Multi-qubit Gates for the Efficient Exploration of Hilbert Space with Superconducting Qubit Systems

The goal of this research project is to explore the potential of multi-qubit gates for quantum computing. The main focus is on speeding up quantum algorithms based on the variational quantum eigensolver (VQE) method on a superconducting qubit platform.

This quantum algorithm determines the groundstate of a given Hamiltonian, for example a molecular electronic configuration Hamiltonian. The quantum state of the system is steered to the target state by varying parameters of a gate sequence on the qubits to optimize a cost function on a classical computer. The advantage of such a hybrid quantum-classical computation over a purely classical one is that high-dimensional multi-qubit states can be stored efficiently on the quantum device, which is not possible on a classical memory because of the exponentially large number of state coefficients. The challenge on today’s quantum computers is, however, that the VQE algorithm has to converge to the target state before decoherence sets in. It's circuit-depth must be short. The main aim of this project is, therefore, to explore the efficient generation of multi-qubit states going beyond the current paradigm of decomposing all state manipulations into single and two-qubit gates. We will investigate multi-qubit operations that will allow us to entangle multiple qubits at the same time. This will result in short-depth efficient algorithms provided that the fidelity of the multi-qubit gate can be kept high. We use fixed-frequency transmon qubits and two-qubit gates based on parametrically driven tunable couplers. We address the question if there is an advantage in using multi-qubit gates over traditional two-qubit gates not only in theory but also in practical experiments. While theoretically the answer is likely to be affirmative, on the experimental side it is not clear what gate fidelities can be reached and how these compare to a decomposition of multi-qubit gates into two-qubit interactions. We explore N-way tunable couplers that are either capacitively and galvanically coupled to N qubits and evaluate the maximum number of qubits. We investigate multi-qubit entangling interactions via parametric frequency-modulation of the coupler. Different methods are compared, such as resonant or dispersive interactions based on simultaneous pulses to generate different classes of entangled states. The final goal is a four-qubit experiment targeting a quantum chemistry problem, such as determining the ground state and energy spectrum of molecular hydrogen (H2), and to assess the efficiency of multi-qubit gates. It is straightforward to then extend the methods that are tested in this project with a few qubits to larger systems to bring practical applications closer within reach by adding building blocks with higher connectivity and multi-qubit gate capabilities.

Filipp, Stefan
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