Digitized adiabatic quantum computing with a superconducting circuit

Abstract

A digitized approach to adiabatic quantum computing, combining the generality of the adiabatic algorithm with the universality of the digital method, is implemented using a superconducting circuit to find the ground states of arbitrary Hamiltonians. Adiabatic quantum computers are analogue machines that, with the help of quantum tunnelling, slowly evolve from a simple input to the desired, more complicated output. Although adiabiatic quantum computers can be very fast at specific tasks, they are limited by noise and errors that cannot be corrected during the computation. In contrast, universal quantum computers are digital devices that use logic gates and allow for error correction. Here, Rami Barends et al. combine the advantages of adiabiatic and universal quantum computers by digitizing an adiabiatic quantum computation. This approach allows for encoding non-stoquastic Hamiltonians, which are crucial for simulating physical and chemical systems with interacting fermions. Quantum mechanics can help to solve complex problems in physics1 and chemistry2, provided they can be programmed in a physical device. In adiabatic quantum computing3,4,5, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing6, which enables the construction of arbitrary interactions and is compatible with error correction7,8, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation9,10,11,12 of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.