The birth, life, and death of Maxwell’s demon provoked a profound discussion about the interplay between thermodynamics, computation, and information. Even after its resolution, the demon continues to inspire a multidisciplinary field. This tutorial offers a comprehensive overview of Maxwell’s demon and its enduring influence, bridging classical concepts with modern insights in thermodynamics, information theory, and quantum mechanics.

Quantum simulators have the potential to solve quantum many-body problems that are beyond the reach of classical computers, especially when they feature long-range entanglement. To fulfill their prospects, quantum simulators must be fully controllable, allowing for precise tuning of the microscopic physical parameters that define their implementation. We consider Rydberg-atom arrays, a promising platform for quantum simulations. Experimental control of such arrays is limited by the imprecision on the optical-tweezer positions when assembling the array, hence introducing uncertainties in the simulated Hamiltonian. In this work, we introduce a scalable approach to Hamiltonian learning using graph neural networks (GNNs). We employ the density-matrix renormalization group to generate ground-state snapshots of the transverse-field Ising model realized by the array, for many realizations of the Hamiltonian parameters. Correlation functions reconstructed from these snapshots serve as input data to carry out the training. We demonstrate that our GNN model has a remarkable capacity to extrapolate beyond its training domain, regarding both the size and the shape of the system, yielding an accurate determination of the Hamiltonian parameters with a minimal set of measurements. We prove a theorem establishing a bijective correspondence between the correlation functions and the interaction parameters in the Hamiltonian, which provides a theoretical foundation for our learning algorithm. Our work could open the road to feedback control of the positions of the optical tweezers, hence providing a decisive improvement of analog quantum simulators.

Characters of irreducible representations are ubiquitous in group theory. However, computing characters of some groups such as the symmetric group $S_n$ is a challenging problem known to be #P-hard in the worst case. Here we describe a matrix product state (MPS) algorithm for characters of $S_n$. The algorithm computes an MPS encoding all irreducible characters of a given permutation. It relies on a mapping from characters of $S_n$ to quantum spin chains proposed by Crichigno and Prakash. We also provide a simpler derivation of this mapping. We complement this result by presenting a $\mathrm{poly}(n)$ size quantum circuit that prepares the corresponding MPS obtaining an efficient quantum algorithm for certain sampling problems based on characters of $S_n$. To assess classical hardness of these problems, we present a general reduction from strong simulation (computing a given probability) to weak simulation (sampling with a small error). This reduction applies to any sampling problem with a certain granularity structure and may be of independent interest.

We theoretically propose a tunable implementation of symmetry-protected topological phases of matter in a synthetic superlattice, taking advantage of the long coherence time and exquisite spectral resolutions offered by gravity-tilted optical lattice clocks. We describe a protocol similar to Rabi spectroscopy that can be used to probe the distinct topological properties of our system. We then demonstrate how the sensitivity of clocks and interferometers can be protected from unwanted experimental imperfections offered by the underlying topological robustness. The proposed implementation opens a path to exploiting the unique opportunities offered by symmetry-protected topological phases in state-of-the-art quantum sensors.

Quantum metrology aims to maximize measurement precision on quantum systems, with a wide range of applications in quantum sensing. Achieving the Heisenberg limit (HL)—the fundamental precision bound set by quantum mechanics—is often hindered by noise-induced decoherence, which typically reduces achievable precision to the standard quantum limit (SQL). While quantum error correction (QEC) can recover the HL under Markovian noise, its applicability to non-Markovian noise remains less explored. In this work, we analyze a hidden Markov model (HMM) in which a quantum probe, coupled to an inaccessible environment, undergoes joint evolution described by Lindbladian dynamics, with the inaccessible degrees of freedom serving as a memory. We derive generalized Knill-Laflamme conditions for the HMM and establish three types of sufficient conditions for achieving the HL under non-Markovian noise using QEC. Additionally, we demonstrate the attainability of the SQL when these sufficient conditions are violated, by analytical solutions for special cases and numerical methods for general scenarios. Our results not only extend prior QEC frameworks for metrology but also provide new insights into precision limits under realistic noise conditions.

We introduce the iterative Clifford circuit renormalization (ICCR), a novel technique designed to handle the dynamics of nonstabilizerness (also known as quantum magic) in generic quantum circuits composed of Clifford and non-Clifford gates, as well as measurements, extending beyond the reach of pre-existing methods. ICCR iteratively adjusts the starting circuit, transforming it into a Clifford circuit where all elements that can alter the nonstabilizerness, such as measurements or $T$ gates, have been removed. In the process the initial state is renormalized in such a way that the new circuit outputs the same final state as the original one. This approach embeds the complex dynamics of nonstabilizerness in the flow of an effective initial state, enabling the efficient evaluation of stabilizer Renyi entropies and magic nullity while avoiding the need for direct and computationally expensive simulation of the original circuit. The initial state renormalization can be computed explicitly using a matrix-product state approximation that can be systematically improved. We implement the ICCR algorithm to evaluate the nonstabilizerness dynamics for systems of size up to $N=1000$, in one and more dimensions. We validate our method by comparing it to tensor-network simulations. Finally, we employ the ICCR technique to study measurement-induced magic transitions in monitored circuits without and with $T$ gates.

