Table of contents

Quantum information technologies demand highly accurate control over quantum systems. Achieving this requires control techniques that perform well despite the presence of decohering noise and other adverse effects. Here, we review a general technique for designing control fields that dynamically correct errors while performing operations using a close relationship between quantum evolution and geometric space curves. This approach provides access to the global solution space of control fields that accomplish a given task, facilitating the design of experimentally feasible gate operations for a wide variety of applications.

Quantum gates and entanglement based on dipole–dipole interactions of neutral Rydberg atoms are relevant to both fundamental physics and quantum information science. The precision and robustness of the Rydberg-mediated entanglement protocols are the key factors limiting their applicability in experiments and near-future industry. There are various methods for generating entangling gates by exploring the Rydberg interactions of neutral atoms, each equipped with its own strengths and weaknesses. The basics and tricks in these protocols are reviewed, with specific attention paid to the achievable fidelity and the robustness to the technical issues and detrimental innate factors.

Tests of the standard model of particle physics should be carried out over the widest possible range of energies. Here we present our plans and progress for an atomic parity non-conservation experiment using the heaviest alkali, francium (Z = 87), which has no stable isotope. Low-energy tests of this kind have sensitivity complementary to higher energy searches, e.g. at the large hadron collider.

Microfabricated ion-trap devices offer a promising pathway towards scalable quantum computing. Research efforts have begun to focus on the engineering challenges associated with developing large-scale ion-trap arrays and networks. However, increasing the size of the array and integrating on-chip electronics can drastically increase the power dissipation within the ion-trap chips. This leads to an increase in the operating temperature of the ion-trap and limits the device performance. Therefore, effective thermal management is an essential consideration for any large-scale architecture. Presented here is the development of a modular cooling system designed for use with multiple ion-trapping experiments simultaneously. The system includes an extensible cryostat that permits scaling of the cooling power to meet the demands of a large network. Following experimental testing on two independent ion-trap experiments, the cooling system is expected to deliver a net cooling power of 111 W at ∼70 K to up to four experiments. The cooling system is a step towards meeting the practical challenges of operating large-scale quantum computers with many qubits.

Quantum technology is approaching a level of maturity, recently demonstrated in space-borne experiments and in-field measurements, which would allow for adoption by non-specialist users. Parallel advancements made in microprocessor-based electronics and database software can be combined to create robust, versatile and modular experimental monitoring systems. Here, we describe a monitoring network used across a number of cold atom laboratories with a shared laser system. The ability to diagnose malfunction, unexpected or unintended behavior and passively collect data for key experimental parameters, such as vacuum chamber pressure, laser beam power, or resistances of important conductors, significantly reduces debugging time. This allows for efficient control over a number of experiments and remote control when access is limited.

The multiple signal classification (MUSIC) algorithm is a well-established method to evaluate the direction of arrival (DOA) of signals. However, the construction and eigen-decomposition of the sample covariance matrix (SCM) are computationally costly for MUSIC in hybrid multiple input multiple output (MIMO) systems, which limits the application and advancement of the algorithm. In this paper, we present a novel quantum method for MUSIC in hybrid MIMO systems. Our scheme makes the following three contributions. First, the quantum subroutine for constructing the approximate SCM is designed, along with the quantum circuit for the steering vector and a proposal for quantum singular vector transformation. Second, the variational density matrix eigensolver is proposed to determine the signal and noise subspaces utilizing the destructive swap test. As a proof of principle, we conduct two numerical experiments using a quantum simulator. Finally, the quantum labelling procedure is explored to determine the DOA. The proposed quantum method can potentially achieve exponential speedup on certain parameters and polynomial speedup on others under specific moderate circumstances, compared with their classical counterparts.

We consider the sensing of scalar valued fields with specific spatial dependence using a network of sensors, e.g. multiple atoms located at different positions within a trap. We show how to harness the spatial correlations to sense only a specific signal, and be insensitive to others at different positions or with unequal spatial dependence by constructing a decoherence-free subspace for noise sources at fixed, known positions. This can be extended to noise sources lying on certain surfaces, where we encounter a connection to mirror charges and equipotential surfaces in classical electrostatics. For general situations, we introduce the notion of an approximate decoherence-free subspace, where noise for all sources within some volume is significantly suppressed, at the cost of reducing the signal strength in a controlled way. We show that one can use this approach to maintain Heisenberg-scaling over long times and for a large number of sensors, despite the presence of multiple noise sources in large volumes. We introduce an efficient formalism to construct internal states and sensor configurations, and apply it to several examples to demonstrate the usefulness and wide applicability of our approach.

