The standard paradigm for state preparation on quantum computers for the simulation of physical systems in the near term has been widely explored with different algorithmic methods. One such approach is the optimization of parameterized circuits, but this becomes increasingly challenging with circuit size. As a consequence, the utility of large-scale circuit optimization is relatively unknown. In this work we demonstrate that purely classical resources can be used to optimize quantum circuits in an approximate but robust manner such that we can bridge the resources that we have from high performance computing and see a direct transition to quantum advantage. We show this through the sparse wave function circuit solvers, which we detail here, and demonstrate a region of efficient classic simulation. With such tools, we can avoid the many problems that plague circuit optimization for circuits with hundreds of qubits using only practical and reasonable classical computing resources. These tools allow us to probe the true benefit of variational optimization approaches on quantum computers, thus opening the window to what can be expected with near term hardware for physical systems. We demonstrate this with a unitary coupled cluster ansatz on various molecules up to 64 qubits with tens of thousands of variational parameters.
The standard paradigm for state preparation on quantum computers for the simulation of physical systems in the near term has been widely explored with different algorithmic methods. One such approach is the optimization of parameterized circuits, but this becomes increasingly challenging with circuit size. As a consequence, the utility of large-scale circuit optimization is relatively unknown. In this work we demonstrate that purely classical resources can be used to optimize quantum circuits in an approximate but robust manner such that we can bridge the resources that we have from high performance computing and see a direct transition to quantum advantage. We show this through the sparse wave function circuit solvers, which we detail here, and demonstrate a region of efficient classic simulation. With such tools, we can avoid the many problems that plague circuit optimization for circuits with hundreds of qubits using only practical and reasonable classical computing resources. These tools allow us to probe the true benefit of variational optimization approaches on quantum computers, thus opening the window to what can be expected with near term hardware for physical systems. We demonstrate this with a unitary coupled cluster ansatz on various molecules up to 64 qubits with tens of thousands of variational parameters.
The ADAPT-VQE algorithm is a promising method for generating a compact ansatz based on derivatives of the underlying cost function, and it yields accurate predictions of electronic energies for molecules. In this work, we report the implementation and performance of ADAPT-VQE with our recently developed sparse wave function circuit solver (SWCS) in terms of accuracy and efficiency for molecular systems with up to 52 spin orbitals. The SWCS can be tuned to balance computational cost and accuracy, which extends the application of ADAPT-VQE for molecular electronic structure calculations to larger basis sets and a larger number of qubits. Using this tunable feature of the SWCS, we propose an alternative optimization procedure for ADAPT-VQE to reduce the computational cost of the optimization. By preoptimizing a quantum simulation with a parametrized ansatz generated with ADAPT-VQE/SWCS, we aim to utilize the power of classical high-performance computing in order to minimize the work required on noisy intermediate-scale quantum hardware, which offers a promising path toward demonstrating quantum advantage for chemical applications.
The unitary coupled cluster (UCC) ansatz is a promising tool for achieving high-precision results using the variational quantum eigensolver (VQE) algorithm in the NISQ era. However, results on quantum hardware are thus far very limited and simulations have only accessed small system sizes. We advance the state of the art of UCC simulations by utilizing an efficient sparse wavefunction circuit solver and studying systems up to 64 qubits. Here we report results obtained using this solver that demonstrate the power of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction, among others. Our approach enables meaningful benchmarking of the UCC ansatz, a crucial step in assessing the utility of VQE for achieving quantum advantage.
Variational quantum algorithms are considered to be appealing applications of near-term quantum computers. However, it has been unclear whether they can outperform classical algorithms or not. To reveal their limitations, we must seek a technique to benchmark them on large-scale problems. Here we propose a perturbative approach for efficient benchmarking of variational quantum algorithms. The proposed technique performs perturbative expansion of a circuit consisting of Clifford and Pauli rotation gates, which is enabled by exploiting the classical simulatability of Clifford circuits. Our method can be applied to a wide family of parameterized quantum circuits consisting of Clifford gates and single-qubit rotation gates. The approximate optimal parameter obtained by the method can also serve as an initial guess for further optimizations on a quantum device. As the first application of the method, we perform a benchmark of so-called hardware-efficient-type ansatzes when they are applied to the variational quantum eigensolver (VQE) of one-dimensional hydrogen chains up to H24, which corresponds to a 48-qubit system using a standard workstation. This is the largest scale benchmark of the VQE to the best of our knowledge and reveals the limitation of hardware-efficient-type ansatzes.
