Quantum annealing with oscillating fields

#Embodiments relate to quantum computing, and in particular, quantum annealing.

#Quantum annealing is an analog quantum computing scheme that solves an optimization problem by adiabatically transferring a many-body quantum system (MBQS) from a ground state of an initial driver Hamiltonian to a ground state of a final problem Hamiltonian. The problem Hamiltonian encodes the optimization problem such that the ground state of the problem Hamiltonian corresponds to the solution of the optimization problem. Quantum annealing utilizes the adiabatic theorem of quantum mechanics to maximize the probability that the MBQS is adiabatically transferred into the ground state of the problem Hamiltonian. After annealing, a final state of the MBQS may be measured to determine if the MBQS was transferred into the ground state, or a different higher-energy state, of the problem Hamiltonian.

#Embodiments herein implement quantum annealing with a novel driver Hamiltonian HD/M(t) that uses oscillating fields to advantageously speed up quantum annealing. The MBQS is formed from a plurality of qubits, and the oscillating fields drive the qubits so as to independently modulate the magnitudes and/or transverse directions of terms of the driver Hamiltonian. Each oscillating field may be an oscillating electric field or an oscillating magnetic field. For clarity, it is assumed that a quantization axis is aligned along a longitudinal z direction such that the transverse directions are the x and y directions.

#FIG. 1 is a functional diagram of an example many-body quantum system (MBQS) with which embodiments described herein may be implemented, in embodiments.

#FIG. 2 is a plot of an energy gap versus an annealing parameter for an instantaneous Hamiltonian, in embodiments.

#FIG. 3 shows the plot of FIG. 2 when a driver Hamiltonian includes several oscillating fields, in embodiments.

#FIG. 1 is a functional diagram of an example many-body quantum system (MBQS) 100 with which embodiments described herein may be implemented. MBQS 100 is formed from a plurality of qubits 102 coupled to each other with a plurality of interqubit couplings 104. MBQS 100 is shown in FIG. 1 as a graph having a plurality of vertices interconnected with a plurality of edges, wherein each of the vertices represents one of qubits 102 and each of the edges represents one of interqubit couplings 104. Each of qubits 102 is a two-level quantum mechanical system 112, or an approximation thereof.

#FIG. 1 also shows a plurality of oscillators 108 driving qubits 102 with oscillating fields 110 according to driver Hamiltonian ĤD/M(t). In one embodiment, each of oscillating fields 110 drives one of qubits 102 such that a number NF of oscillating fields 110 and a number Nq of qubits 102 are equal. In another embodiment, each of oscillating fields 110 has a distinct frequency. While FIG. 1 shows each of qubits 102 being directly driven by one of oscillating fields 110, it should be appreciated that with interqubit couplings 104, each of qubits 102 may be driven by several of oscillating fields 110 via interqubit couplings 104. For clarity, each of oscillating fields 110 with a distinct frequency may be referred to herein as a “tone.”

#While FIG. 1 shows MBQS 100 having ten qubits 102 and ten interqubit couplings 104, MBQS 100 may have any number of qubits 102 and/or any number of interqubit couplings 104, as needed to implement the problem Hamiltonian, without departing from the scope hereof. For example, MBQS 100 may have thousands of qubits 102 and thousands of interqubit couplings 104. While FIG. 1 shows MBQS 100 having qubits coupled to one, two, three, and four other qubits 102, each of qubits 102 may be coupled to any number of other qubits 102, up to a total number of Nq−1 other qubits 102, without departing from the scope hereof.