage subspaces. The assumption of incoherence enables the quantum simulation of leakage at little computational overhead. We motivate the approximation's validity by showing that incoherence is achieved naturally during repeated stabilizer measurements. Additionally, we provide various simulation results which show that the STA yields accurate error correction statistics in the repetition and surface codes with physical error parameters.

Quantum error correcting codes typically do not account for quantum state transitions - leakage - out of the computational subspace. Since these errors can last for multiple detection rounds they can significantly contribute to logical errors. It is therefore important to understand how to numerically model them efficiently. Fully quantum simulations of leakage require more levels per leaked qubit, which substantially limits the system sizes that may be simulated. To address this, we introduce a Random Phase Approximation (RPA) on quantum channels that preserves the incoherence between the computational and leakage subspaces. The assumption of incoherence enables the quantum simulation of leakage at little computational overhead. We motivate the approximation's validity by showing that incoherence is achieved naturally during repeated stabilizer measurements. Additionally, we provide various simulation results which show that the RPA yields accurate error correction statistics in the repetition and surface codes with physical error parameters.

Obtaining accurate representations of the eigenstates of an array of coupled superconducting qubits is a crucial step in the design of circuit quantum electrodynamics (QED)-based quantum processors. However, exact diagonalization of the device Hamiltonian is challenging for system sizes beyond tens of qubits. Here, we employ a variant of the density matrix renormalization group (DMRG) algorithm, DMRG-X, to efficiently obtain localized eigenstates of a 2D transmon array without the need to first compute lower-energy states. We also introduce MTDMRG-X, a new algorithm that combines DMRG-X with multi-target DMRG to efficiently compute excited states even in regimes with strong eigenstate hybridization. We showcase the use of these methods for the analysis of long-range couplings in a multi-transmon Hamiltonian including qubits and couplers, and we discuss eigenstate localization. These developments facilitate the design and parameter optimization of large-scale superconducting quantum processors.

Quantum error-correction is a prerequisite for reliable quantum computation. Towards this goal, we present a recurrent, transformer-based neural network which learns to decode the surface code, the leading quantum error-correction code. Our decoder outperforms state-of-the-art algorithmic decoders on real-world data from Google's Sycamore quantum processor for distance 3 and 5 surface codes. On distances up to 11, the decoder maintains its advantage on simulated data with realistic noise including cross-talk, leakage, and analog readout signals, and sustains its accuracy far beyond the 25 cycles it was trained on. Our work illustrates the ability of machine learning to go beyond human-designed algorithms by learning from data directly, highlighting machine learning as a strong contender for decoding in quantum computers.

We give a novel derivation of Holevo's bound using an important result from nonequilibrium statistical physics, the fluctuation theorem. To do so we develop a general formalism of quantum fluctuation theorems for two-time measurements, which explicitly accounts for the back action of quantum measurements as well as possibly non-unitary time evolution. For a specific choice of observables this fluctuation theorem yields a measurement-dependent correction to the Holevo bound, leading to a tighter inequality. We conclude by analyzing equality conditions for the improved bound.

Superconducting circuits and trapped ions are promising architectures for quantum information processing. However, the natural frequencies for controlling these systems -- radio frequency ion control and microwave domain superconducting qubit control -- make direct Hamiltonian interactions between them weak. In this paper we describe a technique for coupling a trapped ion's motion to the fundamental mode of a superconducting circuit, by applying to the circuit a carefully modulated external magnetic flux. In conjunction with a non-linear element (Josephson junction), this gives the circuit an effective time-dependent inductance. We then show how to tune the external flux to generate a resonant coupling between the circuit and ion's motional mode, and discuss the limitations of this approach compared to using a time-dependent capacitance.

Controllable systems relying on quantum behavior to simulate distinctly quantum models so far rely on increasingly challenging classical computing to verify their results. We develop a general protocol for confirming that an arbitrary many-body system, such as a quantum simulator, can entangle distant objects. The protocol verifies that distant qubits interacting separately with the system can become mutually entangled, and therefore serves as a local test that excitations of the system can create non-local quantum correlations. We derive an inequality analogous to Bell's inequality which can only be violated through entanglement between distant sites of the many-body system. Although our protocol is applicable to general many-body systems, it requires finding system-dependent local operations to violate the inequality. A specific example in quantum magnetism is presented.

For a variety of superconducting qubits, tunable interactions are achieved through mutual inductive coupling to a coupler circuit containing a nonlinear Josephson element. In this paper we derive the general interaction mediated by such a circuit under the Born-Oppenheimer Approximation. This interaction naturally decomposes into a classical part, with origin in the classical circuit equations, and a quantum part, associated with the coupler's zero-point energy. Our result is non-perturbative in the qubit-coupler coupling strengths and in the coupler nonlinearity. This can lead to significant departures from previous, linear theories for the inter-qubit coupling, including non-stoquastic and many-body interactions. Our analysis provides explicit and efficiently computable series for any term in the interaction Hamiltonian and can be applied to any superconducting qubit type. We conclude with a numerical investigation of our theory using a case study of two coupled flux qubits, and in particular study the regime of validity of the Born-Oppenheimer Approximation.