Search Results (13)

Foreign-exchange decisions rest on hierarchically organized evidence whose latent structure is inadequately captured by Euclidean representations. Reinforcement-learning agents trained on flat embeddings inherit stability guarantees that do not transfer to the manifold supporting the latent state. We address both limitations through a hybrid architecture in which a schema-constrained structured chain-of-thought is embedded into a Poincaré ball, transported to a qubit register via angle encoding, and processed by an L-layer hardware-efficient variational ansatz on a state-vector backend. The circuit exposes two read-outs to the policy, namely, a scalar Pauli-Z observable and a projected quantum kernel inducing a fidelity-based similarity over magnet-price attractors, the latter identified via kernel-weighted recurrence density and finite-time Lyapunov statistics. The Lipschitz constraint on the action-value function is lifted from the hyperbolic geodesic distance to a joint metric on ${\mathbb{B}}_{\kappa }^n\times \mathbb{P}\left(\mathcal{H}\right)$. A stability theorem yields an explicit bound depending on the read-out operator norm, on the depth–width product of the ansatz, and on the curvature–Hilbert balance. The pipeline is evaluated on nine major FX crosses over a 2015–2025 out-of-sample window, with rolling-origin walk-forward retraining and broker-published transaction costs. The system attains $2.55\%$ pair-averaged non-compounded monthly P&L and $8.83\%$ maximum drawdown, with Sharpe $1.78$, Calmar $3.43$, and Probabilistic Sharpe Ratio exceeding $0.95$ on every cross. The gain remains significant under a deflated-Sharpe-ratio test with $N_{\mathrm{trials}}=42$ correction. Block-wise ablations exhibit strictly monotone degradation: removing the projected kernel costs $-4.15$ p.p. on annualized P&L, the joint Lipschitz penalty $-6.42$ p.p., the attractor module $-7.64$ p.p., and the hyperbolic embedding $-8.40$ p.p. The quantum block thereby instantiates a structurally non-classical, geometry-aware regularizer identifiable through ablation rather than asymptotically advantageous. Full article

The selection of the right topology (ansatz) for a Variational Quantum Algorithm (VQA) is a complex task that usually involves deep knowledge of a particular problem. The importance of the selection is greater when we consider the current state of quantum hardware, particularly the noise associated with the complexity of Variational Quantum Circuits (VQCs) that implement VQAs. Here, a comparison is presented between two confronted approaches for solving the MaxCut problem: QAOA, which has a theoretical proof of convergence, and the automatic design proposal (QNAS), which relies on evolutionary algorithms (NSGA-II) to discover efficient circuits. The comparison was made across 490 graph instances from different graph topologies and sizes ($n=4$ to $n=16$), accounting for noise models such as depolarizing noise, gate errors, and readout noise. The results show that QAOA achieves an approximation ratio ($r_A$) $\approx 1$ on complete graphs at the cost of being almost 12 times more complex than QNAS in ideal conditions while approaching the random noise floor ($r_A\approx 0.5)$. QNAS was capable of finding circuits less complex while maintaining $69\%$ of the fidelity at a cost of having an $r_A$ on the interval $0.7\le r_A\le 0.8$. However, when the comparison is made across sparse graphs, performance is comparable, while QNAS is less complex. Full article

The quantum approximate optimization algorithm (QAOA) is an efficient method for solving combinatorial optimization problems in quantum computing. These problems involve finding the best solution from a finite set of possibilities. At its core, the QAOA uses an Ansatz circuit composed of alternating unitary operators, the mixing and problem Hamiltonians, that are controlled by a set of parameters. Its goal is to find the optimal parameters so that the final quantum state of the circuit encodes the problem’s solution. While this parameter optimization is often handled by classical optimizers, including constrained optimization by linear approximations (COBYLA) and Nelder–Mead, these methods frequently present local extrema. Therefore, we developed a layerwise grid search (LGS) method as an alternative. Since a full grid search is too time-consuming, the LGS method significantly reduces the search time while still finding a good solution. To demonstrate its effectiveness, we present experimental results for the max-cut problem, comparing the performance of our LGS method against conventional classical optimizers. Full article