Coherent errors in quantum operations are ubiquitous. Whether arising from spurious environmental couplings or errors in control fields, such errors can accumulate rapidly and degrade the performance of a quantum circuit significantly more than an average gate fidelity may indicate. As Hastings (2017 Quantum Inf. Comput.17 488) and Campbell (2017 Phys. Rev. A 95 042306) have recently shown, by replacing the deterministic implementation of a quantum gate with a randomized ensemble of implementations, one can dramatically suppress coherent errors. Our work begins by reformulating the results of Hastings and Campbell as a quantum optimal control problem. We then discuss a family of convex programs able to solve this problem, as well as a set of secondary objectives designed to improve the performance, implementability, and robustness of the resulting mixed quantum gates. Finally, we implement these mixed quantum gates on a superconducting qubit and discuss randomized benchmarking results consistent with a marked reduction in the coherent error.

The non-Markovianity of an arbitrary open quantum system is analyzed in reference to the multi-time statistics given by its monitoring at discrete times. On the one hand, we exploit the hierarchy of inhomogeneous transfer tensors (TTs), which provides us with relevant information about the role of correlations between the system and the environment in the dynamics. The connection between the TT hierarchy and the CP-divisibility property is then investigated, by showing to what extent quantum Markovianity can be linked to a description of the open-system dynamics by means of the composition of one-step TTs only. On the other hand, we introduce the set of stochastic TT transformations associated with local measurements on the open system at different times and conditioned on the measurement outcomes. The use of the TT formalism accounts for different kinds of memory effects in the multi-time statistics and allows us to compare them on a similar footing with the memory effects present in non-monitored non-Markovian dynamics, as we illustrate on a spin-boson case study.

The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum systems and phenomena. However, for interacting many-body quantum systems, its calculation generally involves summing over an exponential number of terms and can thus quickly grow to be intractable. Accurately and efficiently estimating the partition function of its corresponding system Hamiltonian then becomes the key in solving quantum many-body problems. In this paper we develop a hybrid quantum–classical algorithm to estimate the partition function, utilising a novel quantum Clifford sampling technique. Note that previous works on the estimation of partition functions require $\mathcal{O}(1/{\epsilon}\sqrt{{\Delta}})$-depth quantum circuits (Srinivasan et al 2021 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) pp 112–22; Montanaro 2015 Proc. R. Soc. A 471 20150301), where Δ is the minimum spectral gap of stochastic matrices and is the multiplicative error. Our algorithm requires only a shallow $\mathcal{O}(1)$-depth quantum circuit, repeated $\mathcal{O}(n/{{\epsilon}}^{2})$ times, to provide a comparable approximation. Shallow-depth quantum circuits are considered vitally important for currently available noisy intermediate-scale quantum devices.

A while loop tests a termination condition on every iteration. On a quantum computer, such measurements perturb the evolution of the algorithm. We define a while loop primitive using weak measurements, offering a trade-off between the perturbation caused and the amount of information gained per iteration. This trade-off is adjusted with a parameter set by the programmer. We provide sufficient conditions that let us determine, with arbitrarily high probability, a worst-case estimate of the number of iterations the loop will run for. As an example, we solve Grover's search problem using a while loop and prove the quadratic quantum speed-up is maintained.

With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving quadratic unconstrained binary optimization problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (three-regular three-XORSAT, or an Ising spin glass) with a 'golf-course' shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu's digital annealer unit (DAU), the D-Wave advantage quantum annealer, a virtual MemComputing machine, Toshiba's simulated bifurcation machine (SBM), the SATonGPU algorithm from Bernaschi et al, and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.

