Variational quantum algorithms (VQA) combine the advantages of classical and near-term quantum computation for solving problems on today's noisy quantum devices. Variational Quantum Eigensolver (VQE) is one of the widely used VQAs, which aims to find the approximate ground state energy of a given Hamiltonian. While traditional VQE implementation is promising for ansatz-based trial state preparation, it requires an initial fiducial state or a reference state, which can be infeasible for large quantum systems. In this paper, we propose a novel approach for trial state preparation in VQE algorithms. This method leverages passive steering, a circuit-based approach with repeated measurements, eliminating the need for an initial fidu-cial state or a reference state. Experimental results demonstrate that passive steering-based state preparation provides improved accuracy and scalability of VQE compared to traditional ansatz-based solutions. Our proposed solution can also be effectively combined with the existing ansatz-based methods, where passive steering prepares the reference state while ansatz prepares the trial state, facilitating a robust and scalable state preparation for variational quantum algorithms.
Variational quantum algorithms (VQA) combine the advantages of classical and near-term quantum computation for solving problems on today's noisy quantum devices. Variational Quantum Eigensolver (VQE) is one of the widely used VQAs, which aims to find the approximate ground state energy of a given Hamiltonian. While traditional VQE implementation is promising for ansatz-based trial state preparation, it requires an initial fiducial state or a reference state, which can be infeasible for large quantum systems. In this paper, we propose a novel approach for trial state preparation in VQE algorithms. This method leverages passive steering, a circuit-based approach with repeated measurements, eliminating the need for an initial fidu-cial state or a reference state. Experimental results demonstrate that passive steering-based state preparation provides improved accuracy and scalability of VQE compared to traditional ansatz-based solutions. Our proposed solution can also be effectively combined with the existing ansatz-based methods, where passive steering prepares the reference state while ansatz prepares the trial state, facilitating a robust and scalable state preparation for variational quantum algorithms.
Variational quantum algorithms (VQAs) are a modern family of quantum algorithms designed to solve optimization problems using a quantum computer. Typically VQAs rely on a feedback loop between the quantum device and a classical optimization algorithm. The appeal of VQAs lies in their versatility, resistance to noise, and ability to demonstrate some results even with circuits of small depth. We primarily focus on the algorithm called variational quantum eigensolver (VQE), which takes a qubit Hamiltonian and returns its approximate ground state. We first present our numerical findings regarding VQE applied to two spin models and a variant of the Hubbard model. Next, we briefly touch the topic of quantum machine learning by developing a quantum classifier to partition quantum data. We further study the phenomenon of vanishing derivatives in VQAs, also known as barren plateaus phenomenon. We derive a new lower bound on variance of the derivatives, which depends on the causal structure of the ansatz circuit and the individual terms entering the Pauli decomposition of the problem Hamiltonian. In the final chapter of the thesis, we present our results on bounding the fidelity of experimentally prepared Clifford states using their parent Hamiltonians.
Variational quantum eigensolvers (VQEs) are one of the most important and effective applications of quantum computing, especially in the current noisy intermediate-scale quantum (NISQ) era. There are two main approaches for VQEs: problem-agnostic and problem-specific. For problem-agnostic methods, they often suffer from trainability issues. For problem-specific methods, their performance usually relies upon the choice of initial reference states, which are often hard to determine. In this paper, we propose an entanglement-variational hardware-efficient ansatz (EHA), and numerically compare it with some widely used ansatzes by solving benchmark problems in quantum many-body systems and quantum chemistry. Our EHA is problem-agnostic and hardware-efficient, is especially suitable for NISQ devices, and has potential for wide applications. Our EHA can achieve a higher level of accuracy in finding ground states and their energies in most cases, even compared with problem-specific methods. The performance of the EHA is robust to the choice of initial states and to parameter initialization, and it has the ability to quickly adjust the entanglement to the required amount, which is also the fundamental reason for its superiority.
