Co-Design of Almost Universal Quantum Computers
Frank Wilhelm-Mauch (Saarland University)
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Quantum Computing With Stabilized Cat Qubits
Alexandre Blais (Universite de Sherbrooke)Obstacles to State Preparation and Variational Optimization from Symmetry Protection
Robert König (Technical University of Munich)Divide-And-Conquer Hybrid Methods for Smaller Quantum Computers
Vedran Dunjko (University of Leiden)Classical Algorithms for Quantum Mean Values
Sergey Bravyi (IBM T.J. Watson Research Center)The End of the Universe: A Conversation with Katie Mack
Katie Mack Perimeter Institute
PIRSA:20050021Representation theory of the Clifford group: Schur-Weyl Duality for the Clifford Group, Property Testing, and de Finetti Representations
Sepehr Nezami California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy
Designing Hamiltonians for Quantum Adiabatic Optimization
Elizabeth Crosson (University of New Mexico)Ultracold Molecules: From Quantum Chemistry to Quantum Computing
Alan Jamison Institute for Quantum Computing (IQC)
Efficient Classical Simulation of Random Shallow 2d Quantum Circuit
Aram Harrow (MIT)Quantum Simulations and Information Processing with Programmable Atom Arrays
Mikhail Lukin (Harvard)
Co-Design of Almost Universal Quantum Computers
Frank Wilhelm-Mauch (Saarland University)Hardware of quantum computers is limited in qubit count, fidelity, and connectivity now and for the near future. In order to gain maximum advantage from these machines, it is imperative to use these resources in an optimal and efficient way. I will present the example of the SPARQS co-design geared at simulating small clusters of the Fermi Hubbard model at finite nonzero temperature [1], that saves the experimenter the need of intersecting wires and three-dimensional chip integration. I will also show a new example of a co-design of the QAOA-algorithm that permits to avoid programmable interactions [2]. I will finally muse about the fluidity of the line between modern closed-loop gate design and modern variational algorithms, suggesting time-continuous strategies for state preparation [3]. [1] Pierre-Luc Dallaire-Demers and Frank K. Wilhelm, Phys. Rev. A 94, 062304, 2016 [2] David Headley, Thorge Müller, Ana Martin, Enrique Solano, Mikel Sanz, Frank K. Wilhelm, arXiv:2002.12215 [3] Shai Machnes, Nicolas Wittler, Federico Roy, Kevin Pack, Anurag Sasha-Roy, and Frank K. Wilhelm, methodology for Control, Calibration and Characterization of quantum devices,applied to superconducting qubits, in preparationQuantum Computing With Stabilized Cat Qubits
Alexandre Blais (Universite de Sherbrooke)Since the first observation 20 years ago of first coherent quantum behaviour in a superconducting qubit there have been significant developments in the field of superconducting quantum circuits. With improvements of coherence times by over 5 orders of magnitude, it is now possible to execute increasingly complex quantum algorithms with these circuits. Despite these successes, the coherence time of superconducting devices must still be increased for quantum computation to become a reality. One approach is to improve existing devices. Another approach is to design new superconducting qubits with intrinsic protection against certain types of errors. In this talk, I will discuss how quantum information can be robustly encoded in cat states of the electromagnetic field stored in superconducting quantum devices. A feature of this encoding is that it exhibits biased noise. I will present how to realize bias-preserving gates on this qubit, and how these ideas can be further improved with quantum error correction.Obstacles to State Preparation and Variational Optimization from Symmetry Protection
Robert König (Technical University of Munich)Local Hamiltonians with topological quantum order exhibit highly entangled ground states that cannot be prepared by shallow quantum circuits. Here, we show that this property may extend to all low-energy states in the presence of an on-site Z2 symmetry. This proves a version of the No Low-Energy Trivial States (NLTS) conjecture for a family of local Hamiltonians with symmetry protected topological order. A surprising consequence of this result is that the Goemans-Williamson algorithm outperforms the Quantum Approximate Optimization Algorithm (QAOA) for certain instances of MaxCut, at any constant level. We argue that the locality and symmetry of QAOA severely limits its performance. To overcome these limitations, we propose a non-local version of QAOA, and give numerical evidence that it significantly outperforms standard QAOA for frustrated Ising models on random 3-regular graphs. This is joint work with Sergey Bravyi, Alexander Kliesch and Eugene Tang.Divide-And-Conquer Hybrid Methods for Smaller Quantum Computers
Vedran Dunjko (University of Leiden)Theory shows that arbitrary-sized quantum computers may offer computational advantages for many problems. However, quantum computers on a reasonable horizon will be restricted in many ways, including size. Motivated by this, we investigate how a smaller quantum computer can genuinely speed up interesting algorithms, even when the problem size is much larger than the computer itself. To do so, we study hybrid classical-quantum divide-and-conquer strategies, and prove that if certain conditions on the structure and complexities of the underlying classical and quantum algorithms are met, then genuine speed-ups can be obtained. We will demonstrate how these conditions are met for a few exact constraint satisfaction algorithms (for SAT and Hamilton cycles). In closing we will discuss some of the more recent ideas showing how the hybrid methods can be expanded to the heuristic domain, and (hopefully) achieve practically relevant speed-ups in optimization with near-term devices. This talk will be based on the following papers: -VD, Y. Ge, J. I. Cirac, Computational speedups using small quantum devices, Phys. Rev. Lett. 121, 250501 (2018); -Y. Ge, VD, A hybrid algorithm framework for small quantum computers with application to finding Hamiltonian cycles, J. Math. Phys. 61, 012201 (2020); -C. Moussa, H. Calandra, VD, To quantum or not to quantum: towards algorithm selection in near-term quantum optimization, arXiv:2001.08271 (2020);Classical Algorithms for Quantum Mean Values
Sergey Bravyi (IBM T.J. Watson Research Center)Quantum mean value problem is the task of estimating the expected value of a tensor product observable on the output state of a quantum circuit. This task is a common step of NISQ era quantum algorithms such as VQE or QAOA. I will consider the complexity of the quantum mean value problem as a function of circuit depth, qubit connectivity, and the structure of observables to be measured. Polynomial-time classical algorithms are described solving the quantum mean value problem in two special cases: (a) 2D constant-depth variational circuits relevant for VQE, (b) level-1 and level-2 QAOA circuits associated with graph-based optimization problems. As an application, I will describe a classical simulation of the recently proposed Recursive QAOA algorithm applied to graph coloring problems. Based on arXiv:1909.11485 arXiv:1910.08980The End of the Universe: A Conversation with Katie Mack
Katie Mack Perimeter Institute
PIRSA:20050021In a special live webcast with Perimeter Institute on May 6, 2020, theoretical cosmologist and science communicator Katie Mack — known to her many Twitter followers as @AstroKatie — answered questions about her favourite subject: the end of the universe. Mack is currently a Simons Emmy Noether Fellow at Perimeter and an Assistant Professor at North Carolina State University.
