It is known that materials with broken time-reversal symmetry can have Hall responses. Here we show that in addition to the conventional currents, either linear or nonlinear in the electric field, another Hall current can occur in the time-reversal breaking materials within the second-order response to in-plane electric and vertical magnetic fields. Such a Hall response is generated by the oscillation of the electromagnetic field and has a quantum origin arising from a novel dipole associated with the Berry curvature and band velocity. We demonstrate that the massive Dirac model of LaAlO3/LaNiO3/LaAlO3 quantum well can be used to detect this Hall effect. Our work widens the theory of the Hall effect in the time-reversal breaking materials by proposing a new kind of nonlinear electromagnetic response.

We study the momentum distribution of strongly interacting one-dimensional mixtures of particles at zero temperature in a box potential. We find that the magnitude of the $1/k^4$ tail of the momentum distribution is not only due to short-distance correlations, but also to the presence of the rigid walls, breaking the Tan's relation relating this quantity to the adiabatic derivative of the energy with respect to the inverse of the interaction strength. The additional contribution is a finite-size effect that includes a $k$-independent and an oscillating part. This latter, surprisingly, encodes information on long-range spin correlations.

Broadband energy-time entanglement can be used to enhance the rate of two-photon absorption (TPA) by combining a precise two-photon resonance with a very short coincidence time. Because of this short coincidence time, broadband TPA is not sensitive to the spectrum of intermediate levels, making it the optimal choice when the intermediate transitions are entirely virtual. In the case of distinct intermediate resonances, it is possible to enhance TPA by introducing a phase dispersion that matches the intermediate resonances. Here, we consider the effects of a phase flip in the single photon spectrum, where the phases of all frequencies above a certain frequency are shifted by half a wavelength relative to the frequencies below this frequency. The frequency at which the phase is flipped can then be scanned to reveal the position of intermediate resonances. We find that a resonant phase flip maximizes the contributions of the asymmetric imaginary part of the dispersion that characterizes a typical resonance, resulting in a considerable enhancement of the TPA rate. Due to the bosonic symmetry of TPA, the enhancement is strongest when the resonance occurs when the frequency difference of the two photons is much higher than the linewidth of the resonance. Our results indicate that broadband entangled TPA with spectral phase flips may be suitable for phase-sensitive spectroscopy at the lower end of the spectrum where direct photon detection is difficult.

Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. A classic example is computing the edit distance of two strings of length $n$, which can be solved in $O(n^2/w)$ time. In a reasonable classical model of computation, one can assume $w=\Theta(\log n)$, and obtaining significantly better speed-ups is unlikely in the light of conditional lower bounds obtained for such problems.

In this paper, we study the connection of bit-parallelism to quantum computation, aiming to see if a bit-parallel algorithm could be converted to a quantum algorithm with better than logarithmic speed-up. We focus on String Matching in Labeled Graphs, the problem of finding an exact occurrence of a string as the label of a path in a graph. This problem admits a quadratic conditional lower bound under a very restricted class of graphs (Equi et al. ICALP 2019), stating that no algorithm in the classical model of computation can solve the problem in time $O(|P||E|^{1-\epsilon})$ or $O(|P|^{1-\epsilon}|E|)$. We show that a simple bit-parallel algorithm on such restricted family of graphs (level DAGs) can indeed be converted into a realistic quantum algorithm that attains a linear speed-up, with time complexity $O(|E|+|V|+\sqrt{|P|})$.

In this paper we propose a dynamical approach based on the Gorini-Kossakowski-Sudarshan-Lindblad equation for a problem of decision making. More specifically, we consider what was recently called a quantum parliament, asked to approve or not a certain law, and we propose a model of the connections between the various members of the parliament, proposing in particular some special form of the interactions giving rise to a {\em collaborative} or non collaborative behaviour.

We consider the problem of decoding corrupted error correcting codes with NC$^0[\oplus]$ circuits in the classical and quantum settings. We show that any such classical circuit can correctly recover only a vanishingly small fraction of messages, if the codewords are sent over a noisy channel with positive error rate. Previously this was known only for linear codes with non-trivial dual distance, whereas our result applies to any code. By contrast, we give a simple quantum circuit that correctly decodes the Hadamard code with probability $\Omega(\varepsilon^2)$ even if a $(1/2 - \varepsilon)$-fraction of a codeword is adversarially corrupted.

Our classical hardness result is based on an equidistribution phenomenon for multivariate polynomials over a finite field under biased input-distributions. This is proved using a structure-versus-randomness strategy based on a new notion of rank for high-dimensional polynomial maps that may be of independent interest.

Our quantum circuit is inspired by a non-local version of the Bernstein-Vazirani problem, a technique to generate "poor man's cat states" by Watts et al., and a constant-depth quantum circuit for the OR function by Takahashi and Tani.

Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through adaptive measurements, computing the maximum average score of a preparation game over a continuous set of target states and limiting the behavior of a (quantum) finite-state automaton. In this work, we introduce tractable relaxations of this class of optimization problems. To illustrate their performance, we use them to: (a) compute the probability that a finite-state automaton outputs a given sequence of bits; (b) develop a new many-body entanglement detection protocol; (c) let the computer invent an adaptive protocol for magic state detection. As we further show, the maximum score of a sequential problem in the limit of infinitely many time-steps is in general incomputable. Nonetheless, we provide general heuristics to bound this quantity and show that they provide useful estimates in relevant scenarios.

We propose a passive single-photon detector based on the bipolar thermoelectric effect occurring in tunnel junctions between two different superconductors thanks to spontaneous electron-hole symmetry breaking. Our thermoelectric detector (TED) converts a finite temperature difference caused by the absorption of a single photon into an open circuit thermovoltage. Designed with feasible parameters, our TED is able to reveal single-photons of frequency ranging from about 15 GHz to about 150 PHz depending on the chosen design and materials. In particular, this detector is expected to show values of signal-to-noise ratio SNR about 15 at {\nu} = 50 GHz when operated at a temperature of 10 mK. Interestingly, this device can be viewed as a digital single-photon detector, since it generates an almost constant voltage VS for the full operation energies. Our TED can reveal single photons in a frequency range wider than 4 decades with the possibility to discern the energy of the incident photon by measuring the time persistence of the generated thermovoltage. Its broadband operation suggests that our TED could find practical applications in several fields of quantum science and technology, such as quantum computing, telecommunications, optoelectronics, THz spectroscopy and astro-particle physics.

State-of-the-art quantum devices can be exploited to perform quantum simulations that explore exotic and novel physics. In this sense, a new phase transition in the entanglement properties of many-body dynamics has been described when the unitary evolution is interspersed with measurements, thus exhibiting universal properties. These measurement-induced phase transitions can be interpreted as a phase transition in the purification capabilities or error correction properties of quantum circuits, especially relevant in the context of state-of-the-art noisy intermediate-scale quantum devices. Measurement-induced phase transitions have been realized with quantum devices based on trapped ions or superconducting circuits, although they require large amounts of resources, due to the need to post-select trajectories, which consists of keeping track classically of the outcome of each measurement. In this work, we first describe the statistical properties of an interacting transmon array which is repeatedly measured and predict the behavior of relevant quantities in the area-law phase using a combination of the replica method and non-Hermitian perturbation theory. Most importantly, we show that, by using predetermined measurements that force the system to be locally in a certain state after performing a measurement, we can make use of the distribution of the number of bosons measured at a single site as a diagnostic for a measurement-induced phase transition. This indicates that the method of predetermined measurements is a suitable experimental candidate to alleviate post-selection-related issues. We also show numerically that a transmon array, modeled by an attractive Bose-Hubbard model, in which local measurements of the number of bosons are probabilistically interleaved, exhibits a phase transition in the entanglement entropy properties of the ensemble of trajectories in the steady state.

One of the first proposals for the use of quantum computers was the simulation of quantum systems. Over the past three decades, great strides have been made in the development of algorithms for simulating closed quantum systems and the more complex open quantum systems. In this tutorial, we introduce the methods used in the simulation of single qubit Markovian open quantum systems. It combines various existing notations into a common framework that can be extended to more complex open system simulation problems. The only currently available algorithm for the digital simulation of single qubit open quantum systems is discussed in detail. A modification to the implementation of the simpler channels is made that removes the need for classical random sampling, thus making the modified algorithm a strictly quantum algorithm. The modified algorithm makes use of quantum forking to implement the simpler channels that approximate the total channel. This circumvents the need for quantum circuits with a large number of C-NOT gates.

Understanding the evolution of a multi-qubit quantum system, or elucidating what portion of the Hilbert space is occupied by a quantum dataset becomes increasingly hard with the number of qubits. In this context, the visualisation of sets of multi-qubit pure quantum states on a single image can be helpful. However, the current approaches to visualization of this type only allow the representation of a set of single qubits (not allowing multi-qubit systems) or a just a single multi-qubit system (not suitable if we care about sets of states), sometimes with additional restrictions, on symmetry or entanglement for example. [1{3]. In this work we present a mapping that can uniquely represent a set of arbitrary multi-qubit pure states on what we call a Binary Tree of Bloch Spheres. The backbone of this technique is the combination of the Schmidt decomposition and the Bloch sphere representation. We illustrate how this can be used in the context of understanding the time evolution of quantum states, e.g. providing immediate insights into the periodicity of the system and even entanglement properties. We also provide a recursive algorithm which translates from the computational basis state representation to the binary tree of Bloch spheres representation. The algorithm was implemented together with a visualization library in Python released as open source.