The contextual subspace variational quantum eigensolver (CS-VQE) is a hybrid quantum-classical algorithm that approximates the ground-state energy of a given qubit Hamiltonian. It achieves this by separating the Hamiltonian into contextual and noncontextual parts. The ground-state energy is approximated by classically solving the noncontextual problem, followed by solving the contextual problem using VQE, constrained by the noncontextual solution. In general, computation of the contextual correction needs fewer qubits and measurements compared with solving the full Hamiltonian via traditional VQE. We simulate CS-VQE on different tapered molecular Hamiltonians and apply the unitary partitioning measurement reduction strategy to further reduce the number of measurements required to obtain the contextual correction. Our results indicate that CS-VQE combined with measurement reduction is a promising approach to allow feasible eigenvalue computations on noisy intermediate-scale quantum devices. We also provide a modification to the CS-VQE algorithm; the CS-VQE algorithm previously could cause an exponential increase in Hamiltonian terms but with this modification now at worst will scale quadratically.
Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum machines. VQE aims to approximate the lowest eigenvalue of an exponentially sized matrix in polynomial time. It minimizes quantum resource requirements both by co-processing with a classical processor and by structuring computation into many subproblems. Each quantum subproblem involves a separate state preparation terminated by the measurement of one Pauli string. However, the number of such Pauli strings scales as N4 for typical problems of interest--a daunting growth rate that poses a serious limitation for emerging applications such as quantum computational chemistry. We introduce a systematic technique for minimizing requisite state preparations by exploiting the simultaneous measurability of partitions of commuting Pauli strings. Our work encompasses algorithms for efficiently approximating a MIN-COMMUTING-PARTITION, as well as a synthesis tool for compiling simultaneous measurement circuits. For representative problems, we achieve 8-30x reductions in state preparations, with minimal overhead in measurement circuit cost. We demonstrate experimental validation of our techniques by estimating the ground state energy of deuteron on an IBM Q 20-qubit machine. We also investigate the underlying statistics of simultaneous measurement and devise an adaptive strategy for mitigating harmful covariance terms.
Quantum computers have the potential to deliver speed-ups for solving certain important problems that are intractable for classical counterparts, making them a promising avenue for advancing modern computation. However, many quantum algorithms require deep quantum circuits, which are challenging to implement on current noisy devices. To address this limitation, variational quantum algorithms (VQAs) have been actively developed, enabling practical quantum computing in the noisy intermediate-scale quantum (NISQ) era. Among them, the variational quantum eigensolver (VQE) stands out as a leading approach for solving problems in quantum chemistry, many-body physics, and even integer factorization. The VQE algorithm can be implemented on various quantum hardware platforms, including photonic systems, quantum dots, trapped ions, neutral atoms, and superconducting circuits. In particular, photonic platforms offer several advantages: they operate at room temperature, exhibit low decoherence, and support multiple degrees of freedom, making them suitable for scalable, high-dimensional quantum computation. Here we present methodologies for realizing VQE on photonic systems, highlighting their potential for practical quantum computing. We first provide a theoretical overview of the VQE framework, focusing on the procedure for variationally estimating ground state energies. We then explore how photonic systems can implement these processes, showing that a wide variety of problems can be addressed using either multiple qubit states or a single qudit state.
Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the noisy intermediate-scale quantum (NISQ) era. In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware for determining molecular ground-state energies, focusing on the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE). To address the significant computational challenges posed by molecular Hamiltonians, we explore various well known strategies to simplify the Hamiltonian, optimize the ansatz, and improve classical parameter optimization through modifications of the COBYLA optimizer. These enhancements are integrated into a tailored quantum computing implementation designed to minimize the circuit depth and computational cost. Using benzene as a benchmark system, we demonstrate the application of these optimizations on an IBM quantum computer. Despite these improvements, our results highlight the limitations imposed by current quantum hardware, particularly the impact of quantum noise on state preparation and energy measurement. The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Finally, we extrapolate the requirements for future quantum hardware to enable practical and scalable quantum chemistry calculations using VQE algorithms. This work provides an assessment of current quantum algorithms for molecular modeling on real quantum hardware, highlighting the impact of noise and hardware limitations on the achievable accuracy.