[Paper Review] Universal Approach to Quantum Adiabaticity via Ancilla Cavity

Lin Tian|arXiv (Cornell University)|Feb 7, 2018

Quantum Computing Algorithms and Architecture3 citations

TL;DR

This paper proposes a universal method to enhance quantum adiabaticity in adiabatic quantum computing by coupling the system to an ancilla cavity, exploiting intrinsic nonlinear dynamics to slow down evolution in the energy gap region. The approach positions the energy gap between bifurcation points of the cavity-coupled system, enabling strong suppression of diabatic transitions without requiring spectral knowledge or unphysical interactions, as demonstrated numerically on a TLS, Exact Cover problem, and transverse field Ising model.

ABSTRACT

A central challenge in the successful implementation of adiabatic quantum algorithms is to maintain the quantum adiabaticity during the entire evolution. However, the energy gap between the ground and the excited states of interacting many-body systems often decreases quickly with the number of qubits, and the quantum adiabaticity can be severely impaired. Despite numerous previous efforts, a practical method to preserve the quantum adiabaticity has yet to be developed. Here we present a universal approach to enhancing the quantum adiabaticity via cavity or circuit QED. By coupling an adiabatic quantum computer to an ancilla cavity, the coupled system can exhibit a bistable regime with bifurcation points, where the time evolution becomes very slow. Utilizing these generic nonlinear features, we show that the energy gap of the adiabatic quantum computer can be positioned between the bifurcation points, which results in strongly-enhanced quantum adiabaticity. We then apply this method to a quantum two-level system, an Exact Cover problem, and a transverse field Ising model. In contrast to previous works, this approach does not require the spectral knowledge of the quantum system or the construction of unphysical interactions and can be applied to a vast variety of adiabatic quantum processes.

Motivation & Objective

• To address the challenge of rapidly decreasing energy gaps in many-body adiabatic quantum systems, which undermines quantum adiabaticity.
• To develop a practical, universal method to preserve adiabaticity without relying on prior spectral knowledge of the quantum system.
• To leverage intrinsic nonlinear features of operator averages in adiabatic quantum computers to engineer system parameters for enhanced adiabatic evolution.
• To demonstrate the method's applicability across diverse quantum systems, including qubit chains and optimization problems.
• To provide a scalable, experimentally feasible approach using cavity or circuit QED technology for real-world implementation.

Proposed method

• Couple the adiabatic quantum computer to an ancilla cavity via a coupling Hamiltonian $ H_{ ext{int}} = g H_0 a^ au $, where $ H_0 $ is the initial Hamiltonian and $ a^ au $ is the cavity annihilation operator.
• Utilize the steady-state average $ X_{ss} = raket{H_0} $ and its derivative $ X_{ss}' $ as control parameters, which exhibit nonlinear, monotonic growth with $ H_0 $, enabling a bistable regime.
• Identify bifurcation points in the cavity response where the time evolution slows significantly, creating a 'slow manifold' in the gap region.
• Engineer the system so that the energy gap of the adiabatic quantum computer lies between the two bifurcation points, thereby suppressing diabatic transitions.
• Apply time-dependent ramping protocols where the cavity detuning or coupling strength is tuned to position the system within the slow region during critical evolution.
• Use perturbation theory to estimate $ X_{ss} $ and $ X_{ss}' $ at initial and final points, enabling parameter engineering without full spectral knowledge.

Experimental results

Research questions

• RQ1 Can the intrinsic nonlinear response of the operator average $ X_{ss} $ in adiabatic quantum systems be harnessed to enhance quantum adiabaticity?
• RQ2 Is it possible to achieve strong adiabaticity enhancement without requiring knowledge of the full energy spectrum of the quantum system?
• RQ3 Can the energy gap be positioned between bifurcation points of a cavity-coupled system to significantly slow down evolution in the critical gap region?
• RQ4 Does this method remain effective across different quantum systems, such as a two-level system, an Exact Cover problem, and a transverse field Ising model?
• RQ5 Can this approach be implemented using standard cavity QED or circuit QED platforms without requiring unphysical interactions?

Key findings

• The coupled system exhibits a bistable regime with two bifurcation points due to the nonlinear dependence of $ X_{ss} $ and $ X_{ss}' $, creating a region of dramatically slowed evolution.
• Numerical simulations show that the effective ramping rate $ ilde{ u}_c $ in the cavity-coupled system is significantly reduced compared to the linear-ramping model, with $ ilde{ u}_c o 0 $ near the critical point.
• For a 120-qubit transverse field Ising model with $ eta = 5 $, the cavity-coupled system achieves a ramping rate $ ilde{ u}_c $ that is orders of magnitude smaller than the linear-ramping rate $ ilde{ u}_l $, indicating strong adiabaticity enhancement.
• The method successfully enhances adiabaticity in a quantum two-level system and a randomly generated Exact Cover problem instance, demonstrating broad applicability.
• The approach requires only the knowledge of $ X_{ss} $ and $ X_{ss}' $ at the initial and final points, which can be computed via perturbation theory, avoiding the need for full spectral analysis.
• The method remains effective when using alternative couplings such as photon-number coupling $ H_{ ext{int}} = g a^ au a au $, further validating its universality.