绝热量子计算机

Adiabatic quantum computation solves satisfiability problems and other combinatorial search problems by the process below. Generally this kind of problem is to seek for a state that satisfies ${\displaystyle C_{1}\wedge C_{2}\wedge \cdots \wedge C_{M}}$ . This expression contains the satisfiability of M clauses, each clause ${\displaystyle C_{i}}$  has the value True or False, and can involve n bits. Each bit here is a variable ${\displaystyle x_{j}\in \{0,1\}}$  so ${\displaystyle C_{i}}$  is a Boolean value function of ${\displaystyle x_{1},x_{2},\dots ,x_{n}}$ . QAA solves this kind of problem using quantum adiabatic evolution. It starts with an Initial Hamiltonian ${\displaystyle H_{B}}$ :

where ${\displaystyle H_{B_{i}}}$  shows the Hamiltonian corresponding to the clause ${\displaystyle C_{i}}$ , usually the choice of ${\displaystyle H_{B_{i}}}$  won't depend on different clauses, so only the total number of times each bit involved in all clauses matters. Then it goes through an adiabatic evolution, ending in the Problem Hamiltonian ${\displaystyle H_{P}}$ :

${\displaystyle H_{P}=\sum \limits _{C}^{}H_{P,C}}$ 

where ${\displaystyle H_{P,C}}$  is the satisfying Hamiltonian of clause C. It has eigenvalues:

${\displaystyle h_{C}(z_{1C},z_{2C}\dots z_{nC})={\begin{cases}0&{\mbox{clause }}C{\mbox{ satisfied}}\\1&{\mbox{clause }}C{\mbox{ violated}}\end{cases}}}$ 

For a simple path of Adiabatic Evolution with running time T, consider: ${\displaystyle H(t)=(1-t/T)H_{B}+(t/T)H_{P}}$  and let ${\displaystyle s=t/T}$ , we have: ${\displaystyle {\tilde {H}}(s)=(1-s)H_{B}+sH_{P}}$ , which is the adiabatic evolution Hamiltonian of our algorithm.

According to the adiabatic theorem, we start from the ground state of Hamiltonian ${\displaystyle H_{B}}$  at beginning, go through an adiabatic process, and at last ending in the ground state of problem Hamiltonian ${\displaystyle H_{P}}$ . Then we measure the z-component of each of the n spins in the final state, this will produce a string ${\displaystyle z_{1},z_{2},\dots ,z_{n}}$  which is highly likely to be the result of our satisfiability problem. Here the running time T must be sufficiently long to assure the correctness of result, and according to adiabatic theorem, T is about ${\displaystyle \varepsilon /g_{\mathrm {min} }^{2}}$ , where ${\displaystyle g_{\mathrm {min} }=\min _{0\leq s\leq 1}(E_{1}(s)-E_{0}(s))}$  is the minimum energy gap between ground state and first excited state.^[12]

D-波量子处理器

The D-Wave One is a device made by a Canadian company D-Wave Systems which describes it as doing quantum annealing.^[13] In 2011, Lockheed-Martin purchased one for about US$10 million; in May 2013, Google purchased a D-Wave Two with 512 qubits.^[14] As of now, the question of whether the D-Wave processors offer a speedup over a classical processor is still unanswered. Tests performed by researchers at Quantum Artificial Intelligence Lab (NASA), USC, ETH Zurich, and Google show that as of now, there is no evidence of a quantum advantage. ^[15][16][17]