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Abstract Understanding the neural basis of behavior requires monitoring and manipulating combinations of physiological elements and their interactions in behaving animals. We developed a thermal tapering process enabling fabrication of low-cost, flexible probes combining ultrafine features: dense electrodes, optical waveguides, and microfluidic channels. Furthermore, we developed a semi-automated backend connection allowing scalable assembly. We demonstrate T-DOpE (Tapered Drug delivery, Optical stimulation, and Electrophysiology) probes achieve in single neuron-scale devices (1) high-fidelity electrophysiological recording (2) focal drug delivery and (3) optical stimulation. The device tip can be miniaturized (as small as 50 µm) to minimize tissue damage while the ~20 times larger backend allows for industrial-scale connectorization. T-DOpE probes implanted in mouse hippocampus revealed canonical neuronal activity at the level of local field potentials (LFP) and neural spiking. Taking advantage of the triple-functionality of these probes, we monitored LFP while manipulating cannabinoid receptors (CB1R; microfluidic agonist delivery) and CA1 neuronal activity (optogenetics). Focal infusion of CB1R agonist downregulated theta and sharp wave-ripple oscillations (SPW-Rs). Furthermore, we found that CB1R activation reduces sharp wave-ripples by impairing the innate SPW-R-generating ability of the CA1 circuit.

Abstract Large-scale quantum computers have the potential to hold computational capabilities beyond conventional computers. However, the physical qubits are prone to noise which must be corrected in order to perform fault-tolerant quantum computations. Quantum Error Correction (QEC) provides the path for realizing such computations. QEC generates a continuous stream of data that decoders must process at the rate it is received, which can be as fast as 1 μs per QEC round in superconducting quantum computers. If the decoder infrastructure cannot keep up, a data backlog problem is encountered and the computation runs exponentially slower. Today’s leading approaches to quantum error correction are not scalable as existing decoders typically run slower as the problem size is increased, inevitably hitting the backlog problem. Here, we show how to parallelize decoding to achieve almost arbitrary speed, removing this roadblock to scalability. Our parallelization requires some classical feed forward decisions to be delayed, slowing-down the logical clock speed. However, the slow-down is now only polynomial in the size of the QEC code, averting the exponential slowdown. We numerically demonstrate our parallel decoder for the surface code, showing no noticeable reduction in logical fidelity compared to previous decoders and demonstrating the predicted speedup.

Summary: The granular retrosplenial cortex (gRSC) exhibits high-frequency oscillations (HFOs; ∼150 Hz), which can be driven by a hippocampus-subiculum pathway. How the cellular-synaptic and laminar organization of gRSC facilitates HFOs is unknown. Here, we probe gRSC HFO generation and coupling with hippocampal rhythms using focal optogenetics and silicon-probe recordings in behaving mice. ChR2-mediated excitation of CaMKII-expressing cells in L2/3 or L5 induces HFOs, but spontaneous HFOs are found only in L2/3, where HFO power is highest. HFOs couple to CA1 sharp wave-ripples (SPW-Rs) during rest and the descending phase of theta. gRSC HFO current sources and sinks are the same for events during both SPW-Rs and theta oscillations. Independent component analysis shows that high gamma (50–100 Hz) in CA1 stratum lacunosum moleculare is comodulated with HFO power. HFOs may thus facilitate interregional communication of a multisynaptic loop between the gRSC, hippocampus, and medial entorhinal cortex during distinct brain and behavioral states.

