The quantum difference

I have to admit it: D-Wave is starting to produce some impressive results. For the uninitiated, D-Wave came to our attention by loudly and repeatedly claiming that it had built a quantum computer. Many of us were skeptical . Over time, though, D-Wave has answered its critics in the best way possible: by providing evidence. Now, researchers who actually got inside the black box are reporting some key results that come very close to removing any lingering doubts.

When we perform computations in an ordinary computer, we have to manipulate each bit individually. Sure, the computer might make this faster through some sort of parallelization, but there's still a set of transistors flipping individual bits for each operation. A quantum computer is different. First, the information is stored in a quantum state (called a qubit), which means that it holds multiple values simultaneously (called superposition states). The value of a qubit is only determined when the result of a computation is read out. An eight-qubit quantum register can therefore hold values from 0-255 simultaneously, but the probability of obtaining a particular value is modified by the computational operations that are performed prior to reading the register out.

Quantum superposition Superposition is nothing more than addition for waves. Let's say we have two sets of waves that overlap in space and time. At any given point, a trough may line up with a peak, their peaks may line up, or anything in between. Superposition tells us how to add up these waves so that the result reconstructs the patterns that we observe in nature. Read more…

That is not the real power of quantum computation, however. The second bit of magic that a quantum system has is called coherence. When a quantum state is in a superposition state, the probability of obtaining a one or a zero changes with time naturally, like a pendulum swinging back and forth. At a particular time, the chance of measuring a one is unity, while some time later, the chance of measuring a zero is unity. In between, the probability of obtaining a one smoothly varies from unity to zero. When two qubits are coherent, this changing probability happens in concert for the two qubits.

This means that even when you perform an operation on one qubit, it jumps to a new value, but the relationship between the two qubits remains predictable in time. Yet the results from measuring their value is independent. That is, if we measure the two qubits, the individual results are not determined by each other. Only by making many measurements can we see that the two have a mutual relationship in how they change in time.

The final superpower of quantum computation is called entanglement. When two qubits are entangled, their values become correlated. Two entangled qubits are not separate anymore. They are a single entity. As the superposition state of one changes, the other must change in a complementary way. It has no choice. This also means that their measurement results in interconnected values—measuring one tells us the value of the other. It should be noted that there is no communication involved in this process, so "interconnected" should not be taken to mean some sort of driving force or information transfer between the two qubits.

Quantum entanglement Quantum entanglement is one of the most misused concepts around. Entanglement is delicate, rare, and short-lived. At its heart, quantum entanglement is nothing more or less than a correlation between two apparently separate quantum objects. Having discovered that, you might ask "so what is all the fuss about?" The answer lies deep in quantum mechanics. Read more…

By these three powers combined, a quantum computer is able to perform a sort of parallelism that is unlike anything a classical computer can manage. In a sense, a quantum computer explores all possible solutions—including incorrect solutions—at once. When it obtains the outcome, it is probabilistic: the correct solution is the most probable, but all other answers have some nonzero probability as well. To ensure that it picks the right solution, a quantum computer must be run several times to ensure that the most probable outcome dominates the other answers.

The critical point is that without all of these properties—superposition, coherence, and entanglement—there is no proof that a quantum computer offers any speedup.

Fitting D-Wave in d quantum box

And that was the challenge with D-Wave's computer. It's a rather complex beast, consisting of many qubits coupled together in a complicated circuit. Not only was it not easy to determine whether qubits were indeed qubits, but it took some time to figure out a way to define a measure for entanglement in a multiple-qubit system. To get around this, researchers have resorted to scaling arguments. Let the computer solve some problems under different conditions and observe how fast it comes to a solution. Those results were then compared to computer models of quantum and classical systems. The upshot was that the scaling looked more quantum than classical—good news for D-Wave. But these results require that we trust that the computational model includes all relevant physics.

A more direct proof has now been obtained. In the latest paper, the researchers used one of the qubits as a probe to measure the part of the quantum state of the surrounding qubits. They did this for a pair of qubits and for a ring of eight. They showed that the qubits exhibited behavior that can only be obtained if the qubits are entangled and coherent—a clear sign of quantum behavior.

In more detail, the probe qubit is able to measure the occupation of the energetic states of the test qubits. In classical behavior, this occupation will be governed solely by the temperature, and when the gap between the first excited state and the ground state closes (that is, no energy is required to go from one to the other), both levels should be occupied. If the qubits are entangled, this gap never closes—the two approach, come to some minimum gap, and then open up again. This is because the entangled qubits have to maintain complementary values, so it's impossible for them to assume values that close the gap between the excited state and the ground state. In physics-speak, this is called an avoided crossing.

The researchers also used a couple of different measures of entanglement to quantify just how entangled the qubits were. In the case of two qubits, they obtain about half of a maximally entangled state, while for the eight-qubit system it was less than half. There are qubit systems that can be maximally entangled, but given the scale of the D-Wave system, this is an impressive result.

Don't go racing for your credit card just yet, though. Although the qubits are entangled, they are not as entangled as you might like. I'm not sure what this means for proofs of computational speedup other than that the proofs take maximally entangled and coherent qubits as a given. Nevertheless, this is huge because it's now just a question of time—time to make the system cleaner, time to make the system bigger.

On that note, I should point out that making the system bigger is probably one of the biggest problems that D-Wave now faces. In order to solve realistic problems, it has to create much bigger systems. Even though it has 512-qubit systems, the way the qubits are used means that they have effectively less than 100 qubits. The second problem is that D-Wave's qubit layout limits the computational problems they can solve—every problem must be rewritten to suit the qubit layout. Effectively, this reduces the number of qubits even further because some problems map one-to-one (one D-Wave qubit represents one qubit of the original problem), but others map much less efficiently (say 10 qubits to simulate one qubit), while still others can't be mapped at all. Effectively, this means that each system has to be uniquely configured to solve a specific problem efficiently, and not all problems can be solved.

The problem of scaling is something that I expect to see solved reasonably quickly (within a few years, D-Wave has gone from 32 qubits to 512 qubits). A D-Wave system may yet be solving logistical problems on a commercial basis.

Physical Review X, 2014, DOI: 10.1103/PhysRevX.4.021041