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BEGIN:VEVENT
SUMMARY:Mark Webster (University of Sydney)
DTSTART;VALUE=DATE-TIME:20220606T090000Z
DTEND;VALUE=DATE-TIME:20220606T100000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/1
DESCRIPTION:Title: The XP Stabiliser Formalism: a Generalisation of the Pauli Stabili
ser Formalism with Arbitrary Phases\nby Mark Webster (University of Sy
dney) as part of Bilkent University Quantum Computing Seminar\n\n\nAbstrac
t\nMark Webster works in the field of quantum error correction\nand he wil
l be discussing a generalisation of the Pauli stabiliser\nformalism. The n
ew XP stabiliser formalism allows us to represent a much\nwider set of sta
tes and XP codes have a much richer logical operator\nstructure compared t
o the Pauli stabiliser formalism. In addition\, XP\ncodes cannot be classi
cally simulated which suggests that they capture\nsome aspects of quantum
advantage.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Zurel (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20220620T130000Z
DTEND;VALUE=DATE-TIME:20220620T140000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/2
DESCRIPTION:Title: Polytope theory and classical simulation of quantum computation wi
th magic states\nby Michael Zurel (University of British Columbia) as
part of Bilkent University Quantum Computing Seminar\n\n\nAbstract\nPolyto
pes come up in several areas of quantum information science. They appear i
n the foundations of quantum theory\, for example through Bell inequalitie
s and noncontextuality inequalities. They are also useful tools in the stu
dy of quantum information processing tasks like quantum computation and qu
antum communication. Here they can describe separations between the capabi
lities of classical theories\, quantum theory\, and beyond-quantum theorie
s like the no-signalling polytope. In this talk I will give an overview of
some examples of where polytopes are used in quantum computation. In part
icular\, I will focus on a few families of polytopes that provide useful d
escriptions for a universal model of quantum computation and I will descri
be how these families of polytopes can be used to characterize the quantum
computational advantage over classical computation. In addition\, I will
review some of the algorithms and tools used for studying these polytopes.
\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sivert Aasnæss (University of Oxford)
DTSTART;VALUE=DATE-TIME:20220704T130000Z
DTEND;VALUE=DATE-TIME:20220704T140000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/3
DESCRIPTION:Title: Contextuality as a resource for quantum circuits\nby Sivert Aa
snæss (University of Oxford) as part of Bilkent University Quantum Comput
ing Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martti Karvonen (University of Ottawa)
DTSTART;VALUE=DATE-TIME:20220801T130000Z
DTEND;VALUE=DATE-TIME:20220801T140000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/4
DESCRIPTION:Title: Neither Contextuality nor Nonlocality Admits Catalysts\nby Mar
tti Karvonen (University of Ottawa) as part of Bilkent University Quantum
Computing Seminar\n\n\nAbstract\nIn this talk\, I will give an overview of
https://arxiv.org/abs/2102.07637 \, showing that the resource theory of c
ontextuality does not admit catalysts\, i.e.\, there are no correlations t
hat can enable an otherwise impossible resource conversion and still be re
covered afterward. As a corollary\, we observe that the same holds for non
locality. As entanglement allows for catalysts\, this adds a further examp
le to the list of "anomalies of entanglement\," showing that nonlocality a
nd entanglement behave differently as resources. On the way\, I will expla
in the construction of the resource theories of contextuality and nonlocal
ity\, and discuss some categorical aspects of these. Time permitting\, we
will also show that catalysis remains impossible even if\, instead of clas
sical randomness\, we allow some more powerful behaviors to be used freely
in the free transformations of the resource theory.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Pinzani (University of Oxford)
DTSTART;VALUE=DATE-TIME:20220808T130000Z
DTEND;VALUE=DATE-TIME:20220808T140000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/5
DESCRIPTION:Title: The Topology and Geometry of Causality\nby Nicola Pinzani (Uni
versity of Oxford) as part of Bilkent University Quantum Computing Seminar
\n\n\nAbstract\nIn my talk I am going to present a unified operational\nfr
amework for the study of causality\, non-locality and contextuality\, in\n
a fully device-independent and theory-independent setting. Our\ninvestigat
ion proceeds from two complementary fronts: a topological one\,\nusing too
ls from sheaf theory\, and a geometric one\, based on polytopes\nand linea
r programming. From the topological perspective\, we understand\nexperimen
tal outcome probabilities as bundles of compatible contextual\ndata over c
ertain topological spaces\, encoding causality constraints.\n From the geo
metric perspective\, we understand the same experimental\noutcome probabil
ities as points in high-dimensional causal polytopes\,\nwhich we explicitl
y construct and fully characterise.\nOur work is a significant extension o
f both the established\nAbramsky-Brandenburger framework for contextuality
and the current body\nof work on indefinite causality. We provide definit
ions of causal\nfraction and causal separability for empirical models rela
tive to a\nbroad class of causal constraints: this allows us to construct
and\ncharacterise novel examples which explicitly connect causal\ninsepara
bility to non-locality and contextuality. In particular\, we\nclearly demo
nstrate the existence of "causal contextuality"\, a\nphenomenon where caus
al structure is explicitly correlated to the\nclassical inputs and outputs
of local instruments\, so that contextuality\nof the associated empirical
model directly implies causal\ninseparability.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amy Searle (University of Oxford)
