CHEMISTRY 2000 Topics of Interest #2: Quantum Computers

Quantum Computers Calculate Energy of H 2 This month, scientists at Harvard University and the University of Queensland (Australia) reported that they had used a quantum computer to calculate the energy of a hydrogen molecule. This is a significant advance (compared to other recent reports of using quantum computers to factor the number 15 or to solve a Sudoku puzzle). Conventional computers can perform this calculation, but it is anticipated that quantum computers will be able to calculate the exact energies of molecules far larger than those which conventional computers can handle. (The current limit for exact calculations on conventional computers is 4-5 atoms. For larger molecules/systems, we use methods that make approximations.) exact.energy.molecular.hydrogen

Quantum Computers vs. Conventional How do quantum computers differ from conventional computers? Conventional computers store information in bits. A bit has a value of either 0 or 1. Several bits are required to store a single number. e.g. “4” would be stored as (requiring at least three bits) Quantum computers store information in qubits. A qubit can store both values 0 and 1 at the same time. Instead of storing just one number (e.g. “4”), three qubits can store eight numbers simultaneously: = “0”1 0 0 = “4” = “1”1 0 1 = “5” = “2”1 1 0 = “6” = “3”1 1 1 = “7” This is referred to as “superposition”. The most famous example of superposition is the thought experiment known as Schr ö dinger’s Cat. The superposition will only be broken when the qubit is read. Version 1.1 (an online intro. text)

Quantum Computers vs. Conventional Since a three qubit ‘quantum computer’ can store eight times as many values as a three bit ‘conventional computer’, it should be able to do calculations eight times faster and therefore potentially eight times more complex (8 = 2 3 ). (Some leeway has been taken here in an order to avoid maths/physics far beyond the level of this course.) A twenty qubit computer would be able to store 2 20 = 1,048,576 times as many numbers as a twenty bit computer. A hundred qubit computer would be able to store = 1,267,650,600,228,229,401,496,703,205,376 times as many numbers as a hundred bit computer. (For reference, todays computers typically contain Gigabytes where 1 byte = 8 bits so 1 GB = 8,000,000,000 bits. Quantum computers are still operating in the double digit qubit range but are getting bigger.) While this scaling is impressive, the real value of quantum computers is that their quantum nature allows them to run algorithms that conventional computers cannot. There is certainly logic in the idea of applying a quantum computer to solve quantum mechanical problems. Version 1.1 (an online intro. text)

Quantum Computers Still Pretty Small 16 qubit quantum computer (solved a Sudoku): © 2007 D-Wave Systems Inc.