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Elementary cellular automata (ECA) present iconic examples of complex systems. Though described only by one-dimensional strings of binary cells evolving according to nearest-neighbour update rules, certain ECA rules manifest complex dynamics capable of universal computation. Yet, the classification of precisely which rules exhibit complex behaviour remains somewhat an open debate. Here, we approach this question using tools from quantum stochastic modelling, where quantum statistical memory—the memory required to model a stochastic process using a class of quantum machines—can be used to quantify the structure of a stochastic process. By viewing ECA rules as transformations of stochastic patterns, we ask: Does an ECA generate structure as quantified by the quantum statistical memory, and can this be used to identify complex cellular automata? We illustrate how the growth of this measure over time correctly distinguishes simple ECA from complex counterparts. Moreover, it provides a spectrum on which we can rank the complexity of ECA, by the rate at which they generate structure. [ABSTRACT FROM AUTHOR]

Complex systems are embedded in our everyday experience. Stochastic modelling enables us to understand and predict the behaviour of such systems, cementing its utility across the quantitative sciences. Accurate models of highly non-Markovian processes – where the future behaviour depends on events that happened far in the past – must track copious amounts of information about past observations, requiring high-dimensional memories. Quantum technologies can ameliorate this cost, allowing models of the same processes with lower memory dimension than corresponding classical models. Here we implement such memory-efficient quantum models for a family of non-Markovian processes using a photonic setup. We show that with a single qubit of memory our implemented quantum models can attain higher precision than possible with any classical model of the same memory dimension. This heralds a key step towards applying quantum technologies in complex systems modelling. Quantum technologies allow memory advantages in simulating stochastic processes, but a demonstration of this for non-Markovian processes (where the advantage would be stronger) has been missing so far. Here the authors fill this gap analytically and experimentally, using a single qubit memory to model non-Markovian processes. [ABSTRACT FROM AUTHOR]

The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantages, motivating the development of various quantum error-mitigation methods. Here, we derive fundamental bounds concerning how error-mitigation algorithms can reduce the computation error as a function of their sampling overhead. Our bounds place universal performance limits on a general error-mitigation protocol class. We use them to show (1) that the sampling overhead that ensures a certain computational accuracy for mitigating local depolarizing noise in layered circuits scales exponentially with the circuit depth for general error-mitigation protocols and (2) the optimality of probabilistic error cancellation among a wide class of strategies in mitigating the local dephasing noise on an arbitrary number of qubits. Our results provide a means to identify when a given quantum error-mitigation strategy is optimal and when there is potential room for improvement. [ABSTRACT FROM AUTHOR]

Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and entanglement alone. Using tools from complexity science, we characterise such structure. We investigate the structural complexities that can be found within the patterns that manifest from the observational data of these systems. In particular, using two prototypical quantum many-body systems as test cases—the one-dimensional quantum Ising and Bose–Hubbard models—we explore how different information-theoretic measures of complexity are able to identify different features of such patterns. This work furthers the understanding of fully-quantum notions of structure and complexity in quantum systems and dynamics. [ABSTRACT FROM AUTHOR]

Quantum memory—the capacity to faithfully preserve quantum coherence and correlations—is essential for quantum-enhanced technology. There is thus a pressing need for operationally meaningful means to benchmark candidate memories across diverse physical platforms. Here we introduce a universal benchmark distinguished by its relevance across multiple key operational settings, exactly quantifying (1) the memory's robustness to noise, (2) the number of noiseless qubits needed for its synthesis, (3) its potential to speed up statistical sampling tasks, and (4) performance advantage in non-local games beyond classical limits. The measure is analytically computable for low-dimensional systems and can be efficiently bounded in the experiment without tomography. We thus illustrate quantum memory as a meaningful resource, with our benchmark reflecting both its cost of creation and what it can accomplish. We demonstrate the benchmark on the five-qubit IBM Q hardware, and apply it to witness the efficacy of error-suppression techniques and quantify non-Markovian noise. We thus present an experimentally accessible, practically meaningful, and universally relevant quantifier of a memory's capability to preserve quantum advantage. [ABSTRACT FROM AUTHOR]

Thermodynamic resources, beyond their well-known usefulness in work extraction and other thermodynamic tasks, are often important also in tasks that are not evidently thermodynamic. Here we develop a framework for identifying such resources in diverse applications of bosonic continuous-variable systems. Introducing the class of bosonic linear thermal operations to model operationally feasible processes, we apply this model to identify uniquely quantum properties of bosonic states that refine classical notions of thermodynamic resourcefulness. Among these are (1) a suite of temperature-like quantities generalizing the equilibrium temperature to quantum, non-equilibrium scenarios; (2) signal-to-noise ratios quantifying a system's capacity to carry information in phase-space displacement; and (3) well-established non-classicality measures quantifying the resolution in sensing and parameter estimation tasks. [ABSTRACT FROM AUTHOR]