Radar systems serve as foundational components in both civil and military aerospace infrastructures. Modern radar must not only distinguish between detection and non-detection but must also classify detected objects. Signal processing increasingly integrates machine learning models into complex systems, such as radar. Additionally, developments have fused signal processing with quantum computing, creating an emerging field of research. This paper examines the applicability of quantum machine learning models for radar signal classification, focusing on the impact of Ansatz depth on expressibility. Multiple challenges arise due to the immature state of noisy intermediate-scale quantum hardware and the computational complexity of quantum circuit simulation. Nonetheless, results indicate that shallow Ansätze with fewer than 70 gates are sufficient to achieve the maximum available performance per data-encoding operation. Full article

Understanding the capabilities of quantum computer devices and computing the required resources to solve realistic tasks remain critical challenges associated with achieving useful quantum computational advantage. We present a study aimed at reducing the quantum resource overhead in quantum chemistry simulations using the variational quantum eigensolver (VQE). Our approach achieves up to a two-orders-of magnitude reduction in the required number of two-qubit operations for variational problem-inspired ansatzes. We propose and analyze optimization strategies that combine various methods, including molecular point-group symmetries, compact excitation circuits, different types of excitation sets, and qubit tapering. To validate the compatibility and accuracy of these strategies, we first test them on small molecules such as LiH and BeH₂, then apply the most efficient ones to restricted active-space simulations of methylamine. We complete our analysis by computing the resources required for full-valence, active-space simulations of methylamine (26 qubits) and formic acid (28 qubits) molecules. Our best-performing optimization strategy reduces the two-qubit gate count for methylamine from approximately 600,000 to about 12,000 and yields a similar order-of-magnitude improvement for formic acid. This resource analysis represents a valuable step towards the practical use of quantum computers and the development of better methods for optimizing computing resources. Full article

Grover’s search algorithm (GSA) offers quadratic speedup in searching unstructured databases but suffers from exponential circuit depth complexity. Here, we present two quantum circuits called HX and Ry layers for the searching problem. Remarkably, both circuits maintain a fixed circuit depth of two and one, respectively, irrespective of the number of qubits used. When the target element’s position index is known, we prove that either circuit, combined with a single multi-controlled X gate, effectively amplifies the target element’s probability to over 0.99 for any qubit number greater than seven. To search unknown databases, we use the depth-1 Ry layer as the ansatz in the Variational Quantum Search (VQS), whose efficacy is validated through numerical experiments on databases with up to 26 qubits. The VQS with the Ry layer exhibits an exponential advantage, in circuit depth, over the GSA for databases of up to 26 qubits. Full article

This paper presents a system for solving binary-valued linear equations using quantum computers. The system is called Mod2VQLS, which stands for Modulo 2 Variational Quantum Linear Solver. As far as we know, this is the first such proposal. The design is a classical–quantum hybrid. The quantum components are a new circuit design for implementing matrix multiplication modulo 2, and a variational circuit to be optimized. The classical components are the optimizer, which measures the cost function and updates the quantum parameters for each iteration, and the controller that runs the quantum job and classical optimizer iterations. We propose two alternative ansatze or templates for the variational circuit and present results showing that the rotation ansatz designed specifically for this problem provides the most direct path to a valid solution. Numerical experiments in low dimensions indicate that Mod2VQLS, using the custom rotations ansatz, is on par with the block Wiedemann algorithm, which is the best-known to date solution for this problem. Full article

Efficient methods for encoding and compression are likely to pave the way toward the problem of efficient trainability on higher-dimensional Hilbert spaces, overcoming issues of barren plateaus. Here, we propose an alternative approach to variational autoencoders to reduce the dimensionality of states represented in higher dimensional Hilbert spaces. To this end, we build a variational algorithm-based autoencoder circuit that takes as input a dataset and optimizes the parameters of a Parameterized Quantum Circuit (PQC) ansatz to produce an output state that can be represented as a tensor product of two subsystems by minimizing $Tr({\rho }^2)$. The output of this circuit is passed through a series of controlled swap gates and measurements to output a state with half the number of qubits while retaining the features of the starting state in the same spirit as any dimension-reduction technique used in classical algorithms. The output obtained is used for supervised learning to guarantee the working of the encoding procedure thus developed. We make use of the Bars and Stripes (BAS) dataset for an 8 × 8 grid to create efficient encoding states and report a classification accuracy of 95% on the same. Thus, the demonstrated example provides proof for the working of the method in reducing states represented in large Hilbert spaces while maintaining the features required for any further machine learning algorithm that follows. Full article