The quantum asymptotically universal multi-feature (QAUM) encoding architecture was recently introduced and showed improved expressivity and performance in classifying pulsar stars. The circuit uses generalized trainable layers of parameterized single-qubit rotation gates and single-qubit feature encoding gates. Although the improvement in classification accuracy is promising, the single-qubit nature of this architecture, combined with the circuit depth required for accuracy, limits its applications on NISQ devices due to their low coherence times. This work reports on the design, implementation, and evaluation of ensembles of single-qubit QAUM classifiers using classical bagging and boosting techniques. We demonstrate an improvement in validation accuracy for pulsar star classification. We find that this improvement is not problem-specific as we observe consistent improvements for the MNIST Digits and Wisconsin Cancer datasets. We also observe that the boosting ensemble achieves an acceptable level of accuracy with only a small amount of training, while the bagging ensemble achieves higher overall accuracy with ample training time. This shows that classical ensembles of single-qubit circuits present a new approach for certain classification problems.

Recent developments in qudit-based quantum computing open interesting possibilities for scaling quantum processors without increasing the number of physical information carriers. One of the leading platforms in this domain is based on trapped ions, where efficient control of systems up to six levels has been demonstrated. In this work, we propose a method for compiling quantum circuits in the case, where qubits are embedded into qudits of various dimensionalities ($d$). Two approaches, the first, based on using higher qudit levels as ancillas, which can be used already for qutrits ($d=3$), and, the second, embedding qubits into ququarts ($d=4$) are considered. In particular, we develop a decomposition scheme of the generalized Toffoli gate using qudits of various dimensionalities, where the Molmer-Sorensen (MS) gate is used as a basic quantum operation. As our approach uses the MS gate, we expect that our findings are directly applicable to trapped-ion-based qudit processors.

Kernel methods are an important class of techniques in machine learning. To be effective, good feature maps are crucial for mapping non-linearly separable input data into a higher dimensional (feature) space, thus allowing the data to be linearly separable in feature space. Previous work has shown that quantum feature map design can be automated for a given dataset using NSGA-II, a genetic algorithm, while both minimizing circuit size and maximizing classification accuracy. However, the evaluation of the accuracy achieved by a candidate feature map is costly. In this work, we demonstrate the suitability of kernel-target alignment as a substitute for accuracy in genetic algorithm-based quantum feature map design. Kernel-target alignment is faster to evaluate than accuracy and doesn't require some data points to be reserved for its evaluation. To further accelerate the evaluation of genetic fitness, we provide a method to approximate kernel-target alignment. To improve kernel-target alignment and root mean squared error, the final trainable parameters of the generated circuits are further trained using COBYLA to determine whether a hybrid approach applying conventional circuit parameter training can easily complement the genetic structure optimization approach. A total of eight new approaches are compared to the original across nine varied binary classification problems from the UCI machine learning repository, showing that kernel-target alignment and its approximation produce feature map circuits enabling comparable accuracy to the previous work but with larger margins on training data (in excess of 20\% larger) that improve further with circuit parameter training.

The behaviour of genuine EPR steering of three qubit states under various environmental noises is investigated. In particular, we consider the two possible steering scenarios in the tripartite setting: (1 -> 2), where Alice demonstrates genuine steering to Bob-Charlie, and (2 -> 1), where Alice-Bob together demonstrates genuine steering to Charlie. In both these scenarios, we analyze the genuine steerability of the generalized Greenberger-Horne-Zeilinger (gGHZ) states or the W-class states under the action of noise modeled by amplitude damping (AD), phase flip (PF), bit flip (BF), and phase damping (PD) channels. In each case, we consider three different interactions with the noise depending upon the number of parties undergoing decoherence. We observed that the tendency to demonstrate genuine steering decreases as the number of parties undergoing decoherence increases from one to three. We have observed several instances where the genuine steerability of the state revives after collapsing if one keeps on increasing the damping. However, the hidden genuine steerability of a state cannot be revealed solely from the action of noise. So, the parties having a characterized subsystem, perform local pre-processing operations depending upon the steering scenario and the state shared with the dual intent of revealing hidden genuine steerability or enhancing it.

We present a scheme to enhance the atom number in magneto-optical traps of strontium atoms operating on the 461 nm transition. This scheme consists of resonantly driving the $^1$S$_0\to^3$P$_1$ intercombination line at 689 nm, which continuously populates a short-lived reservoir state and, as expected from a theoretical model, partially shields the atomic cloud from losses arising in the 461 nm cooling cycle. We show a factor of two enhancement in the atom number for the bosonic isotopes $^{88}$Sr and $^{84}$Sr, and the fermionic isotope $^{87}$Sr, in good agreement with our model. Our scheme can be applied in the majority of strontium experiments without increasing the experimental complexity of the apparatus, since the employed 689 nm transition is commonly used for further cooling. Our method should thus be beneficial to a broad range of quantum science and technology applications exploiting cold strontium atoms, and could be extended to other atomic species.

