# Seminars

## IQI: Institute for Quantum Information Weekly Seminars

We invite experts to our weekly IQI Seminar Series to tell us about their recent research advances. We also hold more informal group meetings and sponsor IQI Workshops from time to time. Below is a calendar of these and other events of interest to the IQI community.

** Stabilizer Codes for Prime Power Qudits
**

Daniel Gottesman, Perimeter Institute

Tuesday, August 4, 2015 3:00 p.m.

** New location: 213 Annenberg **

There is a standard generalization of stabilizer codes to work with qudits which have prime dimension, and a slightly less standard generalization for qudits whose dimension is a prime power. However, for prime power dimensions, the usual generalization effectively treats the qudit as multiple prime-dimensional qudits instead of one larger object. There is a finite field GF(q) with size equal to any prime power, and it makes sense to label the qudit basis states with elements of the finite field, but the usual stabilizer codes do not make use of the structure of the finite field. I introduce the true GF(q) stabilizer codes, a subset of the usual prime power stabilizer codes which do make full use of the finite field structure. The true GF(q) stabilizer codes have nicer properties than the usual stabilizer codes over prime power qudits and work with a lifted Pauli group, which has some interesting mathematical aspects to it.

**Context-invariant and local quasi hidden variable (qHV) modelling of quantum randomness and violations of Bell-type inequalities by a multipartite quantum state **

Elena R. Loubenets, Moscow State Institute of Electronics and Mathematics

Tuesday, July 28, 2015 3:00 p.m.

** New location: 213 Annenberg **

We prove the existence for each Hilbert space of a new model, *a context-invariant quasi hidden variable (qHV) model*, reproducing all the von Neumann joint probabilities via non-negative values of real-valued measures and every quantum product expectation — via the qHV (classical-like) average of the product of the corresponding random variables. In a context-invariant qHV model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but, in contrast to a contextual HV model, each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence of a context-invariant model for each Hilbert space negates the general opinion that, in terms of random variables, the Hilbert space description of all joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of this new model also implies that every multipartite quantum state admits a local qHV (LqHV) model. Applying this new type of probabilistic modelling for the analysis of quantum violations of Bell inequalities, we introduce a new upper bound on the maximal violation by an N-qudit state of Bell inequalities of any type, either on correlation functions or on joint probabilities..

Based on: doi:10.1063/1.4913864 ;doi:10.1007/s10701-015-9903-8; doi:10.1088/1751-8113/45/18/185306; doi:10.1063/1.3681905

** The power of quantum vs classical proofs and “in-place” oracles
**

Bill Fefferman, UMD/NIST

Tuesday, July 14, 2015 3:00 p.m.

** New location: 213 Annenberg **

How much computational power does an efficient quantum verifier gain when given a polynomial size quantum state to support the validity of a mathematical claim? In particular, is there some problem that can be solved efficiently in this model, that cannot be solved if the verifier was instead given a classical bitstring? This question, the so-called QMA vs QCMA problem, is fundamental in quantum complexity theory. To complexity theorists, the question can be motivated simply by trying to understand the power of quantum nondeterminism, where both QMA and QCMA can by seen as ``quantum analogues'' of NP. More physically, QMA is characterized by the k-local Hamiltonian problem, in which we are asked to decide if the ground state energy of a local Hamiltonian is above or below a specified threshold. In this setting, the QMA vs QCMA question can be rephrased as asking whether or not there exists a purely classical description of the ground state that allows us to make this decision. Despite the importance of this question, little has been proven. Even finding an oracle separation has resisted progress. In this talk we will make progress this question and augment the work of Aaronson and Kuperberg in 2006, where a nonstandard “quantum oracle” separation was proven.

Joint work with Shelby Kimmel (QuICS, UMD/NIST)

**A counterexample to the area law for quantum matter**

Ramis Movassagh, MIT

Tuesday, July 7, 2015 3:00 p.m.

** New location: 213 Annenberg **

Entanglement is a quantum correlation which does not appear classically, and it serves as a resource for quantum technologies such as quantum computing. The area law says that the amount of entanglement between a subsystem and the rest of the system is proportional to the area of the boundary of the subsystem and not its volume. A system that obeys an area law can be simulated more efficiently than an arbitrary quantum system, and an area law provides useful information about the low-energy physics of the system. It was widely believed that the area law could not be violated by more than a logarithmic factor (e.g. based on critical systems and ideas from conformal field theory) in the system’s size. We introduce a class of exactly solvable one-dimensional models which we can prove have exponentially more entanglement than previously expected, and violate the area law by a square root factor. We also prove that the gap closes as n^{-c}, where c \ge 2, which rules out conformal field theories as the continuum limit of these models. It is our hope that the mathematical techniques introduce herein will be of use for solving other problems.

