Abstract
We provide an efficient and general route for preparing non-trivial quantum states that are not adiabatically connected to unentangled product states. Our approach is a hybrid quantum-classical variational protocol that incorporates a feedback loop between a quantum simulator and a classical computer, and is experimentally realizable on near-term quantum devices of synthetic quantum systems. We find explicit protocols which prepare with perfect fidelities (i) the Greenberger-Horne-Zeilinger (GHZ) state, (ii) a quantum critical state, and (iii) a topologically ordered state, with \bm{L}𝐋 variational parameters and physical runtimes \bm{T}𝐓 that scale linearly with the system size \bm{L}𝐋. We furthermore conjecture and support numerically that our protocol can prepare, with perfect fidelity and similar operational costs, the ground state of every point in the one dimensional transverse field Ising model phase diagram. Besides being practically useful, our results also illustrate the utility of such variational Ansätze as good descriptions of non-trivial states of matter.
Highlights
The feedback loop of the protocol allows one to mitigate systematic errors that might be present in the experimental setups. Employing this variational quantum-classical simulation and with local, uniform Hamiltonians, we show here that such protocols can be used to target the GHZ state, the critical state of the 1d transverse field Ising model (TFIM), and the ground state of the 2d toric code, all with perfect fidelities, using 2p = L variational parameters, and with minimum runtimes T that scale linearly with the system size, T ∼ L, where L is the linear dimension of the systems
We have presented a general, efficient approach for preparing non-trivial quantum states based on Variational Quantum-Classical Simulation (VQCS), and demonstrated numerically its efficacy and efficiency in the preparation of a number of target states of interest
The main merits of this approach are its practicality for quantum simulators and its ability to improve based on feedback from the simulator
Summary
Recent experimental advances in designing and controlling well-isolated synthetic quantum systems of many-particles, such as trapped ions [1, 2], cold atoms [3, 4], superconducting qubits [5, 6], etc., have allowed for the study of a plethora of interesting physical phenomena. The entire process is iterated and the simulation terminates when the cost function has been desirably optimized (see Fig. 1); in this way, a good approximation to the ground state of the target Hamiltonian according to the cost function is produced Such variational quantum approaches have been developed and utilized in a number of contexts, such as in quantum chemistry [24, 25], and in classical optimization problems (for example, as the ‘Quantum Approximate Optimization Algorithm’ [26, 27]), with recent experiments demonstrating its success in platforms like photonic quantum processors [24], and programmable, analog quantum simulators of trapped ions [28]. This is in contrast to our method, which only requires time evolution between simple, uniform local Hamiltonians, and provides physically realizable roadmaps for quantum state preparation
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