Demonstration of a Nonstoquastic Hamiltonian in Coupled Superconducting Flux Qubits

Abstract

Hamiltonian-based quantum computation is a class of quantum algorithms in which the problem is encoded in a Hamiltonian and the evolution is performed by a continuous transformation of the Hamiltonian. Universal adiabatic quantum computing, quantum simulation, and quantum annealing are examples of such algorithms. Up to now, all implementations of this approach have been limited to qubits coupled via a single degree of freedom. This gives rise to a stoquastic Hamiltonian that has no sign problem in quantum Monte Carlo simulations. In this paper, we report implementation and measurements of two superconducting flux qubits coupled via two canonically conjugate degrees of freedom-charge and flux-to achieve a nonstoquastic Hamiltonian. We perform microwave spectroscopy to extract circuit parameters and show that the charge coupling manifests itself as a σ y σ y interaction in the computational basis. We observe destructive interference in quantum coherent oscillations between the computational basis states of the two-qubit system. Finally, we show that the extracted Hamiltonian is nonstoquastic over a wide range of parameters.

Effective Hamiltonians for interacting superconducting qubits: local basis reduction and the Schrieffer–Wolff transformation

“…In this subsection we briefly review the reduction method outlined in a recent work by Ozfidan et al [16]. This method starts by writing the low-energy part of the total circuit HamiltonianĤ e.m. , i.e.…”

“…R 1 must therefore be explicitly orthonormalised, for instance using the Gram-Schmidt procedure. This step is only justified if the columns of R 1 are already approximately orthonormal [16]. Since in our case orthogonality follows from normalisation, it suffices to check that…”

“…the higher excited states of the individual circuits. Such mixed states become the new low-energy eigenstates ofĤ e.m. [21,16].…”

“…As we will see below, where such mapping methods do exist (see, for instance, supplementary materials of Ref. [15,16]), they are not guaranteed to reproduce the correct low-energy spectrum of the circuit.…”

Quantum annealing with capacitive-shunted flux qubits

“…Such a controllability is essential for the implementation of the QA. A potential problem is that the FQs used in the QA have a short coherence time such as tens of nano seconds [20]. Such a short coherence time could make it difficult to exploit the quantum advantage for the QA.…”