(Joint work with Peter Shor).

References:

Phys. Rev. Lett. 109, 207202

http://arxiv.org/abs/1408.1657

**The holographic entropy cone**

Michael Walter, the Stanford Institute for Theoretical Physics

Tuesday, June 30, 2015 3:00 p.m.

** New location: 213 Annenberg **

I will discuss a systematic approach to studying multipartite entanglement entropy in the gauge/gravity correspondence. This will lead to hitherto unknown holographic entropy inequalities and identify multiboundary wormhole geometries as sources of extremal entropies.

Joint work with Ning Bao, Sepehr Nezami, Hirosi Ooguri, Bogdan Stoica, and James Sully. See http://arxiv.org/abs/1505.07839.

**Fault Tolerant Error Correction with the Gauge Color Code **

Benjamin Brown, Niels Bohr Institute, University of Copenhagen

Tuesday, June 16, 2015 3:00 p.m.

** New location: 213 Annenberg **

The gauge color code is a quantum error-correcting code with local syndrome measurements that, remarkably, admits a universal transversal gate set without the need for resource-intensive magic state distillation. A result of recent interest, proposed by Bomb\'{i}n, shows that the subsystem structure of the gauge color code admits an error-correction protocol that achieves tolerance to noisy measurements without the need for repeated measurements, so called single-shot error correction. Here, we demonstrate the promise of single-shot error correction by designing a two-part decoder and investigate its performance. We simulate fault-tolerant error correction with the gauge color code over long durations by repeatedly applying our proposed error-correction protocol. We estimate a sustainable error rate, i.e. the threshold for the long time limit, of ∼0.31% for a phenomenological noise model using a simple decoding algorithm.

** Estimating outcome probabilities of quantum circuits using quasiprobabilities
**

Stephen Bartlett, University of Sydney

Tuesday, May 12, 2015 3:00 p.m. 107 Annenberg

I will present a method for estimating the probabilities of outcomes of a quantum circuit using Monte Carlo sampling techniques applied to a quasiprobability representation. This estimate converges to the true quantum probability at a rate determined by the total negativity in the circuit, using a measure of negativity based on the 1-norm of the quasiprobability. If the negativity grows at most polynomially in the size of the circuit, our estimator converges efficiently. These results highlight the role of negativity as a measure of non-classical resources in quantum computation.

Joint work with Hakop Pashayan and Joel Wallman.

See http://arxiv.org/abs/1503.07525

** Topics in adiabatic quantum computing
**

Tameem Albash, USC

Tuesday, May 5, 2015 3:00 p.m. 107 Annenberg

We will present a discussion of topics in adiabatic quantum computing, with a particular focus on the work detailed in http://arxiv.org/abs/1503.08767

** Robust Phase Estimation with Applications to Single-Qubit Process Parameter Estimation **

Shelby Kimmel, UMD/NIST

****Note Special Time** **Wednesday, April 22, 2015 11:00 a.m. 107 Annenberg

With the goal of efficiently estimating specific errors using minimal resources, we develop a parameter estimation technique, which can gauge two key parameters (amplitude and off-resonance errors) in a single-qubit gate with provable robustness and efficiency. In particular, our estimates achieve the optimal efficiency, Heisenberg scaling. Our scheme is robust to state preparation and measurement errors and uncertainty, and requires few resources, in terms of additional gates needed to implement the protocol. Our main theorem making this possible is a robust version of the phase estimation procedure of Higgins et al. [Higgins et al., New J. Phys, 11(7):073023, 2009].

Joint work with Guang Hao Low and Theodore Yoder**
Near-linear constructions of exact unitary 2-designs**

Debbie Leung, Perimeter

Tuesday, April 21, 2015 3:00 p.m. 107 Annenberg

Haar-random unitary matrices facilitate many analysis in quantum information. However, they are highly inefficient to implement or to sample. Unitary 2-designs are distributions on finite sets of unitary matrices that have some specific properties in common with the Haar measure. We present exact unitary 2-designs on n qubits that can be implemented with circuits of Clifford gates, with size O(n log^2 n log log n), depth O(log^2 n), and can be sampled with 5n random bits.

Joint work with Richard Cleve, Li Liu, and Chunhao Wang.**
Operationally-Motivated Uncertainty Relations for Joint Measurability and the Error-Disturbance Tradeoff**

Volker Scholz, ETH

Tuesday, March 24, 2015 3:00 p.m. 107 Annenberg

We derive new Heisenberg-type uncertainty relations for both joint measurability and the error- disturbance tradeoff for arbitrary observables of finite-dimensional systems (I will shortly mention the extension to position/momentum). The relations are formulated in terms of a directly operational quantity, namely the probability of distinguishing the actual operation of a device from its hypothetical ideal, by any possible testing procedure whatsoever. Moreover, they may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment.