DTSTART;VALUE=DATE-TIME:20220919T130000Z
DTEND;VALUE=DATE-TIME:20220919T140000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/6
DESCRIPTION:Title: Classifying the Noncontextual Measurement Spaces via the Sheaf App
roach\nby Amy Searle (University of Oxford) as part of Bilkent Univers
ity Quantum Computing Seminar\n\n\nAbstract\nThe sheaf theoretic approach
to contextuality\, as has been emphasised before\, is favourable because t
he generality of the sheaf approach allows for the uncovering of connectio
ns to other fields\, and also because theoretical developments in the acti
ve field of sheaf theory can be directly applied to the context of quantum
information. One such theoretical development\, the application to contex
tuality of which was first discussed in [1]\, is Vorob'ev's theorem. In th
e context of quantum information\, it allows us to identify which setups c
an never exhibit contextuality. In this sense\, and by negation\, we know
that for observation of non-classical behaviour attention must be focused
on the measurement setups which do not fall into this category. Besides ex
plaining this theorem\, I will discuss some of the other results contained
within [1]\, such as using such principles to derive monogamy of entangle
ment. I will moreover explain why and how we might hope to extend such res
ults to more general setups\, such as setups where some measurements occur
before others so that there is a temporal ordering on the measurement set
.\n\n[1] Soares Barbosa\, Rui 2015\, 'Contextuality in Quantum Mechanics a
nd Beyond'\, PhD thesis\, University of Oxford.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arne Heimendahl (University of Cologne)
DTSTART;VALUE=DATE-TIME:20220912T130000Z
DTEND;VALUE=DATE-TIME:20220912T140000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/7
DESCRIPTION:Title: Wigner’s theorem of stabilizer states\nby Arne Heimendahl (U
niversity of Cologne) as part of Bilkent University Quantum Computing Semi
nar\n\n\nAbstract\nStabilizer states are one of the main components for qu
antum computation with magic states and the basis for the design of quantu
m error correcting codes.\n\nIn this talk\, I will describe the symmetry g
roup of the set of stabilizer states for any number of qubits or qudits wi
th d being an odd prime.\nPreviously\, the group was understood only in th
e qubit case\, where it coincides with the linear and anti-linear Clifford
operations.\nHowever\, for qudits\, the structure is somewhat richer and
depends on whether one or more than one qudit is considered. \n\nFurthermo
re\, I will relate our result to various notions of symmetries that appear
in the context of quantum systems (such as Wigner and Kadison symmetries)
and discuss some (potential) applications of our result.\n\nBased on join
t work with Valentin Obst and David Gross.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20221104T113000Z
DTEND;VALUE=DATE-TIME:20221104T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/8
DESCRIPTION:Title: Introduction to Measurement-Based Quantum Computing\nby Selman
Ipek (Bilkent University) as part of Bilkent University Quantum Computing
Seminar\n\nLecture held in SA 141.\n\nAbstract\nQuantum teleportation is
a basic protocol in quantum information science that harnesses many quinte
ssential features of quantum theory. Here we introduce MBQC by making conn
ections to quantum teleportation. We will show how basic quantum gates fam
iliar from the so-called circuit model of quantum computation are performe
d in the measurement-based framework. \nReferences: arXiv:quant-ph/0508124
\nAdditional sources: arXiv:quant-ph/0504097\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20221111T113000Z
DTEND;VALUE=DATE-TIME:20221111T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/9
DESCRIPTION:Title: Nonlocal correlations as an information-theoretic resource (2005)<
/a>\nby Selman Ipek (Bilkent University) as part of Bilkent University Qua
ntum Computing Seminar\n\nLecture held in SA 141.\n\nAbstract\nThe statist
ics of measurement outcomes coming from quantum theory satisfy a principle
known as no-signaling which prevents faster than light information transf
er. It is possible to study statistical models that satisfy this principle
independently of quantum theory. Here we introduce the notion of nonsigna
ling distributions and the implications of such models for information pro
cessing. \nReferences: arXiv:quant-ph/0404097\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART;VALUE=DATE-TIME:20221202T113000Z
DTEND;VALUE=DATE-TIME:20221202T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/11
DESCRIPTION:Title: The Sheaf-Theoretic Structure of Definite Causality\nby Aziz
Kharoof (Bilkent University) as part of Bilkent University Quantum Computi
ng Seminar\n\nLecture held in SA 141.\n\nAbstract\nIn its full generality
MBQC is adaptive: the outcomes of a prior measurement determine the measur
ement bases of a subsequent measurement. One possible way to incorporate t
his adaptivity is by introducing the notion of a causal order. This can be
done by introducing the notion of partially ordered sets (posets) as a bo
okkeeping device which takes this causal ordering into account. Here the n
otion of causal sheaves is introduced\, which in one sense generalizes the
sheaf-theoretic approach to include causal order\, but at the same time c
onsiders a more restricted set of measurement scenarios dealing only with
space-like separated parties.\nReferences: arXiv:1701.01888\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Kırtışoğlu (Bilkent University)
DTSTART;VALUE=DATE-TIME:20221209T113000Z
DTEND;VALUE=DATE-TIME:20221209T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/12
DESCRIPTION:Title: Simplicial quantum contextuality\nby Mehmet Kırtışoğlu (B
ilkent University) as part of Bilkent University Quantum Computing Seminar
\n\nLecture held in SA 141.\n\nAbstract\nSimplicial sets are well-known in
the mathematics community as combinatorial models of topological spaces.