Traditional quantum algorithms with guaranteed performance generally require fully coherent quantum computers to operate, making error-correction a necessity. In contrast, variational quantum algorithms seek to remove this requirement by formulating the computation as the approximate optimization of a functional. This optimization is carried out in the space of heuristic functions defined by a parameterized (variational) quantum circuit. Taking advantage of the flexibility in the definition of these heuristics, we can expand the operability of variational algorithms within the regime of coherence times of noisy intermediate-scale quantum devices, avoiding the necessity of error-correction. In this dissertation, we present the application of the variational quantum computing approach to problems in quantum simulation, quantum state preparation, quantum error-correction, and generative modeling.\nIn the first part, we investigate the use of the variational quantum eigensolver (VQE) for simulating the ground state of fermionic systems. We start by studying the implementation of VQE using the unitary coupled cluster (UCC) ansatz and propose strategies to reduce its cost. We use these insights to carry out some of the first experimental quantum computations of molecular energies using simplified versions of this ansatz. We also propose an extension of UCC to study problems in condensed matter physics, along with a new low-depth circuit ansatz for preparing non-gaussian fermionic states on quantum computers. We show the potential of our approach to describe strongly correlated fermionic systems.\nIn the second part, we develop three new variational quantum algorithms for problems in quantum computing and machine learning, namely: 1) the quantum autoencoder, to compress ensembles of quantum states, 2) the variational quantum error corrector, to find device-tailored quantum encoding and recovery circuits for quantum error correction, and 3) the variational quantum generator, to generate classical probability distributions. These techniques offer efficient ways to design new quantum circuits for state preparation, to find more effective error-correcting codes and to perform generative modeling with quantum computers. Our work provides insights into the design of variational quantum algorithms and establishes practical guidelines to implement these methods on near-term quantum computers, as well as some future research directions for this field.
Quantum computers exist today that are capable of performing calculations that challenge the largest classical supercomputers. Now the great challenge is to make use of these devices, or their successors, to perform calculations of independent interest. This thesis focuses on a family of algorithms that aim to accomplish this goal, known as variational quantum algorithms, and the challenges that they face. We frame these challenges in terms of two kinds of resources, the number of operations that we can afford to perform in a single quantum circuit, and the overall number of circuit repetitions required. Before turning to our specific contributions, we provide a review of the electronic structure problem, which serves as a central example for our work. We also provide a self-contained introduction to the field of quantum computing and the notion of a variational quantum algorithm.We begin the main body of the thesis by studying a generalization of the standard unitary coupled cluster ansatz. We present a sparse version of unitary coupled cluster and show that it can accurately represent the ground and excited states of small molecular systems using fewer quantum gates than the full unitary coupled cluster. We then introduce a strategy for representing molecular ground states as linear combinations of parameterized wavefunctions, allowing for a tradeoff between the number of operations required for each circuit and the number of circuit repetitions. We provide circuit primitives that allow for the efficient measurement of the required matrix elements between these wavefunctions. Subsequently, we show how the cost of estimating the energy of a quantum chemical wavefunction on a near-term quantum computer can be dramatically reduced by using a factorization of the two-electron integraltensor. Furthermore, we explain how this measurement strategy helps mitigate against errors during state preparation and measurement. We then present a Monte Carlo version of a classical algorithm for calculating the partition function of two-dimensional lattice models that shows a similar kind of tradeoff between two resources, albeit in a different context. Finally, we show how ideas based on tensor networks can inform the design of quantum circuits for machine learning tasks. We argue that this application is especially tolerant to noise and present numerical data substantiating this argument. We conclude by explaining explicitly how our work addresses the problems of the limited resources available to near-term quantum computers and offering some optimism about the future of the field.
Variational quantum eigensolvers are touted as a near-term algorithm capable of impacting many applications. However, the potential has not yet been realized, with few claims of quantum advantage and high resource estimates, especially due to the need for optimization in the presence of noise. Finding algorithms and methods to improve convergence is important to accelerate the capabilities of near-term hardware for VQE or more broad applications of hybrid methods in which optimization is required. To this goal, we look to use modern approaches developed in circuit simulations and stochastic classical optimization, which can be combined to form a surrogate optimization approach to quantum circuits. Using an approximate (classical CPU/GPU) state vector simulator as a surrogate model, we efficiently calculate an approximate Hessian, passed as an input for a quantum processing unit or exact circuit simulator. This method will lend itself well to parallelization across quantum processing units. We demonstrate the capabilities of such an approach with and without sampling noise and a proof-of-principle demonstration on a quantum processing unit utilizing 40 qubits.