Analog Counterdiabatic Quantum Computing for Optimization
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Solution Overview
Problem
Existing analog quantum computing methods face challenges in efficiently solving combinatorial optimization problems, particularly due to long computation times and potential excitations in the energy spectrum, which can lead to incorrect solutions.
Innovation Solution
The implementation of an analog counterdiabatic quantum computing (ACQC) method, which involves calculating counterdiabatic terms as an adiabatic gauge potential for the driving part of the adiabatic Hamiltonian and combining these terms with the adiabatic Hamiltonian to generate a new set of continuous quantum variables that control the analog quantum computer in a time-dependent counterdiabatic manner.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional adiabatic quantum computing methods are used to solve combinatorial optimization problems, then the system evolves towards the ground state of the Hamiltonian, but the computation time becomes excessively long and excitations in the energy spectrum occur leading to incorrect solutions
Solution Approach 1:
The counterdiabatic terms are calculated in advance as an adiabatic gauge potential for the driving part of the Hamiltonian, before the quantum evolution begins. These pre-calculated terms are then combined with the adiabatic Hamiltonian to guide the system evolution, preventing excitations and ensuring the system reaches the correct ground state without requiring excessively long computation time.
2Productivity
If the evolution time is reduced to decrease computational time, then speed improves, but excitations in the energy spectrum increase leading to incorrect solutions
Solution Approach 1:
The counterdiabatic terms act as an intermediary component that is added to the adiabatic Hamiltonian. These terms mediate the system evolution by compensating for non-adiabatic effects, allowing the system to evolve quickly while maintaining high fidelity to the ground state, thus achieving both speed and accuracy simultaneously.
3Reliability
If standard adiabatic quantum computing is implemented without counterdiabatic terms, then the device complexity remains low, but the success probability becomes low due to excitations and long computation times
Solution Approach 1:
The method modifies the Hamiltonian parameters by adding counterdiabatic terms that are derived from the adiabatic gauge potential. This parameter change transforms the standard adiabatic Hamiltonian into an enhanced version that includes additional control terms, thereby increasing the success probability while managing the complexity through analytical solutions.
Data Source
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AI summary
The invention relates to a computer-implemented method, to a computer program and to a computer device as described herein. In particular, the invention relates to a computer-implemented method for solving a computation problem. The invention uses an Ising Hamiltonian in the form HRydtℏ= Ωt2cosφt∑i=1Nσix−sinφt∑i=1Nσiy−Δt∑i=1Nni+∑i<jJi,jninj wherein ni=1−σiz/2, Ω(t) is the Rabi frequency of the transition and can be dynamically controlled by controlling the power of the coupling laser with time t, Δ(t) corresponds to the detuning with regards to the two-photon transition and can be controlled dynamically by controlling the frequency of the coupling laser with time t, φ(t) is the phase of the laser and can be controlled dynamically. Ω(t) , Δ(t) and φ(t) can be controlled independently, wherein the term containing Ji,j is the interactions term, for example implemented via a Rydberg blockade mechanism is optionally rendered site-dependent or dynamically tunable, wherein the problem is solved by finding the ground state of the final Hamiltonian.