Dynamical decoupling (DD) is a low-overhead method for quantum error suppression. Despite extensive work in DD design, finding pulse sequences that optimally decouple computational qubits is not well understood. Using IBM’s superconducting-qubit-based quantum processors, we demonstrate how to empirically tailor DD strategies for an arbitrary quantum circuit and device. These learned DD strategies significantly improve error suppression relative to canonical sequences, with relative improvement increasing with problem size and circuit sophistication. We leverage this to study mirror randomized benchmarking on 100 qubits, Greenberger-Horne-Zeilinger state preparation on 50 qubits, and the Bernstein-Vazirani algorithm on 27 qubits. Our empirical learning method finds strategies, in constant time independent of circuit width and depth, provides stable performance over long time periods without retraining, and generalizes to larger circuits when trained on small subcircuit structures.

Advances in materials and fabrication of superconducting devices allows the exploration of novel quantum effects in synthetic superconducting systems beyond conventional Josephson-junction arrays. As an example, we introduce a new circuit element, the Y splitter, a superconducting loop with three leads and three Josephson junctions, smaller or comparable in size to the superconducting coherence length of the material. By tuning magnetic flux through an array of Y splitters, Cooper-pair transport can be made to interfere destructively, while spatially separated split Cooper pairs propagate coherently. We consider an array of Y splitters connected in a two-dimensional star [Archimedean (3,${12}^2$)] geometry, deformable into the kagome lattice, and find a rich phase diagram that includes topological superconducting phases with Chern numbers $\pm 2$. Experimental realization appears feasible.

Fault-tolerant implementation of non-Clifford gates is a major challenge for achieving universal fault-tolerant quantum computing with quantum error-correcting codes. Magic state distillation is the most well-studied method for this but requires significant resources. Hence, it is crucial to tailor and optimize magic state distillation for specific codes from both logical- and physical-level perspectives. In this work, we perform such optimization for two-dimensional color codes, which are promising due to their higher encoding rates compared to surface codes, transversal implementation of Clifford gates, and efficient lattice surgery. We propose two carefully designed distillation schemes based on the 15-to-1 distillation circuit and lattice surgery, differing in their methods for handling faulty rotations. Our first scheme employs faulty $T$ measurement, achieving infidelities of $O(p^3)$ for physical noise strength $p$. To achieve lower infidelities, our second scheme integrates distillation with “cultivation” (a distillation-free approach to fault tolerantly prepare magic states through transversal Clifford measurements). Our second scheme achieves significantly lower infidelities (e.g., approximately $2\times {10}^{-16}$ at $p={10}^{-3}$), surpassing the capabilities of both cultivation and single-level distillation. Notably, to reach a given target infidelity, our schemes require approximately 2 orders of magnitude fewer resources than the previous best magic-state-distillation schemes for color codes.

We demonstrate that eigenstates of selected interacting spin chains can be efficiently prepared using quantum circuits with polynomial depth in system size and particle number. While this is well established for free-fermionic spin chains, we extend this result to the folded $XXZ$ model, an integrable rigid-rod deformation of the $XX$ model with simple interactions that exhibits Hilbert space fragmentation. We construct explicit quantum circuits that efficiently prepare arbitrary eigenstates of this model on an open chain. Error-mitigated noisy simulations with up to 13 qubits and various qubit connectivities achieve a relative error below 5%. As a byproduct, we extend a recent reformulation of the Bethe ansatz as a quantum circuit to open boundary conditions.

Protecting qubits from environmental noise while maintaining strong coupling for fast high-fidelity control is a central challenge for quantum information processing. Here, we demonstrate a control scheme for superconducting fluxonium qubits that eliminates qubit decay through the control channel by suppressing the environmental density of states at the transition frequency. Adding a low-pass filter on the flux line allows for flux-biasing and, at the same time, coherently controlling the fluxonium qubit by parametrically driving it at integer fractions of its transition frequency. We compare the filtered to the unfiltered configuration and find a 5-times-longer $T_1$, and a 10-times-improved $T_2$-echo time in the filtered case. We demonstrate coherent control with up to 11-photon subharmonic drives, highlighting the strong nonlinearity of the fluxonium potential. Measured Rabi frequencies and drive-induced frequency shifts show excellent agreement with numerical and analytical models. Furthermore, we show the equivalence of a 3-photon subharmonic drive to an on-resonance drive by benchmarking subharmonic gate fidelities above 99.94%. These results open up a scalable path for full qubit control through a single Purcell-protected channel, providing strong suppression of control-induced decoherence and enabling wiring-efficient superconducting quantum processors.