We simulate the logical Hadamard gate in the surface code under a circuit-level noise model, compiling it to a physical circuit on square-grid connectivity hardware. Our paper is the first to do this for a logical unitary gate on a quantum error-correction code. We consider two proposals, both via patch-deformation: one that applies a transversal Hadamard gate (i.e. a domain wall through time) to interchange the logical $X$ and $Z$ strings, and another that applies a domain wall through space to achieve this interchange. We explain in detail why they perform the logical Hadamard gate by tracking how the stabilisers and the logical operators are transformed in each quantum error-correction round. We optimise the physical circuits and evaluate their logical failure probabilities, which we find to be comparable to those of a quantum memory experiment for the same number of quantum error-correction rounds. We present syndrome-extraction circuits that maintain the same effective distance under circuit-level noise as under phenomenological noise. We also explain how a $SWAP$-quantum error-correction round (required to return the patch to its initial position) can be compiled to only four two-qubit gate layers. This can be applied to more general scenarios and, as a byproduct, explains from first principles how the "stepping" circuits of the recent Google paper \cite{McEwenBaconGidney} can be constructed.

The extent of problems in quantum chemistry for which quantum algorithms could provide a speedup is still unclear, as well as the kind of speedup one should expect. Here, the authors look at the problem of ground state energy estimation, and gather theoretical and numerical evidence for the fact that an exponential quantum advantage is unlikely for generic problems of interest.

Quantum phase estimation (QPE) is a key quantum algorithm, which has been widely studied as a method to perform chemistry and solid-state calculations on future fault-tolerant quantum computers. Recently, several authors have proposed statistical alternatives to QPE that have benefits on early fault-tolerant devices, including shorter circuits and better suitability for error-mitigation techniques. However, experimental investigations of the algorithm on real quantum processors are lacking. Here, we implement statistical phase estimation on Rigetti’s superconducting processors. Specifically, we use a modification of the Lin and Tong [PRX Quantum 3, 010318 (2022)] algorithm with the improved Fourier approximation of Wan et al. [Phys. Rev. Lett. 129, 030503 (2022)] and apply a variational-compilation technique to reduce the circuit depth. We then incorporate error-mitigation strategies including zero-noise extrapolation and readout-error mitigation with bit-flip averaging. We propose a new method to estimate energies from the statistical phase estimation data, which is found to improve the accuracy in the final energy estimates by 1–2 orders of magnitude with respect to prior theoretical bounds, reducing the cost of performing accurate phase-estimation calculations. We apply these methods to chemistry problems for active spaces up to four electrons in four orbitals, including the application of a quantum embedding method, and use them to correctly estimate energies within chemical precision. Our work demonstrates that statistical phase estimation has a natural resilience to noise, particularly after mitigating coherent errors, and can achieve far higher accuracy than suggested by previous analysis, demonstrating its potential as a valuable quantum algorithm for early fault-tolerant devices.

Realizing the full potential of quantum computation requires quantum error correction (QEC), with most recent breakthrough demonstrations of QEC using the surface code. QEC codes use multiple noisy physical qubits to encode information in fewer logical qubits, enabling the identification of errors through a decoding process. This process increases the logical fidelity (or accuracy) making the computation more reliable. However, most fast (efficient run-time) decoders neglect important noise characteristics, thereby reducing their accuracy. In this work, we introduce decoders that are both fast and accurate, and can be used with a wide class of QEC codes including the surface code. Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC. Using the surface code threshold as a performance metric, we observe a threshold at 0.94% error probability for our decoders, outperforming the 0.82% threshold for a standard minimum-weight perfect matching decoder. We also test our belief-matching decoders in a theoretical case study of codes tailored to a biased noise model. We find that the decoders lead to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code. Surprisingly, in the well-below-threshold regime, the rectangular surface code becomes more resource efficient than the tailored surface code due to a previously unnoticed phenomenon that we call “fragile boundaries.” Our decoders outperform all other fast decoders in terms of threshold and accuracy, enabling better results in current quantum-error-correction experiments and opening up new areas for theoretical case studies.

