Scalable Architecture for Adiabatic Quantum Computing of Np-Hard Problems

We present a comprehensive review of past research into adiabatic quantum computation and then propose a scalable architecture for an adiabatic quantum computer that can treat NP-Hard Problems without requiring local coherent operations. Instead, computation can be performed entirely by adiabatically varying a magnetic field applied to all the qubits simultaneously. Local (incoherent) operations are needed only for: (1) switching on or off certain pairwise, nearestneighbor inductive couplings in order to set the problem to be solved; and (2) measuring some subset of the qubits in order to obtain the answer to the problem.

[1]  Ari Juels,et al.  Hiding Cliques for Cryptographic Security , 1998, SODA '98.

[2]  Levin,et al.  Cooling-rate dependence for the spin-glass ground-state energy: Implications for optimization by simulated annealing. , 1986, Physical review letters.

[3]  F. Barahona.  On the computational complexity of Ising spin glass models , 1982 .

[4]  Quantum Limit of Decoherence: Environment Induced Superselection of Energy Eigenstates , 1998, quant-ph/9811026.

[5]  N. Cerf,et al.  Quantum search by local adiabatic evolution , 2001, quant-ph/0107015.

[6]  A. Leggett,et al.  Dynamics of the dissipative two-state system , 1987 .

[7]  Lov K. Grover.  Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[8]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[9]  Orlando,et al.  Josephson Persistent-Current Qubit , 2022 .

[10]  Leslie G. Valiant,et al.  Universality considerations in VLSI circuits , 1981, IEEE Transactions on Computers.

[11]  L. Schiff,et al.  Quantum Mechanics, 3rd ed. , 1973 .

[12]  Fisher,et al.  Residual energies after slow cooling of disordered systems. , 1986, Physical review letters.

[13]  R. Car,et al.  Theory of Quantum Annealing of an Ising Spin Glass , 2002, Science.

[14]  Rémi Monasson,et al.  Determining computational complexity from characteristic ‘phase transitions’ , 1999, Nature.

[15]  T. Hogg.  Adiabatic Quantum Computing for Random Satisfiability Problems , 2002, quant-ph/0206059.

[16]  Edward Farhi,et al.  Finding cliques by quantum adiabatic evolution , 2002, Quantum Inf. Comput..

[17]  E. Farhi,et al.  A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem , 2001, Science.

[18]  Andrew M. Childs,et al.  Robustness of adiabatic quantum computation , 2001, quant-ph/0108048.

[19]  A. Messiah.  Quantum Mechanics , 1961 .