Quantum annealing using vacuum states as effective excited states of driven systems

Abstract

Quantum annealing, which is particularly useful for combinatorial optimization, becomes more powerful by using excited states, in addition to ground states. However, such excited-state quantum annealing is prone to errors due to dissipation. Here we propose excited-state quantum annealing started with the most stable state, i.e., vacuum states. This counterintuitive approach becomes possible by using effective energy eigenstates of driven quantum systems. To demonstrate this concept, we use a network of Kerr-nonlinear parametric oscillators, where we can start excited-state quantum annealing with the vacuum state of the network by appropriately setting initial detuning frequencies for the oscillators. By numerical simulations of four oscillators, we show that the present approach can solve some hard instances whose optimal solutions cannot be obtained by standard ground-state quantum annealing because of energy-gap closing. In this approach, a nonadiabatic transition at an energy-gap closing point is rather utilized. We also show that this approach is robust against errors due to dissipation, as expected, compared to quantum annealing started with physical excited (i.e., nonvacuum) states. These results open new possibilities for quantum computation and driven quantum systems.

Quantum Gate for Kerr Nonlinear Parametric Oscillator Using Effective Excited States

“…where T is the gate time, and e denotes the utilized excited state (see Appendix A for details). Equation (15) clarifies that θ g originates from a nonzero E g |A|E e .…”

“…In a superconducting circuit, another method to stabilize a superposition of coherent states has been proposed by using a Kerr-nonlinear parametric oscillator (KPO), which is based on a two-photon drive and Kerr nonlinearity [5][6][7][8]. KPOs have first been studied for application to quantum annealing [5,[9][10][11][12][13][14][15][16], and then universal quantum computation [6,7]. Recently, a set of gate operations for KPOs has been proposed such that a type of error is suppressed [17], and has been developed toward fault-tolerant quantum computation [18][19][20].…”

Effective spin models of Kerr-nonlinear parametric oscillators for quantum annealing

“…QA with KPOs has been intensively studied [15,16,[18][19][20][21][22][23][24][25][26][27]. The efficiency of this method was demonstrated with simulations of small systems [15,16,18].…”

“…The efficiency of this method was demonstrated with simulations of small systems [15,16,18]. Subsequent studies pointed out the possibility of appli-cations to the Lechner-Hauke-Zoller scheme [28] with four-or three-body interactions [18][19][20], Boltzmann sampling [21], and QA using excited states [22,23]. The bifurcation-based approach to QA has also been studied using a spin model [29].…”

Chaos in coupled Kerr-nonlinear parametric oscillators

“…Moreover, a network of KPOs can solve a combinatorial optimization problem (ground-state search in the Ising model) by adiabatic quantum computation [25][26][27] or quantum annealing [28,29], the final state of which is a highly entan-gled state, a superposition of many-mode coherent states corresponding to two optimal solutions [20]. Quantum annealing using KPOs has been developed in this five years [30][31][32][33][34][35]. The KPOs can also be used for qubits in gate-based quantum computing [21,[36][37][38][39][40].…”