Bias-tailoring allows quantum error correction codes to exploit qubit noise asymmetry. Recently, it was shown that a modified form of the surface code, the XZZX code, exhibits considerably improved performance under biased noise. In this work, we demonstrate that quantum low density parity check codes can be similarly bias-tailored. We introduce a bias-tailored lifted product code construction that provides the framework to expand bias-tailoring methods beyond the family of 2D topological codes. We present examples of bias-tailored lifted product codes based on classical quasi-cyclic codes and numerically assess their performance using a belief propagation plus ordered statistics decoder. Our Monte Carlo simulations, performed under asymmetric noise, show that bias-tailored codes achieve several orders of magnitude improvement in their error suppression relative to depolarising noise.

For certain restricted computational tasks, quantum mechanics provides a provable advantage over any possible classical implementation. Several of these results have been proven using the framework of measurement-based quantum computation (MBQC), where nonlocality and more generally contextuality have been identified as necessary resources for certain quantum computations. Here, we consider the computational power of MBQC in more detail by refining its resource requirements, both on the allowed operations and the number of accessible qubits. More precisely, we identify which Boolean functions can be computed in non-adaptive MBQC, with local operations contained within a finite level in the Clifford hierarchy. Moreover, for non-adaptive MBQC restricted to certain subtheories such as stabiliser MBQC, we compute the minimal number of qubits required to compute a given Boolean function. Our results point towards hierarchies of resources that more sharply characterise the power of MBQC beyond the binary of contextuality vs non-contextuality.

Lattice surgery is a measurement-based technique for performing fault-tolerant quantum computation in two dimensions. When using the surface code, the most general lattice surgery operations require lattice irregularities called twist defects. However, implementing twist-based lattice surgery may require additional resources, such as extra device connectivity, and could lower the threshold and overall performance for the surface code. Here we provide an explicit twist-based lattice surgery protocol and its requisite connectivity layout. We also provide new stabilizer measurement circuits for measuring twist defects which are compatible with our chosen gate scheduling. We undertake the first circuit-level error correction simulations during twist-based lattice surgery using a biased depolarizing noise model. Our results indicate a slight decrease in the threshold for timelike logical failures compared to lattice surgery protocols with no twist defects in the bulk. However, comfortably below threshold (i.e., with CNOT infidelities below 5×10^{−3}), the performance degradation is mild and in fact preferable over proposed alternative twist-free schemes. Lastly, we provide an efficient scheme for measuring Y operators along boundaries of surface codes, which bypasses certain steps that were required in previous schemes.

A highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to approximate a Taylor series by truncating after some order. Here we present an adaptation of that method, optimized for Hamiltonians with terms of widely varying magnitude, as is commonly the case in electronic structure calculations. We show that it is more efficient to apply LCU using a truncation that retains larger magnitude terms as determined by an iterative procedure. We obtain bounds on the simulation error for this generalized truncated Taylor method, and for a range of molecular simulations, we report these bounds as well as exact numerical results. We find that our adaptive method can typically improve the simulation accuracy by an order of magnitude, for a given circuit depth.

We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated physical parameters for the hardware, we perform a detailed error analysis of measurements and gates, including cnot and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, we devise a new magic state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits, which are currently intractable for classical computers. Hardware with 18 000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.

Lattice-surgery protocols allow for the efficient implementation of universal gate sets with two-dimensional topological codes where qubits are constrained to interact with one another locally. In this work, we first introduce a decoder capable of correcting spacelike and timelike errors during lattice-surgery protocols. Subsequently, we compute the logical failure rates of a lattice-surgery protocol for a biased circuit-level noise model. We then provide a protocol for performing twist-free lattice surgery, where we avoid twist defects in the bulk of the lattice. Our twist-free protocol eliminates the extra circuit components and gate-scheduling complexities associated with the measurement of higher weight stabilizers when using twist defects. We also provide a protocol for temporally encoded lattice surgery that can be used to reduce both the run times and the total space-time costs of quantum algorithms. Lastly, we propose a layout for a quantum processor that is more efficient for rectangular surface codes exploiting noise bias and that is compatible with the other techniques mentioned above.