Quantum error-correction codes protect information from realistic noisy channels and lie at the heart of quantum computation and communication tasks. Understanding the optimal performance and other information-theoretic properties, such as the achievable rates, of a given code is crucial, as these factors determine the fundamental limits imposed by the encoding in conjunction with the noise channel. Here, we use the transpose channel to analytically obtain the near-optimal performance of any Gottesman-Kitaev-Preskill (GKP) code under pure loss and pure amplification. We present rigorous connections between GKP code’s near-optimal performance and its dual lattice geometry and average input energy. With no energy constraint, we show that when $|\tau /(1-\tau )|$ is an integer, specific families of GKP codes simultaneously achieve the loss and amplification capacity. $\tau$ is the transmissivity (gain) for loss (amplification). Our results establish GKP code as the first structured bosonic code family that achieves the capacity of loss and amplification.

As systems for quantum computing keep growing in size and number of qubits, challenges in scaling the control capabilities are becoming increasingly relevant. Efficient schemes to simultaneously mediate coherent interactions between multiple quantum systems and to reduce decoherence errors can minimize the control overhead in next-generation quantum processors. Here, we present a superconducting qubit architecture based on tunable parametric interactions to perform two-qubit gates, reset, leakage recovery, and to read out the qubits. In this architecture, parametrically driven multielement couplers selectively couple qubits to resonators and neighboring qubits, according to the frequency of the drive. We consider a system with two qubits and one readout resonator interacting via a single coupling circuit and experimentally demonstrate a controlled-$Z$ gate with a fidelity of $98.30\pm 0.23\mathrm{\%}$, a reset operation that unconditionally prepares the qubit ground state with a fidelity of $99.80\pm 0.02\mathrm{\%}$ and a leakage recovery operation with a $98.5\pm 0.3\mathrm{\%}$ success probability. Furthermore, we implement a parametric readout with a single-shot assignment fidelity of $88.0\pm 0.4\mathrm{\%}$. These operations are all realized using a single tunable coupler and a statically decoupled resonator, demonstrating the experimental feasibility of the proposed architecture and its potential for reducing the system complexity in scalable quantum processors.

Quantum transmission links are central elements in essentially all protocols involving the exchange of quantum messages. Emerging progress in quantum technologies involving such links needs to be accompanied by appropriate certification tools. In adversarial scenarios, a certification method can be vulnerable to attacks if too much trust is placed on the underlying system. Here, we propose a protocol in a device-independent framework, which allows for the certification of practical quantum transmission links in scenarios in which minimal assumptions are made about the functioning of the certification setup. In particular, we take unavoidable transmission losses into account by modeling the link as a completely positive trace-decreasing map. We also, crucially, remove the assumption of independent identically distributed samples, which is known to be incompatible with adversarial settings. Particular emphasis is put on a one-sided device-independent scenario, in which the sender possesses trusted resources. Finally, in view of the use of the certified transmitted states for follow-up applications, our protocol moves beyond certification of the channel to allow us to estimate the quality of the transmitted quantum message itself. To illustrate the practical relevance and the feasibility of our protocol with currently available technology, we provide an experimental implementation in the one-sided device-independent setting, based on a state-of-the-art polarization-entangled photon-pair source in a Sagnac configuration, and analyze its robustness for realistic losses and errors.

Although measuring the deterministic waveform of a weak classical force is a well-studied problem, estimating a random waveform, such as the spectral density of a stochastic signal field, is much less well understood despite it being a widespread task at the frontier of experimental physics. State-of-the-art precision sensors of random forces must account for the underlying quantum nature of the measurement but the optimal quantum protocol for interrogating such linear sensors is not known. We derive the fundamental precision limit: the extended-channel quantum Cramér-Rao bound. In the experimentally relevant regime in which losses dominate, we prove that non-Gaussian-state preparation and measurement are required to achieve this fundamental limit and we determine numerically the optimal non-Gaussian protocol. We discuss how this scheme could accelerate searches for signatures of quantum gravity, stochastic gravitational waves, and axionic dark matter.