Realizing a long coherence time quantum memory is a major challenge of current quantum technology. Until now, the longest coherence-time of a single qubit was reported as 660 s in a single 171Yb+ ion-qubit through the technical developments of sympathetic cooling and dynamical decoupling pulses, which addressed heating-induced detection inefficiency and magnetic field fluctuations. However, it was not clear what prohibited further enhancement. Here, we identify and suppress the limiting factors, which are the remaining magnetic-field fluctuations, frequency instability and leakage of the microwave reference-oscillator. Then, we observe the coherence time of around 5500 s for the 171Yb+ ion-qubit, which is the time constant of the exponential decay fit from the measurements up to 960 s. We also systematically study the decoherence process of the quantum memory by using quantum process tomography and analyze the results by applying recently developed resource theories of quantum memory and coherence. Our experimental demonstration will accelerate practical applications of quantum memories for various quantum information processing, especially in the noisy-intermediate-scale quantum regime. Extending qubit coherence times represent one of the key challenges for quantum technologies. Here, after properly suppressing magnetic-field fluctuations, frequency instability and leakage of the microwave reference-oscillator, the authors infer coherence times of 5500 s for an Yb ion qubit. [ABSTRACT FROM AUTHOR]

Experimentally achieving the precision that standard quantum metrology schemes promise is always challenging. Recently, additional controls were applied to design feasible quantum metrology schemes. However, these approaches generally does not consider ease of implementation, raising technological barriers impeding its realization. In this paper, we circumvent this problem by applying closed-loop learning control to propose a practical controlled sequential scheme for quantum metrology. Purity loss of the probe state, which relates to quantum Fisher information, is measured efficiently as the fitness to guide the learning loop. We confirm its feasibility and certain superiorities over standard quantum metrology schemes by numerical analysis and proof-of-principle experiments in a nuclear magnetic resonance system. [ABSTRACT FROM AUTHOR]

Squeezing operation is critical for continuous-variable quantum information, enabling encoding of information in phase space to a resolution otherwise forbidden by vacuum noise1. A universal squeezing gate that can squeeze arbitrary input states is particularly essential for continuous-variable quantum computation2,3. However, the fidelity of existing state-of-the-art implementations is ultimately limited due to their reliance on first synthesizing squeezed vacuum modes of unbounded energy4,5. Here, we circumvent this fundamental limitation by using a heralded squeezing gate. This allows improved gate fidelity without requiring more squeezed ancillary vacuum. For a specific target squeezing level for coherent states, we present measured fidelities higher than what would be possible using non-heralded schemes that utilize up to 15 dB (ref. 6) of best available ancilla squeezing. Our technique can be applied to non-Gaussian states and provides a promising pathway towards high-fidelity gate operations and fault-tolerant continuous-variable quantum computation. A heralded squeezing gate with near unit fidelity is demonstrated, even for modest ancillary squeezing. A heralding filter is implemented in the feed-forward operation. With 6 dB of ancillary squeezing, a fidelity of 0.985 is experimentally obtained. [ABSTRACT FROM AUTHOR]

The process of obtaining solutions to optimal control problems via mesh based techniques suffers from the well known curse of dimensionality. This issue is especially severe in quantum systems whose dimensions grow exponentially with the number of interacting elements (qubits) that they contain. In this article we develop a min-plus curse-of-dimensionality-free framework suitable to a new class of problems that arise in the control of certain quantum systems. This method yields a much more manageable complexity growth that is related to the cardinality of the control set. The growth is attenuated through $$\max $$ -plus projection at each propagation step. The method's efficacy is demonstrated by obtaining an approximate solution to a previously intractable problem on a two qubit system. [ABSTRACT FROM AUTHOR]

Coherent interactions that generate negligible entanglement can still exhibit unique quantum behaviour. This observation has motivated a search beyond entanglement for a complete description of all quantum correlations. Quantum discord is a promising candidate. Here, we demonstrate that under certain measurement constraints, discord between bipartite systems can be consumed to encode information that can only be accessed by coherent quantum interactions. The inability to access this information by any other means allows us to use discord to directly quantify this 'quantum advantage'. We experimentally encode information within the discordant correlations of two separable Gaussian states. The amount of extra information recovered by coherent interaction is quantified and directly linked with the discord consumed during encoding. No entanglement exists at any point of this experiment. Thus we introduce and demonstrate an operational method to use discord as a physical resource. [ABSTRACT FROM AUTHOR]

