Search Results (9)

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