Noisy linear problems have been studied in various science and engineering disciplines. A class of 'hard' noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector b constructed using a finite set of samples, a hidden vector or structure involved in b is obtained by solving a noise-corrupted linear equation $\hat{A}\mathbf{x}\approx \mathbf{b}+\boldsymbol{\eta }$, where η is a noise vector that cannot be identified. For solving such a noisy linear problem, we consider a quantum algorithm based on a divide-and-conquer strategy, wherein a large core process is divided into smaller subprocesses. The algorithm appropriately reduces both the computational complexities and size of a quantum sample. More specifically, if a quantum computer can access a particular reduced form of the quantum samples, polynomial quantum-sample and time complexities are achieved in the main computation. The size of a quantum sample and its executing system can be reduced, e.g., from exponential to sub-exponential with respect to the problem length, which is better than other results we are aware. We analyse the noise model conditions for such a quantum advantage, and show when the divide-and-conquer strategy can be beneficial for quantum noisy linear problems.

Entanglement is one of the key ingredients for enhancing the measurement precision of quantum sensors. Generally, there is a trade-off between state preparation and sensing within a limited coherence time. To fully exploit temporal resources, concurrent entanglement generation and sensing with designed sequence of rotations are proposed. Based on twist-and-turn dynamics, modulated rotations along only one axis may be sufficient to drive the state to the optimal one for tiny estimated parameter. However, when the estimated parameter is not tiny, it may impact the evolved state and hence degrade the final measurement precision. Here, we introduce another modulated rotations along different axis and find out the optimal control sequences by means of machine optimization. The optimal measurement precision bounds become independent on the estimated parameter, which improves the dynamic range of the machine designed sensors. Particularly, by optimizing the interaction strength for different particle number and the time-modulated rotations along two different axes via machine optimization, the Heisenberg-limited precision scaling can be attained. Our work points out a way for designing optimized quantum-enhanced metrology protocols, which is promising for developing practical quantum sensors.

Quantum parameter estimation offers solid conceptual grounds for the design of sensors enjoying quantum advantage. This is realised not only by means of hardware supporting and exploiting quantum properties, but data analysis has its impact and relevance, too. In this respect, Bayesian methods have emerged as an effective and elegant solution, with the perk of incorporating naturally the availability of a priori information. In this article we present an evaluation of Bayesian methods for multiple phase estimation, assessed based on bounds that work beyond the usual limit of large samples assumed in parameter estimation. Importantly, such methods are applied to experimental data generated from the output statistics of a three-arm interferometer seeded by single photons. Our studies provide a blueprint for a more comprehensive data analysis in quantum metrology.

Weak-value amplification employs postselection to enhance the measurement of small parameters of interest. The amplification comes at the expense of reduced success probability, hindering the utility of this technique as a tool for practical metrology. Following other quantum technologies that display a quantum advantage, we formalize a quantum advantage in the success probability and present a scheme based on non-linear collective Hamiltonians that shows a super-extensive growth in success probability while simultaneously displaying an extensive growth in the weak value. We propose an experimental implementation of our scheme.

We develop quantum computational tools to predict the 3D structure of proteins, one of the most important problems in current biochemical research. We explain how to combine recent deep learning advances with the well known technique of quantum walks applied to a Metropolis algorithm. The result, QFold, is a fully scalable hybrid quantum algorithm that, in contrast to previous quantum approaches, does not require a lattice model simplification and instead relies on the much more realistic assumption of parameterization in terms of torsion angles of the amino acids. We compare it with its classical analog for different annealing schedules and find a polynomial quantum advantage, and implement a minimal realization of the quantum Metropolis in IBMQ Casablanca quantum system.

Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are probably approximately correct learnable on a quantum computer via empirical risk minimization: to learn a parametric quantum circuit with at most n^c gates and each gate acting on a constant number of qubits, the sample complexity is bounded by $\tilde{O}({n}^{c+1})$. In particular, we explicitly construct a family of variational quantum circuits with O(n^c+1) elementary gates arranged in a fixed pattern, which can represent all physical quantum circuits consisting of at most n^c elementary gates. Our results provide a valuable guide for quantum machine learning in both theory and practice.