Here they are utilized for modeling measurement scenarios. The resulting s
implicial approach to contextuality generalizes the sheaf-theoretic approa
ch of Abramsky and Brandenberger. Many standard results like the theorems
of Fine\, Kochen and Specker\, and Gleason can be established from this pe
rspective. Owing to its generality\, the simplicial approach is a good can
didate for modeling adaptive MBQC.\nReferences: arXiv:2204.06648\nAddition
al Sources: arXiv:0809.4221\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20221216T113000Z
DTEND;VALUE=DATE-TIME:20221216T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/13
DESCRIPTION:Title: Nonclassical correlations as a resource for computation\nby S
elman Ipek (Bilkent University) as part of Bilkent University Quantum Comp
uting Seminar\n\nLecture held in SA 141.\n\nAbstract\nComputational power
in MBQC resides in the correlations between measurement outcomes. Here we
consider an MBQC scheme that is fully adaptive (feedforward of measurement
outcomes is allowed)\, but where the classical side processing only perfo
rms linear operations (mod 2 arithmetic). Although such a model is not eve
n universal for classical computation\, once supplied with a nonclassical
resource (e.g.\, quantum state\, PR box\, etc.)\, it is possible to comput
e nonlinear functions within this computational model\, thus promoting the
model to classical universality.\nReferences: Anders/Browne (2008): arXiv
:0907.5449\nReferences: Raussendorf (2013): arXiv:0805.1002\nBackground ma
terial: arXiv:0712.0921\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20221223T113000Z
DTEND;VALUE=DATE-TIME:20221223T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/14
DESCRIPTION:Title: Generalized Bell Inequality Experiments and Computation\nby S
elman Ipek (Bilkent University) as part of Bilkent University Quantum Comp
uting Seminar\n\nLecture held in SA 141.\n\nAbstract\nIn the simplified se
tting of non-adaptive MBQC the choice of measurement basis for one local s
ystem (e.g.\, qubit) does not depend on the outcomes of any previous measu
rements. Thus non-adaptive MBQC is similar in spirit to Bell-type experime
nts consisting of distant parties that do not communicate. Following Hoban
\, et al. we consider such Bell-type experiments and study the convex geom
etry of the corresponding local and nonlocal regions. Experimental setups
with classical statistics that are explained by local hidden variable mode
ls (LVH) are found to have limited computational power\, which is related
to Bell-type inequalities.\nReferences: arXiv:1009.5213\nReferences: arXiv
:1108.4798\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ho Yiu Chung (Bilkent University)
DTSTART;VALUE=DATE-TIME:20221230T113000Z
DTEND;VALUE=DATE-TIME:20221230T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/15
DESCRIPTION:Title: Contextuality as a resource for measurement-based quantum computa
tion beyond qubits\nby Ho Yiu Chung (Bilkent University) as part of Bi
lkent University Quantum Computing Seminar\n\nLecture held in SA 141.\n\nA
bstract\nWhen dealing with an MBQC with binary outcome measurements the fo
llowing is true: a nonlinear function is computed if and only if the resou
rce is strongly contextual. However\, this tidy result does not remain tru
e when the set of outcomes is 𝑑>2. Frembs\, et al. consider the more ge
neral case of 𝑑-outcome measurements and establish that strong contextu
ality is needed to compute functions (i.e.\, polynomials) of a certain deg
ree not possible for the classical side-processor.\n\nReferences: arXiv:18
04.07364\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230210T113000Z
DTEND;VALUE=DATE-TIME:20230210T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/16
DESCRIPTION:Title: Cohomological framework for contextual quantum computation\nb
y Igor Sikora (Bilkent University) as part of Bilkent University Quantum C
omputing Seminar\n\nLecture held in SA 141.\n\nAbstract\nCohomological fra
mework for contextual quantum computation (2019) (Igor)\nIn a previous tal
k the topological approach to contextuality was introduced based on chain
complexes and cohomology theory. Here many aspects of this framework are c
arried over with the explicit goal of studying (temporally flat) MBQC more
carefully. Within this framework two types of topological invariants are
identified\; one relevant for the deterministic case\, while the other for
the probabilistic case. An essential takeaway is that the outputs of a co
mputation within this formalism are directly related to these topological
invariants\, thus the “hardness” of the computation is characterized b
y equivalence classes related to topology.\n\nReferences: arXiv:1602.04155
\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230217T113000Z
DTEND;VALUE=DATE-TIME:20230217T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/17
DESCRIPTION:Title: Putting paradoxes to work: contextuality in measurement-based qua
ntum computation\nby Selman Ipek (Bilkent University) as part of Bilke
nt University Quantum Computing Seminar\n\nLecture held in SA 141.\n\nAbst
ract\nThe topological approach to MBQC based on arXiv:1701.01888 and arXiv
:1602.04155 deals with the temporally flat case. One possible avenue to ac
commodating adaptivity is discussed using a so-called “iffy” proof.\n\
nReferences: arXiv:2208.06624\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ho Yiu Chung (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230203T113000Z
DTEND;VALUE=DATE-TIME:20230203T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/18
DESCRIPTION:Title: Contextuality as a resource for measurement-based quantum computa
tion beyond qubits\nby Ho Yiu Chung (Bilkent University) as part of Bi
lkent University Quantum Computing Seminar\n\nLecture held in SA 141.\n\nA
bstract\nWhen dealing with an MBQC with binary outcome measurements the fo