Joint work with Joe Renes and Stefan Huber, ETH Zurich, based on arXiv:1402.6711

**Quantum systems with approximation-robust entanglement**

Lior Eldar, MIT

Tuesday, March 17, 2015 3:00 p.m. 107 Annenberg

Quantum entanglement is considered, by and large, to be a very delicate and nonrobust phenomenon, that is very hard to maintain in the presence of noise, or non-zero temperatures. In recent years however, and motivated, in part, by a quest for a quantum analog of the PCP theorem, researches have tried to establish whether or not we can preserve quantum entanglement at ”constant” temperatures that are independent of system size. This would imply that any quantum state with energy at most, say 0.05 of the total available energy of the Hamiltonian, would be highly-entangled. However to date, no such systems were found, and moreover, it became evident that even embedding local Hamiltonians on robust, albeit ”non-physical” topologies, namely expanders, does not guarantee entanglement robustness. In this talk, we will try to indicate that such robustness may be possible after all, by slightly relaxing the approximation condition, in a way that is reminiscent of classical approximation problems. Instead of asking that any quantum state with fractional energy at most 0.05 be highly-entangled, we just ask that any quantum state violating a fraction at most 0.05 of constraints is highly-entangled. I will then construct an infinite family of (logarithmically)-local Hamiltonians, with the following property of such combinatorial inapproximability: any quantum state that violates a fraction at most 0.05 of all local terms cannot be even approximately simulated by classical circuits whose depth is logarithmic. Alternatively, this will show that in a system of n qubits, it is possible to enforce a robust form of entanglement on the order of sqrt(n) qubits, using quantum constraints whose support is polylog(n). Several open questions follow from this construction that are related both to previous approximability results, the definition of entanglement-robust systems called NLTS, quantum locally testable codes, linear distance LDPC codes, and quantum circuit lower bounds.

**Two little results in topology, motivated by quantum computation**

Gorjan Alagic, University of Copenhagen

Tuesday, March 10, 2015 3:00 p.m. 107 Annenberg

Quantum computation has taken much from the scientific fields it sprouted from. Occasionally, it has also given back. I will discuss two recent results, both of which employ basic methods and ideas from quantum computation to prove a new theorem about low-dimensional topology. In the first result, we show the existence of 3-manifold diagrams which cannot be made ``very thin'' via local transformations. The key to the proof is establishing the #P-hardness of certain 3-manifold invariants, which we achieve via an application of the Solovay-Kitaev universality theorem with exponential precision. In the second result, we prove a relationship between the distinguishing power of a link invariant, and the entangling power of the linear operator that describes braiding. More precisely, we show that link invariants derived from non-entangling solutions to the Yang-Baxter equation are trivial. The former is joint work with Catharine Lo (Caltech), and the latter is joint work with Stephen Jordan and Michael Jarett (UMD).

**Characterizing Topological Order with Matrix Product Operators**

Burak Sahinoglu, Universitat Wien

Tuesday, February 17, 2015 3:00 p.m. 107 Annenberg

In this talk, we focus on describing topologically ordered ground state spaces of local Hamiltonians. This description includes a set of rules (tensor equations) which are satisfied by a matrix product operator (MPO) and the local tensor of the tensor network state (TNS). We see that these rules are satisfied for string-net models by showing that the consistency equations for these models correspond to our set of rules for a specific local tensor and MPO. At the end, we will discuss possible future directions.

**Topological quantum computation with anyons**

Claire Levaillant, UCSB

Tuesday, February 10, 2015 3:00 p.m. 107 Annenberg

We present computational schemes available at SU(2)_4 for universal quantum computation.

**Phase transitions in non-Abelian string nets **

Julien Vidal, Laboratoire de Physique de la Matière Condensée

CNRS/Université Pierre et Marie Curie, Paris

Tuesday, February 3, 2015 3:00 p.m. 107 Annenberg

Phase transitions in topologically ordered systems remain a widely unexplored domain mainly due to the lack of theoretical tools to analyze them. In the absence of effective field theory, microscopic models are important to investigate the possible condensation mechanisms driving transitions. In this context, the string-net model introduced ten years ago by M. Levin and X.-G. Wen is especially attractive since it allows to study any (doubled achiral) topological phase. In the absence of perturbation, string-net condensates can be seen as deconfined phases in which excitations are anyons. In this talk, I will discuss the influence of a string tension in non-Abelian string-net models and I will show that it leads to phase transitions which depend on the anyon theory considered. I will also address the issue of anyonic bound states that may be generated by this string tension and their possible relevance to understand the nature of the phase transitions.