We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting commutativity of the target Hamiltonian, sparsity of interactions, and prior knowledge of the initial state. We achieve this using Trotterization for a class of interacting electrons that encompasses various physical systems, including the plane-wave-basis electronic structure and the Fermi-Hubbard model. We estimate the simulation error by taking the transition amplitude of nested commutators of the Hamiltonian terms within the $\eta$-electron manifold. We develop multiple techniques for bounding the transition amplitude and expectation of general fermionic operators, which may be of independent interest. We show that it suffices to use $\left(\frac{n^{5/3}}{\eta^{2/3}}+n^{4/3}\eta^{2/3}\right)n^{o(1)}$ gates to simulate electronic structure in the plane-wave basis with $n$ spin orbitals and $\eta$ electrons, improving the best previous result in second quantization up to a negligible factor while outperforming the first-quantized simulation when $n=\eta^{2-o(1)}$. We also obtain an improvement for simulating the Fermi-Hubbard model. We construct concrete examples for which our bounds are almost saturated, giving a nearly tight Trotterization of interacting electrons.

Single-shot error correction corrects data noise using only a single round of noisy measurements on the data qubits, removing the need for intensive measurement repetition. We introduce a general concept of confinement for quantum codes, which roughly stipulates qubit errors cannot grow without triggering more measurement syndromes. We prove confinement is sufficient for single-shot decoding of adversarial errors and linear confinement is sufficient for single-shot decoding of local stochastic errors. Further to this, we prove that all three-dimensional homological product codes exhibit confinement in their X components and are therefore single shot for adversarial phase-flip noise. For local stochastic phase-flip noise, we numerically explore these codes and again find evidence of single-shot protection. Our Monte Carlo simulations indicate sustainable thresholds of 3.08(4)% and 2.90(2)% for three-dimensional (3D) surface and toric codes, respectively, the highest observed single-shot thresholds to date. To demonstrate single-shot error correction beyond the class of topological codes, we also run simulations on a randomly constructed family of 3D homological product codes.

Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by establishing precise connections with a family of magic monotones. Our first simulator introduces a new class of quasiprobability distributions and connects its runtime to a generalized notion of negativity. We prove that this algorithm has significantly improved exponential scaling compared to all prior quasiprobability simulators for qubits. Our second simulator is a new variant of the stabilizer-rank simulation algorithm, extended to work with mixed states and with significantly improved runtime bounds. Our third simulator trades precision for speed by discarding negative quasiprobabilities. We connect each algorithm’s performance to a corresponding magic monotone and, by comprehensively characterizing the monotones, we obtain a precise understanding of the simulation runtime and error bounds. Our analysis reveals a deep connection between all three seemingly unrelated simulation techniques and their associated monotones. For tensor products of single-qubit states, we prove that our monotones are all equal to each other, multiplicative and efficiently computable, allowing us to make clear-cut comparisons of the simulators’ performance scaling. Furthermore, our monotones establish several asymptotic and nonasymptotic bounds on state interconversion and distillation rates. Beyond the theory of magic states, our classical simulators can be adapted to other resource theories under certain axioms, which we demonstrate through an explicit application to the theory of quantum coherence.

Malware detection is in a coevolutionary arms race where the attackers and defenders are constantly seeking advantage. This arms race is asymmetric: detection is harder and more expensive than evasion. White hats must be conservative to avoid false positives when searching for malicious behaviour. We seek to redress this imbalance. Most of the time, black hats need only make incremental changes to evade them. On occasion, white hats make a disruptive move and find a new technique that forces black hats to work harder. Examples include system calls, signatures and machine learning. We present a method, called Hothouse, that combines simulation and search to accelerate the white hat’s ability to counter the black hat’s incremental moves, thereby forcing black hats to perform disruptive moves more often. To realise Hothouse, we evolve EEE, an entropy-based polymorphic packer for Windows executables. Playing the role of a black hat, EEE uses evolutionary computation to disrupt the creation of malware signatures. We enter EEE into the detection arms race with VirusTotal, the most prominent cloud service for running anti-virus tools on software. During our 6 month study, we continually improved EEE in response to VirusTotal, eventually learning a packer that produces packed malware whose evasiveness goes from an initial 51.8% median to 19.6%. We report both how well VirusTotal learns to detect EEE-packed binaries and how well VirusTotal forgets in order to reduce false positives. VirusTotal’s tools learn and forget fast, actually in about 3 days. We also show where VirusTotal focuses its detection efforts, by analysing EEE’s variants.