llowing is true: a nonlinear function is computed if and only if the resou
rce is strongly contextual. However\, this tidy result does not remain tru
e when the set of outcomes is $d>2$. Frembs\, et al. consider the more gen
eral case of $d$-outcome measurements and establish that strong contextual
ity is needed to compute functions (i.e.\, polynomials) of a certain degre
e not possible for the classical side-processor.\n\nReferences: arXiv:1804
.07364\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230303T113000Z
DTEND;VALUE=DATE-TIME:20230303T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/19
DESCRIPTION:Title: Introduction to the Stabilizer Formalism\nby Selman Ipek (Bil
kent University) as part of Bilkent University Quantum Computing Seminar\n
\nLecture held in SA 141.\n\nAbstract\nIn the finite-dimensional regime ce
rtain pure quantum states can be completely characterized by maximal abeli
an (i.e.\, commuting) subgroups of the Pauli group. These are called stabi
lizer states and well-known examples include Bell as well as Greenberger\,
Horne\, Zeilinger states. The stabilizer formalism is a subtheory of fini
te-dimensional quantum mechanics consisting of stabilizer states\, Cliffor
d unitaries (i.e.\, unitaries that map one Pauli operator to another)\, an
d measurement of Pauli observables. The ability to fully describe such qua
ntum states in group theoretic terms makes their analysis extremely conven
ient and they play an important role in quantum information processing and
also quantum error correction. A key result for our purposes in this semi
nar is the celebrated Gottesman-Knill theorem which establishes that any q
uantum circuit built out of stabilizer states\, Clifford unitaries\, and P
auli measurements (called stabilizer circuits) can be efficiently simulate
d on a classical computer.\n\nReferences: arXiv:quant-ph/9807006\n\nRefere
nces: Nielsen/Chuang: QCQI (Ch. 10)\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230317T113000Z
DTEND;VALUE=DATE-TIME:20230317T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/20
DESCRIPTION:Title: Improved Simulation of Stabilizer Circuits\nby Selman Ipek (B
ilkent University) as part of Bilkent University Quantum Computing Seminar
\n\nLecture held in SA 141.\n\nAbstract\nThe Gottesman-Knill theorem estab
lishes that stabilizer circuits (defined previously) can be simulated effi
ciently on a classical computer. In arXiv:quant-ph/0406196 Aaronson and Go
ttesman improve the efficiency of the classical simulation and demonstrate
that stabilizer circuits are (most likely) not universal for classical co
mputation. Circuits that are otherwise stabilizer with the exception of a
small number of non-Clifford gates are also considered and the complexity
of such circuits scales exponentially with the number of non-Clifford gate
s.\n\nReferences: arXiv:quant-ph/0406196\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230324T113000Z
DTEND;VALUE=DATE-TIME:20230324T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/21
DESCRIPTION:Title: Universal Quantum Computation with ideal Clifford gates and noisy
ancillas\nby Selman Ipek (Bilkent University) as part of Bilkent Univ
ersity Quantum Computing Seminar\n\nLecture held in SA 141.\n\nAbstract\nI
n studying the resources necessary to achieve a quantum speedup it is usef
ul to distinguish between operations that are (a) free\, or (b) costly. Th
e fact that stabilizer circuits can be efficiently classically simulated s
uggests that stabilizer operations be designated as free. This begs the qu
estion of whether it is possible to augment the free stabilizer operations
with an additional costly resource (to be consumed) which promotes stabil
izer circuits to quantum universality. Bravyi and Kitaev (arXiv:quant-ph/0
403025) demonstrate that there are certain quantum states (deemed “magic
”) which achieve precisely this. They also detail a protocol for distill
ing such magic states from a collection of noisy ancilla states.\n\nRefere
nces: arXiv:quant-ph/0403025\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230331T113000Z
DTEND;VALUE=DATE-TIME:20230331T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/22
DESCRIPTION:Title: Quantum universality and magic state distillation\nby Selman
Ipek (Bilkent University) as part of Bilkent University Quantum Computing
Seminar\n\nLecture held in SA 141.\n\nAbstract\nStabilizer circuits can be
promoted to quantum universality via the injection of magic states. An op
en question is the determination of precisely which non-stabilizer quantum
states can be considered “magic”. Following Reichardt\, we discuss ma
gic state distillation protocols that tighten the boundary between the cla
ssically efficiently simulatable regime and that of full universal quantum
computation.\n\nReferences: arXiv:0608085\n\nReferences: https://core.ac.
uk/download/pdf/44132852.pdf\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230414T113000Z
DTEND;VALUE=DATE-TIME:20230414T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/23
DESCRIPTION:Title: Trading classical and quantum resources\nby Selman Ipek (Bilk
ent University) as part of Bilkent University Quantum Computing Seminar\n\
nLecture held in SA 141.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20230522T103000Z
DTEND;VALUE=DATE-TIME:20230522T120000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/24
DESCRIPTION:Title: Quasiprobability methods in classical simulation (I)\nby Selm
an Ipek (Bilkent University) as part of Bilkent University Quantum Computi
ng Seminar\n\nLecture held in SA 141.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Howard (University of Galway)
DTSTART;VALUE=DATE-TIME:20230407T113000Z
DTEND;VALUE=DATE-TIME:20230407T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/25