**Wigner functions negativity and contextuality in quantum computation**

Nicolas Delfosse, Sherbrooke

Tuesday, January 27, 2015 3:00 p.m. 107 Annenberg

One of the most common way to obtain universality in quantum computation is by the injection of magic states. This raises the question: Which quantum properties of these states are responsible for the gain in computational power? Wigner functions negativity and contextuality have recently been proposed to explain this extra power for qupits (p-level systems for odd p). Unfortunately the case of qubits seems much more involved. In this talk, I will recall the construction of Discrete Wigner functions and their relation with contextuality and quantum computation for qupits. Then I will consider the case of real 2-level systems and I will explain how to resurrect most of the previous results. This is a first step toward qubits.

Based on joint work with Philippe Allard Guerin, Jacob Bian and Robert Raussendorf. http://arxiv.org/abs/1409.5170

**Verifying entanglement in physical systems**

Dvir Kafri, JQI

Tuesday, January 6, 2015 3:00 p.m. 107 Annenberg

Interactions consistent with Lorentz invariance are fundamentally local, with non-local force laws arising once we “integrate out” the force carriers. Since at a local level quantum mechanics describes reality very well, this brings up the question of why we observe classical behavior at most macroscopic length scales. In this talk, I argue that classical behavior could be due to an inability of the force carriers to convey entanglement, and provide a model describing how this comes about. The model gives a local test that allows one to verify that entanglement has been generated, falsifying the classical hypothesis. Crucially, the local test allows noise measurements to directly verify entanglement generation. I then describe applications of these test in the context of the gravitational force, measurement and feedback, and simulated many-body systems.

**Information Causality, Szemeredi-Trotter, and algebraic variants
of CHSH **

Mohammad Bavarian, MIT

Tuesday, November 18, 2014, 3:00 p.m. 107 Annenberg

In this work, we consider the following family of two prover one-round games. In the CHSH_q game, two parties are given x,y in F_q uniformly at random, and each must produce an output a,b in F_q without communicating with the other. The players' objective is to maximize the probability that their outputs satisfy a+b=xy in F_q. This game was introduced by Buhrman and Massar (PRA 2005) as a large alphabet generalization of the celebrated CHSH game---which is one of the most well-studied two-prover games in quantum information theory, and which has a large number of applications to quantum cryptography and quantum complexity. Our main contributions in this paper are the first asymptotic and explicit bounds on the entangled and classical values of CHSH_q, and the realization of a rather surprising connection between CHSH_q and geometric incidence theory. On the way to these results, we also resolve a problem of Pawlowski and Winter about pairwise independent Information Causality, which, beside being interesting on its own, gives as an application a short proof of our upper bound for the entangled value of CHSH_q.

Joint work with Peter W. Shor.

**Entanglement in one-dimensional quantum systems **

Yichen Huang, UC Berkeley

Tuesday, October 14, 2014, 3:00 p.m. 107 Annenberg

Quantum entanglement, a concept from quantum information theory, has been widely used in condensed matter physics to characterize quantum correlations that are difficult to study using conventional methods. It provides unique insights into the physics of critical states and topological order. It is also quantitatively related to the difficulty of describing ground states using matrix-product-state representations in numerical approximations. In this talk, I will discuss some recent examples in these directions in the context of 1D quantum systems. I will focus on conceptual messages rather than technical perspectives.

Area law: Starting with a review of known rigorous results on the relation between gapped states, correlation decay, area law, and efficient matrix-product-state representations, I will discuss area law for Renyi entropy and possible generalizations in the presence of ground-state degeneracy.

Entanglement and topological order: It is argued that topological order is essentially a pattern of long-range entanglement. I will discuss a quantitative characterization of long-range entanglement using local quantum circuits. In particular, I will show that to generate a topologically ordered state from a product state a local quantum circuit of linear (in system size) depth is necessary and (up to small errors) sufficient.

Entanglement in critical disordered systems: Many-body localization studies how disorder leads to localized states in strongly correlated systems. It is a property associated with all eigenstates (not just the ground state) of disordered systems. I will show how to use entanglement for probing the singularities of all eigenstates.

References:

http://arxiv.org/abs/1403.0327

http://arxiv.org/abs/1401.3820

http://arxiv.org/abs/1405.1817

For a complete listing of IQI seminars from 2001 through April 2012, see the archived IQI web page

[IQI Archive - includes IQI Seminars from 2001 through September 2012]