Which research result excited you the most in the past year? We’re not asking for the one you thought most important, or the one that would be most exciting to everyone, but which one got you, personally, most excited.
I’ll start things off with a result that delighted me so much I went around smiling all day, only feeling sad that more people couldn’t appreciate it! The result, that appeared in two papers almost simultaneously, is that some quantum states are too entangled to be able to compute one way. The result enchants me because it is surprising, fundamental, and related to topics close to my heart. Prior to these papers, the conventional wisdom held that more entanglement could only help quantum computation. It came as a complete surprise that it could hurt! Dave Bacon writes beautifully and succinctly about these startling results in his viewpoint, published in Physics, about the two papers published together in Physics Review Letters 102 last May. Here I give an briefer account in order to explain why these result delighted me so much.
Entanglement is the quintessential quantum mechanical property. It is also the most cited reason for the power of quantum computation. For years I’ve been dissatisfied with that answer. At first, I was dissatisfied because entanglement, particularly between large numbers of subsystems such as the qubits that make up a quantum computer, remains poorly understood. Then because various results, including those I surveyed in the final section of my Certainty and Uncertainty paper, suggested that it couldn’t be the complete answer.
Cluster state, or one-way, quantum computation, an alternative, but equally powerful, model of quantum computation to the standard circuit model, caught my fancy because of its crystal clear use of entanglement. Cluster state quantum computation starts with a highly entangled state, a cluster state, that depends only on the size of computation to be performed, not on the type of computation. In this way, the cluster states provide a universal resource for quantum computation. The computation then proceeds by a sequence of single qubit measurements. Such measurements can only decrease entanglement, the reason for the one-way name. That the cluster state model provided a break through for optical approaches to implementing quantum computing only increased the charm of this model.
After the cluster state model was developed, a number of other states were shown to be universal resources for quantum computation. I, like many others, suspected that any sufficiently entangled state could be used in this way in theory, but that in practice, for most states, it would be prohibitively difficult to find the measurement strategies that would carry out the computations. Thus, Gross, Flammia and Eisert “Most Quantum States Are Too Entangled To Be Useful As Computational Resources” and Bremner, Mora, and Winter, “Are Random Pure States Useful for Quantum Computation?” came as a complete surprise. I was also delighted that the one-way model, that seemed to show how vital entanglement is to quantum computation, could be used to show that too much of it is useless for one-way quantum computation (though not for some quantum protocols such as teleportation)!
The beauty and strength of these results is further enhanced by the fact that most states are highly entangled, so most states are useless for quantum computation. “Most” here means in the abstract sense of most of the quantum states we can write down mathematically. But what about most states that we can construct? For a brief period it seemed possible that most efficiently computable states with a lot of entanglement would be useful for one-way quantum computation. Low exhibits, however, in a follow up paper, classes of highly entangled, efficiently constructable quantum states that are useless for one-way quantum computation.
We are left to contemplate what Vlatko Vedral calls “The Elusive Source of Quantum Effectiveness.”