The estimation of multiple parameters in quantum metrology is important for a vast array of applications in quantum information processing. However, the unattainability of fundamental precision bounds for incompatible observables greatly diminishes the applicability of estimation theory in many practical implementations. The Holevo Cramér-Rao bound (HCRB) provides the most fundamental, simultaneously attainable bound for multiparameter estimation problems. A general closed form for the HCRB is not known given that it requires a complex optimization over multiple variables. In this work, we develop an analytic approach to solving the HCRB for two parameters. Our analysis reveals the role of the HCRB and its interplay with alternative bounds in estimation theory. For more parameters, we generate a lower bound to the HCRB. Our work greatly reduces the complexity of determining the HCRB to solving a set of linear equations that even numerically permits a quadratic speedup over previous state-of-the-art approaches. We apply our results to compare the performance of different probe states in magnetic field sensing and characterize the performance of state tomography on the code space of noisy bosonic error-correcting codes. The sensitivity of state tomography on noisy binomial code states can be improved by tuning two coding parameters that relate to the number of correctable phase and amplitude damping errors. Our work provides fundamental insights and makes significant progress toward the estimation of multiple incompatible observables.

Malware concealment is the predominant strategy for malware propagation. Black hats create variants of malware based on polymorphism and metamorphism. Malware variants, by definition, share some information. Although the concealment strategy alters this information, there are still patterns on the software. Given a zoo of labelled malware and benign-ware, we ask whether a suspect program is more similar to our malware or to our benign-ware. Normalized Compression Distance (NCD) is a generic metric that measures the shared information content of two strings. This measure opens a new front in the malware arms race, one where the countermeasures promise to be more costly for malware writers, who must now obfuscate patterns as strings qua strings, without reference to execution, in their variants. Our approach classifies disk-resident malware with 97.4% accuracy and a false positive rate of 3%. We demonstrate that its accuracy can be improved by combining NCD with the compressibility rates of executables using decision forests, paving the way for future improvements. We demonstrate that malware reported within a narrow time frame of a few days is more homogeneous than malware reported over two years, but that our method still classifies the latter with 95.2% accuracy and a 5% false positive rate. Due to its use of compression, the time and computation cost of our method is nontrivial. We show that simple approximation techniques can improve its running time by up to 63%. We compare our results to the results of applying the 59 anti-malware programs used on the VirusTotal website to our malware. Our approach outperforms each one used alone and matches that of all of them used collectively.

Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the effect of each term during time-evolution is individually computed. For many physical systems, the Hamiltonian has a large number of terms, constraining the scalability of established simulation methods. To address this limitation we introduce a new scheme that approximates the actual Hamiltonian with a sparser Hamiltonian containing fewer terms. By stochastically sparsifying weaker Hamiltonian terms, we benefit from a quadratic suppression of errors relative to deterministic approaches. Relying on optimality conditions from convex optimisation theory, we derive an appropriate probability distribution for the weaker Hamiltonian terms, and compare its error bounds with other probability ansatzes for some electronic structure Hamiltonians. Tuning the sparsity of our approximate Hamiltonians allows our scheme to interpolate between two recent random compilers: qDRIFT and randomized first order Trotter. Our scheme is thus an algorithm that combines the strengths of randomised Trotterisation with the efficiency of qDRIFT, and for intermediate gate budgets, outperforms both of these prior methods.