Solid-state quantum registers are exceptional for storing quantum information at room temperature with long coherence time. Nevertheless, practical applications toward quantum supremacy require even longer coherence time to allow for more complex algorithms. In this work we propose a quantum register that lies in a decoherence-protected subspace to be implemented with nuclear spins nearby a nitrogen-vacancy center in diamond. The quantum information is encoded in two logical states composed of two carbon-13 nuclear spins, while an electron spin is used as ancilla for initialization and control. Moreover, by tuning an off-axis magnetic field we enable non-nuclear-spin-preserving transitions that we use for preparing and manipulating the register through stimulating Raman adiabatic passage. Furthermore, we consider more elaborated sequences to improve simultaneous control over the system yielding decreased gate time.

We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements. The experiment consists in a state discrimination task where either measurement is used according to some partial intermediate information. The success statistics of the task provides an upper bound for the amount of incompatibility of the two measurements, as it is quantified by means of their incompatibility robustness. For a broad class of unbiased and possibly noisy qubit measurements, one can make this upper bound coincide with the true value of the robustness by suitably tuning the preparation of the experiment. We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons' polarization degrees of freedom, and incompatibility is directly accessed by virtue of a refined control on the amplitude, phase and purity of the final projection stage of the measurements. Our work thus establishes the practical feasibility of a recently proposed method for the detection of quantum incompatibility.

Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo process that allows sampling of the Gibbs distribution of a multivariate model. To demonstrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm.

Quantum repeater is an essential ingredient for quantum networks that link distant quantum modules such as quantum computers and sensors. Motivated by distributed quantum computing and communication, quantum repeaters that relay discrete-variable quantum information have been extensively studied; while continuous-variable (CV) quantum information underpins a variety of quantum sensing and communication application, a quantum-repeater architecture for genuine CV quantum information remains largely unexplored. This paper reports a CV quantum-repeater architecture based on CV quantum teleportation assisted by the Gottesman–Kitaev–Preskill code to significantly suppress the physical noise. The designed CV quantum-repeater architecture is shown to significantly improve the performance of entanglement-assisted communication, target detection based on quantum illumination and CV quantum key distribution, as three representative use cases for quantum communication and sensing.

Individual optical emitters coupled via coherent interactions are attractive qubits for quantum communications applications. Here, we present the first study of single pairs of interacting rare earth ions and determine the interactions between ions in the pair with high resolution. We identify two examples of Er³⁺ pair sites in Er implanted Si and characterise the interactions using optical Zeeman spectroscopy. We identify one pair as two Er³⁺ ions in sites of at least C₂ symmetry coupled via a large, 200 GHz, Ising-like spin interaction in both optical ground and excited states. The high measurement resolution allows non-Ising contributions to the interaction of $< 1$% to be observed, attributed to site distortion. By bringing two optical transitions into resonance with a magnetic field, we observe a 0.8 GHz optical interaction of unusual magnetic-dipole/electric-dipole character with strong polarization selection rules. We discuss the use of this type of strongly coupled, field-tunable rare earth pair system for quantum processing.

The study of advanced quantum devices for energy storage has attracted the attention of the scientific community in the past few years. Although several theoretical progresses have been achieved recently, experimental proposals of platforms operating as quantum batteries under ambient conditions are still lacking. In this context, this work presents a feasible realization of a quantum battery in a carboxylate-based metal complex, which can store a finite amount of extractable work under the form of quantum discord at room temperature, and recharge by thermalization with a reservoir. Moreover, the stored work can be evaluated through non-destructive measurements of the compound's magnetic susceptibility. These results pave the way for the development of enhanced energy storage platforms through material engineering.

Two-qubit gates are important components of quantum computing. However, unwanted interactions between qubits (so-called parasitic gates) can be particularly problematic and degrade the performance of quantum applications. In this work, we present two software methods to mitigate parasitic two-qubit gate errors. The first approach is built upon the Cartan's KAK decomposition and keeps the original unitary decomposition for the error-free native two-qubit gate. It counteracts a parasitic two-qubit gate by only applying single-qubit rotations and therefore has no two-qubit gate overhead. We show the optimal choice of single-qubit mitigation gates. The second approach applies a numerical optimisation algorithm to re-compile a target unitary into the error-parasitic two-qubit gate plus single-qubit gates. We demonstrate these approaches on the CPhase-parasitic iSWAP-like gates. The KAK-based approach helps decrease unitary infidelity by a factor of 3 compared to the noisy implementation without error mitigation. When arbitrary single-qubit rotations are allowed, recompilation could completely mitigate the effect of parasitic errors but may require more native gates than the KAK-based approach. We also compare their average gate fidelity under realistic noise models, including relaxation and depolarising errors. Numerical results suggest that different approaches are advantageous in different error regimes, providing error mitigation guidance for near-term quantum computers.