Multi-class classification problems are fundamental in many varied domains in research and industry. To solve multi-class classification problems, heuristic strategies such as One-vs-One or One-vs-All can be employed. However, these strategies require the number of binary classification models developed to grow with the number of classes. Recent work in quantum machine learning has seen the development of multi-class quantum classifiers that circumvent this growth by learning a mapping between the data and a set of label states. This work presents the first multi-class SWAP-Test classifier inspired by its binary predecessor and the use of label states in recent work. With this classifier, the cost of developing multiple models is avoided. In contrast to previous work, the number of qubits required, the measurement strategy, and the topology of the circuits used is invariant to the number of classes. In addition, unlike other architectures for multi-class quantum classifiers, the state reconstruction of a single qubit yields sufficient information for multi-class classification tasks. Both analytical results and numerical simulations show that this classifier is not only effective when applied to diverse classification problems but also robust to certain conditions of noise.

Since the 1990's, many observed cognitive behaviors have been shown to violate rules based on classical probability and set theory. For example, the order in which questions are posed affects whether participants answer 'yes' or 'no', so the population that answers 'yes' to both questions cannot be modeled as the intersection of two fixed sets. It can however be modeled as a sequence of projections carried out in different orders. This and other examples have been described successfully using quantum probability, which relies on comparing angles between subspaces rather than volumes between subsets. Now in the early 2020's, quantum computers have reached the point where some of these quantum cognitive models can be implemented and investigated on quantum hardware, representing the mental states in qubit registers, and the cognitive operations and decisions using different gates and measurements. This paper develops such quantum circuit representations for quantum cognitive models, focusing particularly on modeling order effects and decision-making under uncertainty. The claim is not that the human brain uses qubits and quantum circuits explicitly (just like the use of Boolean set theory does not require the brain to be using classical bits), but that the mathematics shared between quantum cognition and quantum computing motivates the exploration of quantum computers for cognition modelling. Key quantum properties include superposition, entanglement, and collapse, as these mathematical elements provide a common language between cognitive models, quantum hardware, and circuit implementations.

Preparing the ground state of a local Hamiltonian is a crucial problem in understanding quantum many-body systems, with applications in a variety of physics fields and connections to combinatorial optimization. While various quantum algorithms exist which can prepare the ground state with high precision and provable guarantees from an initial approximation, current devices are limited to shallow circuits. Here we consider the setting where Alice and Bob, in a distributed quantum computing architecture, want to prepare the same Hamiltonian eigenstate. We demonstrate that the circuit depth of the eigenstate preparation algorithm can be reduced when the devices can share limited entanglement. Especially so in the case where one of them has a near-perfect eigenstate, which is more efficiently broadcast to the other device. Our approach requires only a single auxiliary qubit per device to be entangled with the outside. We show that, in the near-convergent regime, the average relative suppression of unwanted amplitudes is improved to $1/(2\sqrt{e}) \approx 0.30$ per run of the protocol, outperforming the average relative suppression of $1/e\approx 0.37$ achieved with a single device alone for the same protocol.

For families of Hamiltonians defined by parts that are local, the most general definition of a symmetry algebra is the commutant algebra, i.e., the algebra of operators that commute with each local part. Thinking about symmetry algebras as commutant algebras allows for the treatment of conventional symmetries and unconventional symmetries (e.g., those responsible for weak ergodicity breaking phenomena) on equal algebraic footing. In this work, we discuss two methods for numerically constructing this commutant algebra starting from a family of Hamiltonians. First, we use the equivalence of this problem to that of simultaneous block-diagonalization of a given set of local operators, and discuss a probabilistic method that has been found to work with probability 1 for both Abelian and non-Abelian symmetries or commutant algebras. Second, we map this problem onto the problem of determining frustration-free ground states of certain Hamiltonians, and we use ideas from tensor network algorithms to efficiently solve this problem in one dimension. These numerical methods are useful in detecting standard and non-standard conserved quantities in families of Hamiltonians, which includes examples of regular symmetries, Hilbert space fragmentation, and quantum many-body scars, and we show many such examples. In addition, they are necessary for verifying several conjectures on the structure of the commutant algebras in these cases, which we have put forward in earlier works. Finally, we also discuss similar methods for the inverse problem of determining local operators with a given symmetry or commutant algebra, which connects to existing methods in the literature.