Search

Recently double-bracket quantum algorithms have been proposed as a way to compile circuits for approximating eigenstates. Physically, they consist of appropriately composing evolutions under an input Hamiltonian together with diagonal evolutions. Here, we present strategies to optimize the choice of the double-bracket evolutions to enhance the diagonalization efficiency. This can be done by finding optimal generators and durations of the evolutions. We present numerical results regarding the preparation of double-bracket iterations, both in ideal cases where the algorithm's setup provides analytical convergence guarantees and in more heuristic cases, where we use an adaptive and variational approach to optimize the generators of the evolutions. As an example, we discuss the efficacy of these optimization strategies when considering a spin-chain Hamiltonian as the target. To propose algorithms that can be executed starting today, fully aware of the limitations of the quantum technologies at our disposal, we finally present a selection of diagonal evolution parametrizations that can be directly compiled into CNOTs and single-qubit rotation gates. We discuss the advantages and limitations of this compilation and propose a way to take advantage of this approach when used in synergy with other existing methods., Comment: Submitted to ACAT 2024, 8 pages

Ground state preparation is a key area where quantum computers are expected to prove advantageous. Double-bracket quantum algorithms (DBQAs) have been recently proposed to diagonalize Hamiltonians and in this work we show how to use them to prepare ground states. We propose to improve an initial state preparation by adding a few steps of DBQAs. The interfaced method systematically achieves a better fidelity while significantly reducing the computational cost of the procedure. For a Heisenberg model, we compile our algorithm using CZ and single-qubit gates into circuits that match capabilities of near-term quantum devices. Moreover, we show that DBQAs can benefit from the experimental availability of increasing circuit depths. Whenever an approximate ground state can be prepared without exhausting the available circuit depth, then DBQAs can be enlisted to algorithmically seek a higher fidelity preparation., Comment: 5 pages + appendix, 4 figures, code available at: https://github.com/qiboteam/boostvqe

Quantum state preparation is a crucial process within numerous quantum algorithms, and the need for efficient initialization of quantum registers is ever increasing as demand for useful quantum computing grows. The problem arises as the number of qubits to be initialized grows, the circuits required to implement the desired state also exponentially increase in size leading to loss of fidelity to noise. This is mainly due to the susceptibility to environmental effects of the non-Clifford T gate, whose use should thus be reduced as much as possible. In this paper, we present and utilize a genetic algorithm for state preparation circuits consisting of gates from the Clifford + T gate set and optimize them in T-Count as to reduce the impact of noise. Whilst the method presented here does not always produce the most accurate circuits in terms of fidelity, it can generate high-fidelity, non-trivial quantum states such as quantum Fourier transform states. In addition, our algorithm does automatically generate fault tolerantly implementable solutions where the number of the most error prone components is reduced. We present an evaluation of the algorithm when trialed against preparing random, Poisson probability distribution, W, GHZ, and quantum Fourier transform states. We also experimentally demonstrate the scalability issues as qubit count increases, which highlights the need for further optimization of the search process., Comment: To appear in IEEE QSW 2024 proceedings