DESCRIPTION:Title: Topics in Stabilizer Quantum Computation\nby Mark Howard (Uni
versity of Galway) as part of Bilkent University Quantum Computing Seminar
\n\nLecture held in SA 141.\n\nAbstract\nThe central question in quantum i
nformation theory is to delineate the operational capabilities achievable
under the rules of quantum mechanics but not achievable with classical phy
sics. As such\, it can be useful to tinker with hypothetical theories havi
ng different sets of allowed state preparations\, transformations and meas
urements\; different combinations can give us theories that are less power
ful than\, equal to\, or more powerful than quantum mechanics. When we att
empt to understand the computational power of circuits\, so-called stabili
zer circuits comprise a restricted class that are provably weaker than a g
eneral (“universal”) quantum computer. For stabilizer circuits\, the d
escription of the achievable states and their updates is efficient leading
to a classical simulation algorithm that is polynomial in the number of q
ubits. Remarkably\, it is easy to boost the power of stabilizer circuits t
o that of a universal quantum computer by adding access to non-stabilizer
states or operations. When error-correction is used these additional state
s or operations are typically very costly. All of the above naturally sugg
ests a few questions that I will address:\n\n1) How should we classically
simulate stabilizer circuits interspersed with a few non-stabilizer gates\
, and how does the runtime scale?\n\n2) How can we minimize the use of cos
tly non-stabilizer operations?\n\n3) What quantum mechanical property is m
issing from stabilizer circuits but present in universal quantum computers
?\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hakop Pashayan (Freie Universität Berlin)
DTSTART;VALUE=DATE-TIME:20230526T113000Z
DTEND;VALUE=DATE-TIME:20230526T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/26
DESCRIPTION:Title: Classical simulation of quantum circuits\nby Hakop Pashayan (
Freie Universität Berlin) as part of Bilkent University Quantum Computing
Seminar\n\nLecture held in SA 141.\n\nAbstract\nI will give some backgrou
nd on classical simulation then I will present a general framework for sim
ulating quantum circuits using quasiprobabilistic methods. Through example
s\, I will demonstrate the strengths of this approach in its runtime perfo
rmance\, flexibility and generality.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Seddon (Phasecraft)
DTSTART;VALUE=DATE-TIME:20230512T113000Z
DTEND;VALUE=DATE-TIME:20230512T130000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/27
DESCRIPTION:Title: Stabilizer simulation methods for mixed magic states and noisy ch
annels\nby James Seddon (Phasecraft) as part of Bilkent University Qua
ntum Computing Seminar\n\nLecture held in SA 141.\n\nAbstract\nIt has been
known since the early days of the stabilizer formalism that while Cliffor
d circuits with stabilizer state inputs can be simulated efficiently in th
e number of qubits and operations\, more general circuits can be simulated
with an overhead growing exponentially with\, for example\, the number of
T gates\, or some other "magic" resource. Quantifiers of magic resource k
nown as magic monotones formalize the notion that some states/operations a
re harder to simulate than others\, and various classical simulation algor
ithms have been proposed where performance guarantees depend explicitly on
some magic monotone. A sequence of works on stabilizer rank culminated in
the powerful simulator of Ref. [1]\, which reduces runtime by replacing a
n exact stabilizer decomposition with a sparsified approximation\, but is
largely restricted to simulating pure state evolution. Meanwhile\, a paral
lel avenue of research developed links between quasiprobability simulation
methods and robustness-type monotones [2\, 3]\, yielding the insight that
noisier circuits can be easier to simulate. Simulators of this type admit
mixed initial states and more general quantum channels\, but tend to be s
lower than stabilizer rank-based methods. In this seminar I will outline h
ow stabilizer rank methods can be extended to deal with mixed magic states
[4] and noisy non-Clifford operations [5]\, in the process improving on t
he runtime bounds of Ref. [1]. I will also discuss how this method (and th
e others introduced in Ref. [4]) can be situated within a broader framewor
k of simulators for general quantum circuits on qubits\, each with an asso
ciated magic monotone\, showing that stabilizer rank and quasiprobability
methods are more closely related than they first appear.\n\n[1] Bravyi\, B
rowne\, Calpin\, Campbell\, Gosset & Howard (2019) arxiv:1808.00128\n\n[2]
Pashayan\, Wallman & Bartlett (2015) arxiv:1503.07525\n\n[3] Howard & Cam
pbell (2017) arxiv:1609.07488\n\n[4] Seddon\, Regula\, Pashayan\, Ouyang a
nd Campbell (2021) arxiv:2002.06181\n\n[5] Seddon (2022) https://discovery
.ucl.ac.uk/id/eprint/10146361/\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240209T110000Z
DTEND;VALUE=DATE-TIME:20240209T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/28
DESCRIPTION:Title: Introduction to Category Theory\nby Walker Stern (Bilkent Uni
versity) as part of Bilkent University Quantum Computing Seminar\n\nLectur
e held in SA 141.\n\nAbstract\nThough category theory often feels abstruse
when first encountered\, it rests upon a few simple definitions which dra
w on commonalities in mathematical arguments. In this preliminary talk\, w
e present some of the basic definitions of category theory\, and illustrat
e them through numerous examples. To wit\, we will discuss categories\, fu
nctors\, natural transformations. The talk will conclude with a discussion
of universal properties and (co)limits\, with a particular emphasis on (c
o)products.\n\nReferences:\n\n1. Emily Riehl. Category theory in Context.
