CQuIC PhD student Jacob Miller defended his PhD dissertation on May 3, 2017 and has completed all the requirements to be awarded a PhD in Physics. Jacob’s dissertation, entitled Measurement-Based Quantum Computation and Symmetry-Protected Topological Order, was supervised by Akimasa Miyake, for whom this is also a milestone, as Jacob is Akimasa’s first PhD student. Congratulations to both Jacob and Akimasa! We look forward to further great things from both of them.
Jacob Miller and Akimasa Miyake have recently published a paper in Nature Partner Journal Quantum Information showing that quantum computers with distinct operational advantages can be built using a form of symmetric topological matter. Their work deals with measurement-based quantum computation (MQC), a way of powering computation with only single-spin measurements and a large entangled quantum “resource” state. MQC is a natural way to study the connection between different forms of quantum topological order, the types of quantum computation they can power, and what measurements are needed for this computation.
The authors show that two complementary forms of symmetric topological order are particularly useful for quantum computation. While previous resource states have only utilized the first form, a new Union Jack state is constructed to study the second, stronger form. While both are sufficient to achieve any desired computation, the quantum order found in the Union Jack state can achieve this using simpler measurements, pointing towards a surprising new resource for simplifying quantum computation.
The full article is available online at http://www.nature.com/articles/npjqi201636.
(Left) The Union Jack state, a new state with a strong form of symmetric quantum order which makes it useful for quantum computation. (Right) One step in the procedure for computing with the Union Jack state. Measurements on half of the sites drive the system through a quantum phase transition, which leads to a computationally useful graph state being randomly condensed on the unmeasured spins.
Adrian Chapman and Akimasa Miyake have recently published their paper in Physical Review E, demonstrating that a Maxwell demon can exploit correlations in its memory to enhance its thermodynamic performance over the demon which cannot. In this classic thought experiment, the demon uses information, rather than energy, to perform a thermodynamic task such as refrigeration. One example is realized by a demon who controls the door of a bipartite container filled with gas. Using a microscopic measuring device, the demon allows only faster molecules to one side while allowing only slower molecules to the other, apparently performing cooling for free. Only when one accounts for the inevitable energy cost of erasing the device’s memory does one see that this supposed perpetual motion machine is actually a refrigerator. This fact suggests that information has value in thermodynamics.
In their paper, the authors consider a simple concrete model of physical system, which acts as an autonomous Maxwell demon. In many previous models, the assumption has been that the demon’s information is uncorrelated: its actions at one time do not depend on what it has learned at earlier times. This convenient assumption may neglect some important physics however, especially in a quantum world, where information can be correlated in a “spooky” way. The authors construct a framework for their model in which quantum correlations can be incorporated in full generality and find that correlations can be thermodynamically useful in the same way as energy or uncorrelated information in the original thought experiment. Their framework relies on techniques from condensed matter physics, which are specialized for handling correlations.
Correlated states of knowledge are not the exception, but rather the rule for realistic thermodynamic systems. This research will thus likely cross-fertilize the fields of thermodynamics and condensed matter physics and ignite further such analyses that incorporate correlations.
The full article is available online at http://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.062125.
Jacob Miller and Akimasa Miyake have recently published a paper in Physical Review Letters showing that a particular class of one-dimensional spin chains, belonging to a type of quantum phase, are uniformly useful for certain quantum information processing tasks. Our work takes place in the context of measurement-based quantum computation, a means of using entangled many-body systems to perform quantum computation requiring only measurements on individual spins. One advantage of this formalism is that it lets us make interesting connections between quantum information science, which deals with concepts like entanglement and quantum computation, and condensed matter physics, which is concerned with emergent phenomena and phases of matter.
Our result is that a particular phase of one-dimensional spin chains -- known as a symmetry-protected topological phase -- can be used to perform any single-qubit information processing task we would like. In particular, while standard measurement-based protocols require knowledge of all of the microscopic details of the many-body systems being worked with, our protocol works for any arbitrary state in this phase (so long as two minimal conditions on the state are met). Since 1D spin chains are limited to single-qubit operations in measurement-based quantum computation, this can be thought of as the best resource characterization we could hope for in a 1D symmetry-protected topological phase.
The full article is available online at http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.114.120506.
The close relationship between gate fidelity and a string order parameter for a class of states within our phase. Gate fidelity here quantifies how useful a state is for quantum information processing, while string order parameters are standard quantities used to characterize symmetry-protected topological phases. Our protocol works by first purifying arbitrary states into a "fixed-point" form, with the different curves here representing different degrees of purification. As the purification increases (red → yellow → green), the gate fidelity and string order parameter behave identically, demonstrating the close relationship between the quantum information and condensed matter aspects of this phase.