IEEE Transactions on Pattern Analysis and Machine Intelligence

Physical Review B

We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp's 21 NP-complete problems This collects and extends mappings to the Ising model from partitioning, covering and satisfiability In each case, the required number of spins is at most cubic in the size of the problem This work may be useful in designing adiabatic quantum optimization algorithms

Ising formulations of many NP problems

저작근 근전도에 관한 정상교합자와 ii급 부정교합자의 비교 연구

An ongoing theme in quantum physics is the interaction of small quantum systems with an environment. If that environment has many degrees of freedom and is weakly coupled, it can often be reasonable to treat its decohering effect on the small system using a ``memoryless,'' or Markovian description. This Colloquium shows that for many phenomena a more refined, non-Markovian, treatment is necessary. The suite of developing theoretical tools is reviewed, with which recent progress on this problem has been based.

/pdf/colloquium-non-markovian-dynamics-in-open-quantum-systems-141503q23f.pdf

Colloquium: Non-Markovian dynamics in open quantum systems

Quantum annealing is the quantum computational equivalent of the classical approach to solving optimization problems known as simulated annealing. Boixo et al. report experimental evidence for the realization of quantum annealing processes that are unexpectedly robust against noise and imperfections.

/pdf/experimental-signature-of-programmable-quantum-annealing-3d8bjw6eao.pdf

Experimental signature of programmable quantum annealing

I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm (QAA). Such protocols will have numerous advantages over simple quantum annealing. By using such searches the effect of problem mis-specification can be reduced, as only energy differences between the searched states will be relevant. The QAA is an analogue of simulated annealing, a classical numerical technique which has now been superseded. Hence, I explore two strategies to use an annealer in a way which takes advantage of modern classical optimization algorithms. Specifically, I show how sequential calls to quantum annealers can be used to construct analogues of population annealing and parallel tempering which use quantum searches as subroutines. The techniques given here can be applied not only to optimization, but also to sampling. I examine the feasibility of these protocols on real devices and note that implementing such protocols should require minimal if any change to the current design of the flux qubit-based annealers by D-Wave Systems Inc. I further provide proof-of-principle numerical experiments based on quantum Monte Carlo that demonstrate simple examples of the discussed techniques.

https://iopscience.iop.org/article/10.1088/1367-2630/aa59c4/pdf

Modernizing quantum annealing using local searches.

Quantum annealing provides a way of solving optimization problems by encoding them as Ising spin models which are implemented using physical qubits. The solution of the optimization problem then corresponds to the ground state of the system. Quantum tunneling is harnessed to enable the system to move to the ground state in a potentially high non-convex energy landscape. A major difficulty in encoding optimization problems in physical quantum annealing devices is the fact that many real world optimization problems require interactions of higher connectivity, as well as multi-body terms beyond the limitations of the physical hardware. In this work we address the question of how to implement multi-body interactions using hardware which natively only provides two-body interactions. The main result is an efficient circuit design of such multi-body terms using superconducting flux qubits in which effective N-body interactions are implemented using N ancilla qubits and only two inductive couplers. It is then shown how this circuit can be used as the unit cell of a scalable architecture by applying it to a recently proposed embedding technique for constructing an architecture of logical qubits with arbitrary connectivity using physical qubits which have nearest-neighbor four-body interactions. It is further shown that this design is robust to non-linear effects in the coupling loops, as well as mismatches in some of the circuit parameters.

/pdf/circuit-design-for-multi-body-interactions-in-34z4h8ynmj.pdf

Circuit design for multi-body interactions in superconducting quantum annealing systems with applications to a scalable architecture

I describe how real quantum annealers may be used to perform local (in state space) searches around specified states, rather than the global searches traditionally implemented in the quantum annealing algorithm. Such protocols will have numerous advantages over simple quantum annealing. By using such searches the effect of problem mis-specification can be reduced, as only energy differences between the searched states will be relevant. The quantum annealing algorithm is an analogue of simulated annealing, a classical numerical technique which has now been superseded. Hence, I explore two strategies to use an annealer in a way which takes advantage of modern classical optimization algorithms. Specifically, I show how sequential calls to quantum annealers can be used to construct analogues of population annealing and parallel tempering which use quantum searches as subroutines. The techniques given here can be applied not only to optimization, but also to sampling. I examine the feasibility of these protocols on real devices and note that implementing such protocols should require minimal if any change to the current design of the flux qubit-based annealers by D-Wave Systems Inc. I further provide proof-of-principle numerical experiments based on quantum Monte Carlo that demonstrate simple examples of the discussed techniques.

Modernizing Quantum Annealing using Local Searches

Quantum annealing provides a way of solving optimization problems by encoding them as Ising spin models which are implemented using physical qubits. The solution of the optimization problem then corresponds to the ground state of the system. Quantum tunnelling is harnessed to enable the system to move to the ground state in a potentially highly non-convex energy landscape. A major difficulty in encoding optimization problems in physical quantum annealing devices is the fact that many real world optimization problems require interactions of higher connectivity as well as multi-body terms beyond the limitations of the physical hardware. In this work we address the question of how to implement multi-body interactions using hardware which natively only provides two-body interactions. The main result is an efficient circuit design of such multi-body terms using superconducting flux qubits in which effective N-body interactions are implemented using N ancilla qubits and only two inductive couplers. It is then shown how this circuit can be used as the unit cell of a scalable architecture by applying it to a recently proposed embedding technique for constructing an architecture of logical qubits with arbitrary connectivity using physical qubits which have nearest-neighbor four-body interactions. It is further shown that this design is robust to non-linear effects in the coupling loops as well as mismatches in some of the circuit parameters.

/pdf/circuit-design-for-multi-body-interactions-in-3h5abyttd1.pdf

Nicholas Chancellor

Papers

Experimental signature of programmable quantum annealing

Modernizing quantum annealing using local searches.

Circuit design for multi-body interactions in superconducting quantum annealing systems with applications to a scalable architecture

Modernizing Quantum Annealing using Local Searches

Circuit design for multi-body interactions in superconducting quantum annealing system with applications to a scalable architecture