Dover\, 2016. Chapters 1 & 2\n\n2. Tom Leinster. Basic Category Theory. Ca
mbridge\, 2014. Chapter 1\n\n3. Saunders Mac Lane. Categories for the Work
ing Mathematician. Springer GTM volume 5\, 1978.\nChapter\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240216T110000Z
DTEND;VALUE=DATE-TIME:20240216T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/29
DESCRIPTION:Title: Motivating Categorical Quantum Mechanics\nby Selman Ipek (Bil
kent University) as part of Bilkent University Quantum Computing Seminar\n
\nLecture held in SA 141.\n\nAbstract\nCircuit diagrams\, such as those th
at implement quantum protocols have long been a useful tool in the\nfield
of quantum information and computation. Such diagrams\, in fact\, have a m
arked similarity to string\ndiagrams appearing in category theory\, an ana
logy that was made precise by the seminal work of Abramsky\nand Coecke [1]
. Here we illustrate the naturalness of the categorical setting for descri
bing quantum protocols\nusing the example of quantum teleportation [1\, §
2.1] and motivate the kind of structures that will be needed\nto faithfull
y realize such quantum processes. Key notions in quantum theory\, such as
state\, transformation\,\nand measurement will be stated in a fully catego
rical language [1\, §6] whose precise meaning will be unpacked\nin subseq
uent talks.\n\nReferences:\n\n1. Abramsky\, Samson\, and Bob Coecke. “Ca
tegorical quantum mechanics.” Handbook of quantum logic\nand quantum str
uctures 2 (2009): 261-325. Section 2.\n\n2. Heunen\, Chris\, and Jamie Vic
ary. Categories for Quantum Theory: an introduction. Oxford University\nPr
ess\, 2019. Chapter 0.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240223T110000Z
DTEND;VALUE=DATE-TIME:20240223T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/30
DESCRIPTION:Title: Symmetric Monoidal Categories (I)\nby Walker Stern (Bilkent U
niversity) as part of Bilkent University Quantum Computing Seminar\n\nLect
ure held in SA 141.\n\nAbstract\nWe will introduce monoidal categories and
symmetric monoidal categories (SMCs) as well as the string\ndiagrams whic
h provide graphical calculi for computations in SMCs (Primary reference: [
1\,Ch. 1]\, secondary\nreferences: [2\, §3.1\, §3.3]\, [5\, Ch. XI]\, [3
\, Ch. 3]\, [4\, Track 1]). We define dual objects and duality data\nin a
SMC (Primary reference: [1\, Ch. 3]\, secondary references: [2\,§3.3]\, [
4\, Track 1]). We illustrate these\ndefinitions with examples drawn from c
ategories of vector spaces\, categories of finite dimensional Hilbert\nspa
ces\, and several others.\n\nReferences:\n\n1. Heunen\, Chris\, and Jamie
Vicary. Categories for Quantum Theory: an introduction. Oxford University\
nPress\, 2019.\n\n2. Samson Abramsky and Bob Coecke. Categorical Quantum M
echanics. arXiv:0808.1023\n\n3. Peter Selinger. A survey of graphical lang
uages for monoidal categories. arXiv:0908.3347\n\n4. John Baez. Quantum Gr
avity Seminar - Fall 2000. online notes\n\n5. Saunders Mac Lane. Categorie
s for the Working Mathematician. Springer GTM volume 5\, 1978.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240301T110000Z
DTEND;VALUE=DATE-TIME:20240301T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/31
DESCRIPTION:Title: Symmetric Monoidal Categories (II)\nby Redi Haderi (Bilkent U
niversity) as part of Bilkent University Quantum Computing Seminar\n\nLect
ure held in SA 141.\n\nAbstract\nThe structure involved in a symmetric mon
oidal category is very broad\, which is of benefit to the general\ntheory.
However\, quantum mechanics\, which is typically formulated using Hilbert
spaces\, requires substantially more structure than is present in an arb
itrary SMC. In particular\, the notions of conjugation and transpose are o
f key import in the study of quantum mechanics. In this talk\, we introduc
e dagger structures\non categories\, and dagger SMCs\, which axiomatize so
me of the necessary structure (Primary reference: [1\,\n§4.3]\, secondary
reference: [2\,§2.3.1]). We then discuss internal mapping objects and co
mpact closed categories (Primary reference: [1.§4.3]\, secondary referen
ces: [2\,§3.4]\, [3]). We motivate these definitions for the\nfeatures of
the category of finite dimensional Hilbert Spaces\, and provide other exa
mples throughout.\n\nReferences:\n\n1. Abramsky\, Samson\, and Bob Coecke.
Categorical quantum mechanics. Handbook of quantum logic\nand quantum str
uctures 2 (2009): 261-325.\n\n2. Heunen\, Chris\, and Jamie Vicary. Catego
ries for Quantum Theory: an introduction. Oxford University\nPress\, 2019.
\n\n3. Brian Day Note on compact closed categories. (doi: 10.1017/S1446788
700020334).\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240315T110000Z
DTEND;VALUE=DATE-TIME:20240315T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/32
DESCRIPTION:Title: Symmetric Monoidal Categories (III)\nby Walker Stern (Bilkent
University) as part of Bilkent University Quantum Computing Seminar\n\nLe
cture held in SA 141.\n\nAbstract\nIn a symmetric monoidal category\, the
set of maps from the monoidal unit to itself inherits additional\nstructur
e. These scalars in the category are inspired by\, for instance\, the isom
orphism between linear maps\nfrom $\\mathbb{C}$ to itself and the field $\
\mathbb{C}$. However\, the additive structure and the notion of traces whi
ch are key to\nthe computation of quantum probabilities require some devel
opment. In this talk\, we describe biproducts\nand distributivity in (symm
etric monoidal) category\, and the concomitant structures induced on scala
rs in\na symmetric monoidal category (Primary reference: [1\, §5]\, secon
dary references: [2\,§2.2.3]). We introduce\ncategorical definitions of t
races and partial traces\, the latter familiar in quantum information theo
ry as\na procedure for obtaining information about a subsystem (Primary re
ference: [2\, §4.6\, §5.1]\, secondary\nreference: [1\, §2.1\, §2.2]\,
[3]).\n\nReferences:\n\n1. Abramsky\, Samson\, and Bob Coecke. Categorica
