In a paper published in the journal Physical Review Letters, Levitin and Toffoli present an equation for the minimum sliver of time it takes for an elementary quantum operation to occur. This establishes the speed limit for all possible computers. Using their equation, Levitin and Toffoli calculated that, for every unit of energy, a perfect quantum computer spits out ten quadrillion more operations each second than today’s fastest processors.
(A quadrillion is 10^15 or 1000 trillions)
The question of how fast a quantum state can evolve has attracted a considerable attention in connection with quantum measurement, metrology, and information processing. Since only orthogonal states can be unambiguously distinguished, a transition from a state to an orthogonal one can be taken as the elementary step of a computational process. Therefore, such a transition can be interpreted as the operation of “flipping a qubit”, and the number of orthogonal states visited by the system per unit time can be viewed as the maximum rate of operation.
A lower bound on the orthogonalization time, based on the energy spread DeltaE, was found by Mandelstam and Tamm. Another bound, based on the average energy E, was established by Margolus and Levitin. The bounds coincide, and can be exactly attained by certain initial states if DeltaE=E; however, the problem remained open of what the situation is otherwise.
Here we consider the unified bound that takes into account both DeltaE and E. We prove that there exist no initial states that saturate the bound if DeltaE is not equal to E. However, the bound remains tight: for any given values of DeltaE and E, there exists a one-parameter family of initial states that can approach the bound arbitrarily close when the parameter approaches its limit value. The relation between the largest energy level, the average energy, and the orthogonalization time is also discussed. These results establish the fundamental quantum limit on the rate of operation of any information-processing system.