First realizations

Motivated by Shor’s algorithm (Shor 1994), during late 90s there was quite some motivation to provide a physical realization of what up to that moment was mostly theoretical work.

Any two-level physical system could be a good candidate for a qubit but we need to a find a physical realization that allows for operation and performing the set of tasks we could consider an algorithm.

In 1998, using nuclear magnetic resonance (NMR) both Oxford University and Stanford achieved the first implementations of two qubit algorithms (Chuang, Gershenfeld, and Kubinec 1998). More or less in the same period, Yasunobu Nakamura and Jaw-Shen Tsai demonstrated how a superconducting chip can be used as a qubit by controlling the current through it (Nakamura, Pashkin, and Tsai 2001).

2007 is known to be a key date as the first transmon was born. It is the equivalent of the transistor in the quantum regime (Koch et al. 2007). So first qubits exist since early 2000 which is not much but from manufacturing a qubit to building a whole computer… that is a long road.

Many metrics will be used to compare different devices and realizations in following sections so better get them clear now.

T1 time

Also known as the relaxation time, identifies how much time it would take a qubit to transition from an excited state (\(|1\rangle\)) to its ground state (\(|0\rangle\)). T1 time is not an actual time from state to state but rather identifies the time in which a state might transition and flips states once exited (\(P(|1\rangle) = e^{-\frac{t}{T1}}\)).

T2 time

Known as the phase coherence time. Basically quantifies the time in which the phase associated to a state is stable.

\[ |+\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}} \quad \xrightarrow[T2]{} \quad |-\rangle = \frac{|0\rangle -|1\rangle}{\sqrt{2}} \]

These two time-metrics characterize our qubits coherence time, the time in which our qubits are actually qubits and not classical bits playing tricks on us.

Another measure we will often refer to is the fidelity. Basically it measures the gap between theoretical state and physical outcome as a qubit quality metric. Fidelity attends to the more general state of closeness between two quantum states but in this following sections it will provide a measure to understand how well each operation renders the expected result.

\[ F(\rho, \sigma) = |\langle \psi | \phi \rangle | ^2 \]

NOTE

This is the case just when considering both states to be pure

Building the thing

There is more than one type of quantum computer. Actually we yet don’t know the one that will win the podium, but the race is interesting at this point. The physical realization conditions many aspects of the whole machine so it is relevant to understand a bit of their inner workings so that we can select the most appropriate option.

There is one general definition of how a quantum computer may look like and it is given by the DiVincenzo criteria (DiVincenzo 1997).

• Must be scalable and well characterized qubits.
• System may be able to be initialized (\(|00...\rangle\) state is the common choice)
• Qubit coherence time must be much larger than the actuation time
• Enable a universal set of gates/operations
• Capable of measuring from specific qubits

With this recipe many platforms have been proposed using different physical realizations for the technology.

Chuang, Isaac L, Neil Gershenfeld, and Mark Kubinec. 1998. “Experimental Implementation of Fast Quantum Searching.” Physical Review Letters 80 (15): 3408.

DiVincenzo, David P. 1997. “Topics in Quantum Computers.” In Mesoscopic Electron Transport, 657–77. Springer.

Koch, Jens, Terri M Yu, Jay Gambetta, Andrew A Houck, David I Schuster, Johannes Majer, Alexandre Blais, Michel H Devoret, Steven M Girvin, and Robert J Schoelkopf. 2007. “Charge-Insensitive Qubit Design Derived from the Cooper Pair Box.” Physical Review A—Atomic, Molecular, and Optical Physics 76 (4): 042319.

Nakamura, Y, Yu A Pashkin, and Jaw Shen Tsai. 2001. “Rabi Oscillations in a Josephson-Junction Charge Two-Level System.” Physical Review Letters 87 (24): 246601.

Shor, Peter W. 1994. “Algorithms for Quantum Computation: Discrete Logarithms and Factoring.” In Proceedings 35th Annual Symposium on Foundations of Computer Science, 124–34. Ieee.