l quantum mechanics. Handbook of quantum logic\nand quantum structures 2 (
2009): 261-325.\n\n2. Heunen\, Chris\, and Jamie Vicary. Categories for Qu
antum Theory: an introduction. Oxford University\nPress\, 2019.\n\n3. Andr
e Joyal\, Ross Street\, and Dominic Verity. Traced Monoidal Categories. (d
oi:10.1017/S0305004100074338).\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240322T110000Z
DTEND;VALUE=DATE-TIME:20240322T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/33
DESCRIPTION:Title: Categorical Quantum Mechanics\nby Selman Ipek (Bilkent Univer
sity) as part of Bilkent University Quantum Computing Seminar\n\nLecture h
eld in SA 141.\n\nAbstract\nHaving built up the machinery of dagger SMCs\,
we revisit the motivating discussion and restate the\naxioms of quantum m
echanics in a categorical language [1\, §6]. The Born rule for computing
probabilities\ncan be derived from this point of view [1\, §6.1]. A numbe
r of quantum protocols can also be described within\nthis formalism (e.g.\
, logic gate teleportation and entanglement swapping) with the aid of the
diagramatic\ncalculus.\n\nReferences:\n\n1. Abramsky\, Samson\, and Bob Co
ecke. Categorical quantum mechanics. Handbook of quantum logic\nand quantu
m structures 2 (2009): 261-325. Section 6.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240329T110000Z
DTEND;VALUE=DATE-TIME:20240329T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/34
DESCRIPTION:Title: No-cloning theorem in categorical quantum mechanics\nby Redi
Haderi (Bilkent University) as part of Bilkent University Quantum Computin
g Seminar\n\nLecture held in SA 141.\n\nAbstract\nAs with many algebraic s
tructures\, the conditions and data which define a monoid structure on a s
et can\nbe reframed diagrammatically\, leading to the notion of a monoid o
bject in a monoidal category. Dualizing this\ndefinition provides the noti
on of a comonoid. In this talk\, we introduce and discuss monoids and como
noids\nin SMCs. These structures can be used to prove that any category wi
th a notion of uniform deleting or\nuniform copying (or cloning) cannot de
scribe quantum theory.\n\nReferences:\n\n1. Heunen\, Chris\, and Jamie Vic
ary. Categories for Quantum Theory: an introduction. Oxford University\nPr
ess\, 2019. Chapter 4.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Torres Castillo (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240405T110000Z
DTEND;VALUE=DATE-TIME:20240405T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/35
DESCRIPTION:Title: Frobenius algebras and complementarity\nby Victor Torres Cast
illo (Bilkent University) as part of Bilkent University Quantum Computing
Seminar\n\nLecture held in SA 141.\n\nAbstract\nIn quantum theory observab
les that do not commute are considered incompatible. Maximally incompatibl
e\, or complementary\, observables are such that measurement of one destro
ys all information about the\nother. This property is modeled in CQM using
the notion of Frobenius algebras. These Frobenius algebras\nmay be seen a
s an enhancement of the monoids discussed in the previous talk using the t
heory of duality in\nsymmetric monoidal categories. We will additionally d
iscuss extra properties and structures on Frobenius\nalgebras\, in particu
lar\, dagger Frobenius algebras. Frobenius algebras are also of substantia
l importance in\nthe study of topological quantum field theory (TQFT).\n\n
References:\n\n1. Heunen\, Chris\, and Jamie Vicary. Categories for Quantu
m Theory: an introduction. Oxford University\nPress\, 2019. Chapter 5\, Ch
apter 6.\n\n2. Joachim Kock. Frobenius algebras and 2D topological quantum
field theories. Cambridge\, 2010.\nSection 3.6.\n\n3. Bob Coecke\, Dusko
Pavlovic and Jamie Vicary. A new description of orthogonal bases. Mathemat
ical\nStructures in Computer Science (2012).\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240503T110000Z
DTEND;VALUE=DATE-TIME:20240503T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/37
DESCRIPTION:Title: Complete positivity\nby Selman Ipek (Bilkent University) as p
art of Bilkent University Quantum Computing Seminar\n\nInteractive livestr
eam: https://zoom.us/j/97145850864?pwd=djhqT09CU3hiRlU1Wk1DL01mdFdSQT09\nL
ecture held in SA 141.\n\nAbstract\nTo handle a theory of mixed states —
essential to the study of quantum mechanics — it is necessary to\nconsi
der completely positive maps in a compact closed dagger monoidal category
$\\mathcal{C}$. We will define mixed\nstates and completely positive maps\
, and show how this leads to the construction of a category $\\text{CP}(\\
mathcal{C})$\, whose\nobjects are certain Frobenius algebras in $\\mathcal
{C}$\, and whose morphisms are completely positive morphisms. We\nwill the
n discuss how both classical statistical mechanics and quantum mechanics c
an be expressed in the\ncategory $\\text{CP}(\\mathcal{C})$.\n\nReferences
:\n\n1. Heunen\, Chris\, and Jamie Vicary. Categories for Quantum Theory:
an introduction. Oxford University\nPress\, 2019. Chapter 7\n\n2. Selinger
\, Peter. Dagger Compact Closed Categories and Completely Positive Maps. E
lectronic Notes\nin Theoretical Computer Science 170 (2007) 139–163\n\n3
. Coecke\, Bob and Heunen\, Chris. Pictures of complete positivity in arbi
trary dimension. Information\nand Computation 250 (2016) 50–58\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/37/
URL:https://zoom.us/j/97145850864?pwd=djhqT09CU3hiRlU1Wk1DL01mdFdSQT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240510T110000Z
DTEND;VALUE=DATE-TIME:20240510T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/38
DESCRIPTION:Title: Bicategories and monoidal bicategories\nby Redi Haderi (Bilke
nt University) as part of Bilkent University Quantum Computing Seminar\n\n
Interactive livestream: https://zoom.us/j/97145850864?pwd=djhqT09CU3hiRlU1
Wk1DL01mdFdSQT09\nLecture held in SA 141.\n\nAbstract\nTo study categorifi
cations of Hilbert spaces\, it is necessary to consider higher categories.