Representation theory of the Clifford group: Schur-Weyl Duality for the Clifford Group, Property Testing, and de Finetti Representations
Sepehr Nezami California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy
Schur-Weyl duality is a ubiquitous tool in quantum information. At its heart is the statement that the space of operators that commute with the tensor powers of all unitaries is spanned by the permutations of the tensor factors. In this work, we describe a similar duality theory for tensor powers of Clifford unitaries. The Clifford group is a central object in many subfields of quantum information, most prominently in the theory of fault-tolerance. The duality theory has a simple and clean description in terms of finite geometries. We demonstrate its effectiveness in several applications: (1) We resolve an open problem in quantum property testing by showing that "stabilizerness" is efficiently testable: There is a protocol that, given access to six copies of an unknown state, can determine whether it is a stabilizer state, or whether it is far away from the set of stabilizer states. We give a related membership test for the Clifford group. (2) We find that tensor powers of stabilizer states have an increased symmetry group. We provide corresponding de Finetti theorems, showing that the reductions of arbitrary states with this symmetry are well-approximated by mixtures of stabilizer tensor powers (in some cases, exponentially well). (3) We show that the distance of a pure state to the set of stabilizers can be lower-bounded in terms of the sum-negativity of its Wigner function. This gives a new quantitative meaning to the sum-negativity (and the related mana) -- a measure relevant to fault-tolerant quantum computation. The result constitutes a robust generalization of the discrete Hudson theorem. (4) We show that complex projective designs of arbitrary order can be obtained from a finite number (independent of the number of qudits) of Clifford orbits. To prove this result, we give explicit formulas for arbitrary moments of random stabilizer states. (5) Lastly, we comment on the structure of the irreducible representations of the Clifford group.
Designing Hamiltonians for Quantum Adiabatic Optimization
Elizabeth Crosson (University of New Mexico)No abstract available.The Power of Random Quantum Circuits
Bill Fefferman (University of Chicago)A critical goal for the field of quantum computing is quantum supremacy -- a demonstration of a quantum computation that is prohibitively hard for classical computers. Besides dispelling any skepticism about the experimental viability of quantum computers, quantum supremacy also provides a test of quantum theory in the realm of high complexity. A leading near-term candidate, put forth and recently implemented experimentally by the Google/UCSB team is sampling from the probability distributions of randomly chosen quantum circuits, called Random Circuit Sampling (RCS). In this talk we'll discuss the power of random quantum circuits from two perspectives. First we'll talk about classical hardness evidence (joint work with Adam Bouland, Chinmay Nirkhe and Umesh Vazirani, https://arxiv.org/abs/1803.04402) and second we'll discuss very new easiness evidence concerning a restrictive subclass of random quantum circuits (joint work with Kyungjoo Noh and Liang Jiang, https://arxiv.org/abs/2003.13163).Ultracold Molecules: From Quantum Chemistry to Quantum Computing
Alan Jamison Institute for Quantum Computing (IQC)
Cooling atomic gases to ultracold temperatures revolutionized the field of atomic physics, connecting with and impacting many other areas in physics. Advances in producing ultracold molecules suggest similarly dramatic discoveries are on the horizon. First, I will review the physics of ultracold molecules, including our work bringing a new class of molecules to nanokelvin temperatures. Chemistry at these temperatures has a very different character than at room temperature. One striking effect is our recent result using spin states of reactants to control chemical reaction pathways. I will also describe how the strong electric dipole moments of ultracold molecules present an exciting new tool for quantum information and quantum computing.
Efficient Classical Simulation of Random Shallow 2d Quantum Circuit
Aram Harrow (MIT)No abstract available.Quantum Simulations and Information Processing with Programmable Atom Arrays
Mikhail Lukin (Harvard)We describe the recent advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Within this system we performed quantum simulations of 1D spin models, created large-scale entangled states and realized high-fidelity, parallel multi-qubit logic operations. We will also describe our recent technical upgrades that now allow the control over 200 atoms in two-dimensional arrays. Ongoing efforts to study exotic many-body phenomena and to realize and test quantum optimization algorithms within such systems will be discussed.