Quantum dynamics on curved spacetime has never been directly probed beyond the Newtonian limit. Although we can describe such dynamics theoretically, experiments would provide empirical evidence that quantum theory holds even in this extreme limit. The practical challenge is the minute spacetime curvature difference over the length scale of the typical extent of quantum effects. Here, we propose a quantum network of alkaline earth (like) atomic processors for constructing a distributed quantum state that is sensitive to the differential proper time between its constituent atomic processor nodes, implementing a quantum observable that is affected by post-Newtonian curved spacetime. Conceptually, we propose to delocalize one clock between three locations by encoding the presence or absence of a clock into the state of the local atoms. By separating three atomic nodes over approximately kilometer-scale elevation differences and distributing one clock between them via a $W$ state, we demonstrate that the curvature of spacetime is manifest in the interference of the three different proper times that give rise to three distinct beat notes in our nonlocal observable. We further demonstrate that $N$-atom entanglement within each node enhances the interrogation bandwidth by a factor of $N$. We discuss how our proposed system can probe new facets of fundamental physics, such as the linearity, unitarity, and probabilistic nature of quantum theory on curved spacetime. Our protocol combines several recent advances with neutral atom and trapped ions to realize a novel quantum probe of gravity uniquely enabled by quantum networks.

We consider the estimation of an unknown parameter $\theta$ via a many-body probe. The probe is initially prepared in a product state and many-body time-independent interactions enhance its $\theta$ sensitivity during the dynamics and/or in the steady state. We present bounds on the quantum Fisher information, and corresponding optimal interacting Hamiltonians, for two paradigmatic scenarios for encoding $\theta$: (i) via unitary Hamiltonian dynamics (dynamical metrology), and (ii) in the Gibbs and diagonal ensembles (time-averaged dephased state), two ubiquitous steady states of many-body open dynamics. We then move to the specific problem of estimating the strength of a magnetic field via interacting spins and derive two-body interacting Hamiltonians that can approach the fundamental precision bounds. In this case, we additionally analyze the transient regime leading to the steady states and characterize trade-offs between equilibration times and measurement precision. Overall, our results provide a comprehensive picture of the potential of many-body control in quantum sensing.

The advent of digital neutral-atom quantum computers relies on the development of fast and robust protocols for high-fidelity quantum operations. In this work, we introduce a novel scheme for entangling gates using four atomic levels per atom: a ground-state qubit and two Rydberg states. A laser field couples the qubit to one of the two Rydberg states, while a microwave field drives transitions between the two Rydberg states, enabling a resonant dipole-dipole interaction between different atoms. We show that controlled-$Z$ gates can be realized in this scheme without requiring optical phase modulation and relying solely on a microwave field with time-dependent phase and amplitude. We demonstrate that such gates are faster and less sensitive to Rydberg decay than state-of-the-art Rydberg gates based on van der Waals interactions. Moreover, we systematically stabilize our protocol against interatomic distance fluctuations and analyze its performance in realistic setups with rubidium or cesium atoms. Our results open up new avenues to the use of microwave-driven dipolar interactions for quantum computation with neutral atoms.

Device error rates on current quantum computers have improved enough to where demonstrations of error correction below break even are now possible. Still, the circuits required for quantum error correction introduce significant overhead and sometimes inject more errors than they correct. In this work, we introduce adaptive syndrome extraction as a scheme to improve code performance and reduce the quantum error-correction cycle time by measuring only the stabilizer generators that are likely to provide useful syndrome information. We provide a concrete example of the scheme through the [[4,2,2]] code concatenated with a hypergraph product code and a syndrome-extraction cycle that uses quantum error detection to modify the syndrome-extraction circuits in real time. Compared to nonconcatenated codes and nonadaptive syndrome extraction, we find that the adaptive scheme achieves over an order of magnitude lower logical error rates while requiring fewer cnot gates and physical qubits. Furthermore, we show how to achieve fault-tolerant universal logical computation with [[4,2,2]]-concatenated hypergraph product codes.

Exploiting inherent symmetries is a common and effective approach to speed up the simulation of quantum systems. However, efficiently accounting for non-Abelian symmetries, such as the global SU(2) spin symmetry, remains a major challenge. In fact, expressing total-spin eigenstates in terms of the computational basis can require an exponentially large number of coefficients. In this work, we introduce a novel formalism for designing quantum algorithms directly in an eigenbasis of the total-spin operator. Our strategy relies on the symmetric group approach in conjunction with a truncation scheme for the internal degrees of freedom of total-spin eigenstates. For the case of the antiferromagnetic Heisenberg model, we show that this formalism yields a hierarchy of spin-adapted Hamiltonians, for each truncation threshold, whose ground-state energy and wave function quickly converge to their exact counterparts, calculated on the full model. These truncated Hamiltonians can be encoded with sparse and local qubit Hamiltonians that are suitable for quantum simulations. We demonstrate this by developing a state-preparation schedule to construct shallow quantum-circuit approximations, expressed in a total-spin eigenbasis, for the ground states of the Heisenberg Hamiltonian in different symmetry sectors.