In this talk we will\ndevelop the idea of bicategories and monoidal bicat
egories\, and explain the graphical calculus which will\nuse them. We will
then discuss duality and fully dualizability in monoidal categories\, and
finish the talk by\ndiscussing oriented structures and oriented duals.\n\
nReferences:\n\n1. Heunen\, Chris\, and Jamie Vicary. Categories for Quant
um Theory: an introduction. Oxford University\nPress\, 2019. Chapter 8\n\n
2. Leinster\, Tom. Higher Operads\, Higher Categories. Cambridge Universit
y Press\, 2010. Section 1.5\n\n3. Baez\, John and Neuchl\, Martin. Higher-
Dimensional Algebra I: Braided Monoidal 2-Categories.\narXiv:q-alg/9511013
\n\n4. Schommer-Pries\, Christopher. The Classification of Two-Dimensional
Extended Topological Field\nTheories. arXiv:1112.1000. Chapter 2.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/38/
URL:https://zoom.us/j/97145850864?pwd=djhqT09CU3hiRlU1Wk1DL01mdFdSQT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240517T110000Z
DTEND;VALUE=DATE-TIME:20240517T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/39
DESCRIPTION:Title: Higher quantum theory and 2-Hilbert spaces\nby Redi Haderi (B
ilkent University) as part of Bilkent University Quantum Computing Seminar
\n\nInteractive livestream: https://zoom.us/j/97145850864?pwd=djhqT09CU3hi
RlU1Wk1DL01mdFdSQT09\nLecture held in SA 141.\n\nAbstract\nIn this talk\,
we will discuss categorifications of Hilbert spaces\, called $\\textit{2-H
ilbert spaces}$. In much the same\nway as Hilbert spaces are sets with lin
ear structures and inner products satisfying a completeness condition\,\n2
-Hilbert spaces are categories with linear structures and inner products o
n their hom-sets\, satisfying a\ncategorical completeness condition. We wi
ll develop the monoidal bicategory of 2-Hilbert spaces\, and discuss\nhow
teleportation and quantum dense coding manifest in this framework.\n\nRefe
rences:\n\n1. Heunen\, Chris\, and Jamie Vicary. Categories for Quantum Th
eory: an introduction. Oxford University\nPress\, 2019. Chapter 8\n\n2. Ba
ez\, John. Higher-dimensional algebra II: 2-Hilbert spaces. Advances in Ma
thematics\, 127(2):125–189\,\n1997. Chapters 1-4\n\n3. Bartlett\, Bruce.
On unitary 2-representations of finite groups and topological quantum fie
ld theory.\narXiv:0901.3975. Sections 3.1\, 3.2\, & 3.3.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/39/
URL:https://zoom.us/j/97145850864?pwd=djhqT09CU3hiRlU1Wk1DL01mdFdSQT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240419T110000Z
DTEND;VALUE=DATE-TIME:20240419T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/40
DESCRIPTION:Title: Categorical treatment of the Deutsch-Jozsa algorithm\nby Selm
an Ipek (Bilkent University) as part of Bilkent University Quantum Computi
ng Seminar\n\nLecture held in SA 141.\n\nAbstract\nThe Deutsch-Jozsa probl
em is a canonical example of a problem that can be solved by a quantum com
puter exponentially faster than a classical deterministic computer. Here w
e begin by describing the Deutsch-Jozsa problem and its solution according
to standard quantum theory [1\, §I.B]. We then describe how the solution
works in categorical terms by building off of the notion of complementary
structures and Frobenius algebras built up in the previous talks.\n\nRefe
rences:\n\n1. Vicary\, Jamie. Topological structure of quantum algorithms.
arXiv preprint arXiv:1209.3917 (2013).\n\n2. Heunen\, Chris\, and Jamie V
icary. Categories for Quantum Theory: an introduction. Oxford University\n
Press\, 2019. Chapter 6\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART;VALUE=DATE-TIME:20240426T110000Z
DTEND;VALUE=DATE-TIME:20240426T123000Z
DTSTAMP;VALUE=DATE-TIME:20240423T105402Z
UID:BilkentMathGrad/41
DESCRIPTION:Title: Applications of Categorical Quantum Mechanics to quantum computat
ion: ZX calculus\nby Selman Ipek (Bilkent University) as part of Bilke
nt University Quantum Computing Seminar\n\nInteractive livestream: https:/
/zoom.us/j/97145850864?pwd=djhqT09CU3hiRlU1Wk1DL01mdFdSQT09\nLecture held
in SA 141.\n\nAbstract\nSeveral quintessentially quantum notions\, such as
no-cloning\, no-deleting\, as well as classical and complementary structu
res can be made precise in the categorical approach to quantum mechanics.
The so-called ZX calculus consists of two complementary classical structur
es on an underlying object in a compact dagger category. Many quantum gate
s used in quantum computation have natural representations in the ZX-calcu
lus. In this talk we will give the main definition of the ZX-calculus and
highlight interesting aspects of the formalism\; e.g.\, ZX-calculus is sou
nd and (approximately) universal for quantum computation. Time permitting\
, we will make connections to the measurement-based model of quantum compu
tation. \n\nReferences:\n\n1. Heunen\, Chris\, and Jamie Vicary. Categorie
s for Quantum Theory: an introduction. Oxford University\nPress\, 2019. Ch
apter 6\n\n2. Coecke\, Bob\, and Ross Duncan. Interacting quantum observab
les: categorical algebra and diagrammatics. New J. Phys (13)\, 2011. arXiv
: 0906.4725\n\n3. Duncan\, Ross. A graphical approach to measurement-based
quantum computing. arXiv preprint arXiv:1203.6242\, 2012.\n
LOCATION:https://researchseminars.org/talk/BilkentMathGrad/41/
URL:https://zoom.us/j/97145850864?pwd=djhqT09CU3hiRlU1Wk1DL01mdFdSQT09
END:VEVENT
END:VCALENDAR