Modern computation relies crucially on modular architectures, breaking a complex algorithm into self-contained subroutines. A client can then call upon a remote server to implement parts of the computation independently via an application programming interface (API). Present APIs relay only classical information. Here we implement a quantum API that enables a client to estimate the absolute value of the trace of a server-provided unitary operation U . We demonstrate that the algorithm functions correctly irrespective of what unitary U the server implements or how the server specifically realizes U . Our experiment involves pioneering techniques to coherently swap qubits encoded within the motional states of a trapped 171 Yb + ion, controlled on its hyperfine state. This constitutes the first demonstration of modular computation in the quantum regime, providing a step towards scalable, parallelization of quantum computation. Modern computation relies on modular architectures, breaking a complex algorithm into self-contained subroutines, whereas current quantum computers do not have such capability. Here, the authors provide an experimental demonstration of a modular quantum computation protocol using a trapped Yb ion. [ABSTRACT FROM AUTHOR]

Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices that execute a simulation using less memory than possible by classical means. To realise this advantage it is essential that the memory register remains coherent, and coherently interacts with the processor, allowing the simulator to operate over many time steps. Here we report a multi-time-step experimental simulation of a stochastic process using less memory than the classical limit. A key feature of the photonic quantum information processor is that it creates a quantum superposition of all possible future trajectories that the system can evolve into. This superposition allows us to introduce, and demonstrate, the idea of comparing statistical futures of two classical processes via quantum interference. We demonstrate interference of two 16-dimensional quantum states, representing statistical futures of our process, with a visibility of 0.96 ± 0.02. Quantum devices should allow simulating stochastic processes using less memory than classical counterparts, but only if quantum coherence is maintained through multiple steps. Here, the authors demonstrate a coherence-preserving three-step stochastic simulation using photons. [ABSTRACT FROM AUTHOR]

Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of information about past behaviour, even for relatively simple models, enforcing limits on precision due to the finite memory of the machine. However, quantum machines can require less information about the past than even their optimal classical counterparts to simulate the future of discrete-time processes, and we demonstrate that this advantage extends to the continuous-time regime. Moreover, we show that this reduction in the memory requirement can be unboundedly large, allowing for arbitrary precision even with a finite quantum memory. We provide a systematic method for finding superior quantum constructions, and a protocol for analogue simulation of continuous-time renewal processes with a quantum machine. Quantum simulation: quantum advantage for simulating continuous-time stochastic processes Quantum machines can simulate continuous-time stochastic processes with an unboundedly large reduction in memory requirements over classical approaches. Thomas J. Elliott and Mile Gu from Singapore's Nanyang Technological University and Centre for Quantum Technologies have derived a systematic approach for designing quantum machines that are able to simulate renewal processes—classical stochastic processes that are continuous in time. Whereas in a classical setting it would normally be necessary to know the entire past behaviour of a process in order to exactly simulate its future, often leading to cutoff errors, the authors' quantum machine could achieve the simulation with lower internal memory requirements. Such quantum advantage has been shown to reach, in specific cases, arbitrarily large values—compressing the need for an infinite classical memory into a finite quantum one. [ABSTRACT FROM AUTHOR]

All natural things process and transform information. They receive environmental information as input, and transform it into appropriate output responses. Much of science is dedicated to building models of such systems—algorithmic abstractions of their input–output behavior that allow us to simulate how such systems can behave in the future, conditioned on what has transpired in the past. Here, we show that classical models cannot avoid inefficiency—storing past information that is unnecessary for correct future simulation. We construct quantum models that mitigate this waste, whenever it is physically possible to do so. This suggests that the complexity of general input–output processes depends fundamentally on what sort of information theory we use to describe them. Responding to the environment is easier with quantum mechanics: Can a quantum goldfish exhibit more complex behaviour than a classical dolphin? In complexity science, the complexity of an input-output process – a system that reacts differently when supplied with different environmental stimuli – can be quantified by the minimal memory needed to reproduce the process's observed behaviour. This reflects the intuition that a goldfish – that remembers very little – can only exhibit fairly simple input-output behaviour. Here we show how these ideas can radically change when generalized to the quantum domain. A quantum system may exhibit behaviour that appears considerably more complex than a classical system that has significantly more memory. [ABSTRACT FROM AUTHOR]