We explore whether quantum advantages can be found for the zeroth-order online convex optimization (OCO) problem, which is also known as bandit convex optimization with multi-point feedback. In this setting, given access to zeroth-order oracles (that is, the loss function is accessed as a black box that returns the function value for any queried input), a player attempts to minimize a sequence of adversarially generated convex loss functions. This procedure can be described as a T round iterative game between the player and the adversary. In this paper, we present quantum algorithms for the problem and show for the first time that potential quantum advantages are possible for problems of OCO. Specifically, our contributions are as follows. (i) When the player is allowed to query zeroth-order oracles O(1) times in each round as feedback, we give a quantum algorithm that achieves $O(\sqrt{T})$ regret without additional dependence of the dimension n, which outperforms the already known optimal classical algorithm only achieving $O(\sqrt{nT})$ regret. Note that the regret of our quantum algorithm has achieved the lower bound of classical first-order methods. (ii) We show that for strongly convex loss functions, the quantum algorithm can achieve O(log T) regret with O(1) queries as well, which means that the quantum algorithm can achieve the same regret bound as the classical algorithms in the full information setting.

A high-quality quantum dot (QD) single-photon source is a key resource for quantum information processing. Exciting a QD emitter resonantly can greatly suppress decoherence processes and lead to highly indistinguishable single-photon generation. It has, however, remained a challenge to implement strict resonant excitation in a stable and scalable way, without compromising any of the key specs of the source (efficiency, purity, and indistinguishability). In this work, we propose a novel dual-mode photonic-crystal waveguide that realizes direct in-plane resonant excitation of the embedded QDs. The device relies on a two-mode waveguide design, which allows exploiting one mode for excitation of the QD and the other mode for collecting the emitted single photons with high efficiency. By proper engineering of the photonic bandstructure, we propose a design with single-photon collection efficiency of β > 0.95 together with a single-photon impurity of < 5 × 10⁻³ over a broad spectral and spatial range. The device has a compact footprint of $\sim 50\enspace \mu {\mathrm{m}}^{2}$ and would enable stable and scalable excitation of multiple emitters for multi-photon quantum applications.

The spin-1/2 antiferromagnetic (AF) Heisenberg systems are studied on three typical diamond-type hierarchical lattices (systems A, B and C) with fractal dimensions 1.63, 2 and 2.58, respectively, and the phase diagrams, critical phenomena and quantum correlations are calculated by a combination of the equivalent transformation and real-space renormalization group methods. We find that there exist a reentrant behavior for system A and a finite temperature phase transition in the isotropic Heisenberg limit for system C (not for system B). Unlike the ferromagnetic case, the Néel temperatures of AF systems A and B are inversely proportional to $\mathrm{ln}\left({{\Delta}}_{\text{c}}-{\Delta}\right)$ (when Δ → Δ_c) and ln Δ (when Δ → 0), respectively. And we also find that there is a turning point of quantum correlation in the isotropic Heisenberg limit Δ = 0 where there is a 'peak' of the contour and no matter how large the size of system is, quantum correlation will change to zero in the Ising limit for the three systems. The quantum correlation decreases with the increase of lattice size L and it is almost zero when L ⩾ 30 for system A, and for systems B and C, they still exist when L is larger than that of system A. Moreover, we discuss the effects of quantum fluctuation and analyze the errors of results in the above three systems, which are induced by the noncommutativity.

Efficient generation of single photons is one of the key challenges of building photonic quantum technology, such as quantum computers and long-distance quantum networks. Photon source multiplexing—where successful pair generation is heralded by the detection of one of the photons, and its partner is routed to a single mode output—has long been known to offer a concrete solution, with output probability tending toward unity as loss is reduced. Here, we present a temporally multiplexed integrated single photon source based on a silicon waveguide and a low-loss fibre switch and loop architecture, which achieves enhancement of the single photon output probability of 4.5 ± 0.5, while retaining g⁽²⁾(0) = 0.01.

