量子計算的優點 受到平行計算和概率算法的啟發，1980年代 Deutsch和姚期智等計算科學家利用了量子力學對 物理世界的理解，即一個系統可以同時存在於兩 個或更多狀態所組成的叠加態上，發明了量子圖 靈機的數學模型。也就是說，假設2到7之間每個 數字都能表示為一個物理狀態的話，我們只需要 一個量子系統就能組成它們的叠加態，並平行地 試驗哪一個是14的因數，而不需要增加計算機的 數量。同時，由於在這個叠加態內每個表示數字 的物理狀態都依附於一個概率，這些概率的數值 會通過量子算法的施行，併發地增大或減小，最 後概率接近1的物理態反映的就是14的真因數。 所以量子計算的優點是既省卻了計算所需空間 量，又縮短了計算複雜性的時間長。1995年，貝 爾實驗室的Shor就第一次提出了基於量子計算模 型的大數因子化算法。不過量子計算在那個時候 仍然是紙上談兵。 到了2000年以後，Girvin、Martinis、Tsai等物 理學家們通過超導材料的約瑟夫森效應成功試驗 出一個稱為超導量子比特的系統，從此量子計 算所需的叠加態就能可控地在一個固態電路上生 成。2012年Martinis小組就在四個超導量子比特 組成的超導電路下，實現了執行Shor算法的整數 15因子化。 The Merits of Quantum Computing Inspired by the concepts of parallel computing and probabilistic algorithms, Deutsch, C C Yao, and other computer scientists employed the world view of quantum mechanics – a system can retain a superposition state to simultaneously coexist on two different physical settings – in 1980’s to have invented the mathematical model of quantum Turing machines. In other words, supposing every integer between 2 and 7 can be represented as a physical state, we then only need one quantum system to form their superposition state and try out the factors in parallel without increasing the number of computing cores. Meanwhile, since there is a probability associated with each state of integer out of the collective superposition state, these probabilities would increase or decrease concurrently through the execution of quantum algorithms. The probabilities associated with the real factors of 14 would gradually approach 1 in consequence. Therefore, the advantage of quantum computation is that it reduces the consumption of memory space while alleviating the computing time in temporal complexity. Shor of Bell Laboratory proposed just such a probabilistic integer-factoring algorithm geared specifically for quantum computer in 1995. But so far quantum computation still rests on paper. After the year 2000, quantum physicists including Girvin, Martinis, and Tsai successfully fabricated what they called superconducting quantum-bit (or qubit) systems by carefully manipulating the Josephson effects on superconducting materials. Thereafter, the superposition state necessary for quantum computation can be generated in a solid-state circuit in a controllable fashion. The Martinis group has implemented Shor’s algorithm to factor the integer 15 using a superconducting circuit comprising four qubits. It seems then the making of the quantum computer has already succeeded and we can make a head start on commercialising them. But in reality, there is a long road ahead before one can buy a personal quantum computer. The two most imminent problems are: (i) the effective data storage time in a qubit is not sufficiently long, being only on the scale of microseconds; and (ii) the scaling mechanism to share data across qubits has not yet existed. The latter is also the reason why we can only factor a small integer like 15 so far. Therefore, one of the current research directions in our research group at UM is to make use the properties of solitons on superconducting circuits to prolong the effective storage time, thus solving the first problem. 學院專欄 FACULTY COLUMN umagazine issue 19 60
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