Computational complexity reduction is at the basis of a new formulation of many-body quantum states according to tensor network ansatz, originally framed in one-dimensional lattices. In order to include long-range entanglement characterizing phase transitions, the multiscale entanglement renormalization ansatz (MERA) defines a sequence of coarse-grained lattices, obtained by targeting the map of a scale-invariant system into an identical coarse-grained one. The quantum circuit associated with this hierarchical structure includes the definition of causal relations and unitary extensions, leading to the definition of ground subspaces as stabilizer codes. The emerging error correcting codes are referred to logical indices located at the highest hierarchical level and to physical indices yielded by redundancy, framed in the AdS-CFT correspondence as holographic quantum codes with bulk and boundary indices, respectively. In a use-case scenario based on errors consisting of spin erasure, the correction is implemented as the reconstruction of a bulk local operator. Full article

Coherent states, known as displaced vacuum states, play an important role in quantum information processing, quantum machine learning, and quantum optics. In this article, two ways to digitally prepare coherent states in quantum circuits are introduced. First, we construct the displacement operator by decomposing it into Pauli matrices via ladder operators, i.e., creation and annihilation operators. The high fidelity of the digitally generated coherent states is verified compared with the Poissonian distribution in Fock space. Secondly, by using Variational Quantum Algorithms, we choose different ansatzes to generate coherent states. The quantum resources—such as numbers of quantum gates, layers and iterations—are analyzed for quantum circuit learning. The simulation results show that quantum circuit learning can provide high fidelity on learning coherent states by choosing appropriate ansatzes. Full article

The quantum alternating operator ansatz (QAOA) and constrained quantum annealing (CQA) restrict the evolution of a quantum system to remain in a constrained space, often with a dimension much smaller than the whole Hilbert space. A natural question when using quantum annealing or a QAOA protocol to solve an optimization problem is to select an initial state for the wavefunction and what operators to use to evolve it into a solution state. In this work, we construct several ansatzes tailored to solve the combinational circuit fault diagnostic (CCFD) problem in different subspaces related to the structure of the problem, including superpolynomially smaller subspaces than the whole Hilbert space. We introduce a family of dense and highly connected circuits that include small instances but can be scaled to larger sizes as a useful collection of circuits for comparing different quantum algorithms. We compare the different ansätzes on instances randomly generated from this family under different parameter selection methods. The results support that ansätzes more closely tailored to exploiting the structure of the underlying optimization problems can have better performance than more generic ansätzes. Full article

We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally trained unitary that maps any vector output by ansatz $A(\overrightarrow{\alpha })$ from a defined subspace to a vector in the symmetry space. The parameters are trained varitionally to minimize the energy, thus keeping the output within the labelled symmetry value. The method was tested for a spin XXZ Hamiltonian using rotation and reflection symmetry and $H_2$ Hamiltonian within $S_z=0$ subspace using $S^2$ symmetry. We have found the variationally trained unitary gives good results with very low depth circuits and can thus be used to prepare symmetry states within near term quantum computers. Full article

The next few years will be exciting as prototype universal quantum processors emerge, enabling the implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation and which have the potential to significantly expand the breadth of applications for which quantum computers have an established advantage. A leading candidate is Farhi et al.’s quantum approximate optimization algorithm, which alternates between applying a cost function based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach, in the spirit of the quantum approximate optimization algorithm, to a wide variety of approximate optimization, exact optimization, and sampling problems. In addition to introducing the quantum alternating operator ansatz, we lay out design criteria for mixing operators, detail mappings for eight problems, and provide a compendium with brief descriptions of mappings for a diverse array of problems. Full article