The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse power iteration method. A key ingredient is constructing an inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution. We first consider a continuous-variable quantum mode (qumode) for realizing such a linear combination as an integral, with weights being encoded into a qumode resource state. We demonstrate the quantum algorithm with numerical simulations under finite squeezing for various physical systems, including molecules and quantum many-body models. We also discuss a hybrid quantum–classical algorithm that directly sums up Hamiltonian evolution with different durations for comparison. It is revealed that continuous-variable resources are valuable for reducing the coherent evolution time of Hamiltonians in quantum algorithms.

In order to solve the information leakage caused by dishonest intermediate nodes in quantum network coding, we apply quantum homomorphic encryption to the butterfly network, and propose a secure protocol for crossing two qubits. Firstly, in the communication process between two senders and the first intermediate node, two senders encrypt their measured particles and send them to the first intermediate node for encoding. If two intermediate nodes are dishonest and know the encryption rules between two senders and two receivers, or there is an external eavesdropper, none of them can recover the transmitted qubits of two senders from the encrypted transmitted particles. In this way, our protocol can transmit two qubits safely and crossly in the butterfly network. Secondly, by analyzing the internal participant attack and the external eavesdropper attack launched by dishonest intermediate nodes and an external eavesdropper respectively, it is confirmed that our protocol is secure. Finally, the experimental simulation results based on the Qiskit framework prove that our protocol is feasible.

Developing strategies to effectively discriminate between different quantum states is a fundamental issue in quantum information and communication. The actual realization of generally optimal protocols in this task is often limited by the need of supplemental resources and very complex receivers. We have experimentally implemented two discrimination schemes in a minimum-error scenario based on a receiver featured by a network structure and a dynamical processing of information. The first protocol implemented in our experiment, directly inspired to a recent theoretical proposal, achieves binary optimal discrimination, while the second one provides a novel approach to multi-state quantum discrimination, relying on the dynamical features of the network-like receiver. This strategy exploits the arrival time degree of freedom as an encoding variable, achieving optimal results, without the need for supplemental systems or devices. Our results further reveal the potential of dynamical approaches to quantum state discrimination tasks, providing a possible starting point for efficient alternatives to current experimental strategies.

Quantum annealing solves combinatorial optimization problems by finding the energetic ground states of an embedded Hamiltonian. However, quantum annealing dynamics under the embedded Hamiltonian may violate the principles of adiabatic evolution and generate excitations that correspond to errors in the computed solution. Here we empirically benchmark the probability of chain breaks and identify sweet spots for solving a suite of embedded Hamiltonians. We further correlate the physical location of chain breaks in the quantum annealing hardware with the underlying embedding technique and use these localized rates in a tailored post-processing strategies. Our results demonstrate how to use characterization of the quantum annealing hardware to tune the embedded Hamiltonian and remove computational errors.

Heisenberg scaling characterizes the ultimate precision of parameter estimation enabled by quantum mechanics, which represents an important quantum advantage of both theoretical and technological interest. Here, we present a comprehensive and rigorous study of the attainability of strong, global notions of Heisenberg scaling (in contrast to the commonly studied local estimation based on e.g. quantum Fisher information) in the fundamental problem of quantum metrology, in noisy environments. As our first contribution, we formally define two useful notions of Heisenberg scaling in global estimation respectively based on the average estimation error and the limiting distribution of estimation error (which we highlight as a practically important figure of merit). A main result of this work is that for the standard phase damping noise, an O(n⁻¹) noise rate is a necessary and sufficient condition for attaining global Heisenberg scaling. We first prove that O(n⁻¹) is an upper bound on the noise rate for Heisenberg scaling to be possible, and then show by constructing a 'robust' estimation procedure that global Heisenberg scaling in both senses can indeed be achieved under Θ(n⁻¹) noise. In addition, we provide a practically more friendly adaptive protocol using only an one-qubit memory, which achieves global Heisenberg scaling in terms of limiting distribution as well under O(n⁻¹) noise.