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BEGIN:VEVENT
SUMMARY:Mark Webster (University of Sydney)
DTSTART:20220606T090000Z
DTEND:20220606T100000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/1
DESCRIPTION:Title: The XP Stabiliser Formalism: a Generalisation of the Pauli
Stabiliser Formalism with Arbitrary Phases\nby Mark Webster (Universit
y of Sydney) as part of Bilkent Quantum Computing Seminar\n\n\nAbstract\nM
ark Webster works in the field of quantum error correction\nand he will be
discussing a generalisation of the Pauli stabiliser\nformalism. The new X
P stabiliser formalism allows us to represent a much\nwider set of states
and XP codes have a much richer logical operator\nstructure compared to th
e Pauli stabiliser formalism. In addition\, XP\ncodes cannot be classicall
y simulated which suggests that they capture\nsome aspects of quantum adva
ntage.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Zurel (University of British Columbia)
DTSTART:20220620T130000Z
DTEND:20220620T140000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/2
DESCRIPTION:Title: Polytope theory and classical simulation of quantum computa
tion with magic states\nby Michael Zurel (University of British Columb
ia) as part of Bilkent Quantum Computing Seminar\n\n\nAbstract\nPolytopes
come up in several areas of quantum information science. They appear in th
e foundations of quantum theory\, for example through Bell inequalities an
d noncontextuality inequalities. They are also useful tools in the study o
f quantum information processing tasks like quantum computation and quantu
m communication. Here they can describe separations between the capabiliti
es of classical theories\, quantum theory\, and beyond-quantum theories li
ke the no-signalling polytope. In this talk I will give an overview of som
e examples of where polytopes are used in quantum computation. In particul
ar\, I will focus on a few families of polytopes that provide useful descr
iptions for a universal model of quantum computation and I will describe h
ow these families of polytopes can be used to characterize the quantum com
putational advantage over classical computation. In addition\, I will revi
ew some of the algorithms and tools used for studying these polytopes.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sivert Aasnæss (University of Oxford)
DTSTART:20220704T130000Z
DTEND:20220704T140000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/3
DESCRIPTION:Title: Contextuality as a resource for quantum circuits\nby Si
vert Aasnæss (University of Oxford) as part of Bilkent Quantum Computing
Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martti Karvonen (University of Ottawa)
DTSTART:20220801T130000Z
DTEND:20220801T140000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/4
DESCRIPTION:Title: Neither Contextuality nor Nonlocality Admits Catalysts\
nby Martti Karvonen (University of Ottawa) as part of Bilkent Quantum Comp
uting Seminar\n\n\nAbstract\nIn this talk\, I will give an overview of htt
ps://arxiv.org/abs/2102.07637 \, showing that the resource theory of conte
xtuality does not admit catalysts\, i.e.\, there are no correlations that
can enable an otherwise impossible resource conversion and still be recove
red afterward. As a corollary\, we observe that the same holds for nonloca
lity. As entanglement allows for catalysts\, this adds a further example t
o the list of "anomalies of entanglement\," showing that nonlocality and e
ntanglement behave differently as resources. On the way\, I will explain t
he construction of the resource theories of contextuality and nonlocality\
, and discuss some categorical aspects of these. Time permitting\, we will
also show that catalysis remains impossible even if\, instead of classica
l randomness\, we allow some more powerful behaviors to be used freely in
the free transformations of the resource theory.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicola Pinzani (University of Oxford)
DTSTART:20220808T130000Z
DTEND:20220808T140000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/5
DESCRIPTION:Title: The Topology and Geometry of Causality\nby Nicola Pinza
ni (University of Oxford) as part of Bilkent Quantum Computing Seminar\n\n
\nAbstract\nIn my talk I am going to present a unified operational\nframew
ork for the study of causality\, non-locality and contextuality\, in\na fu
lly device-independent and theory-independent setting. Our\ninvestigation
proceeds from two complementary fronts: a topological one\,\nusing tools f
rom sheaf theory\, and a geometric one\, based on polytopes\nand linear pr
ogramming. From the topological perspective\, we understand\nexperimental
outcome probabilities as bundles of compatible contextual\ndata over certa
in topological spaces\, encoding causality constraints.\n From the geometr
ic perspective\, we understand the same experimental\noutcome probabilitie
s as points in high-dimensional causal polytopes\,\nwhich we explicitly co
nstruct and fully characterise.\nOur work is a significant extension of bo
th the established\nAbramsky-Brandenburger framework for contextuality and
the current body\nof work on indefinite causality. We provide definitions
of causal\nfraction and causal separability for empirical models relative
to a\nbroad class of causal constraints: this allows us to construct and\
ncharacterise novel examples which explicitly connect causal\ninseparabili
ty to non-locality and contextuality. In particular\, we\nclearly demonstr
ate the existence of "causal contextuality"\, a\nphenomenon where causal s
tructure is explicitly correlated to the\nclassical inputs and outputs of
local instruments\, so that contextuality\nof the associated empirical mod
el directly implies causal\ninseparability.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amy Searle (University of Oxford)
DTSTART:20220919T130000Z
DTEND:20220919T140000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/6
DESCRIPTION:Title: Classifying the Noncontextual Measurement Spaces via the Sh
eaf Approach\nby Amy Searle (University of Oxford) as part of Bilkent
Quantum Computing Seminar\n\n\nAbstract\nThe sheaf theoretic approach to c
ontextuality\, as has been emphasised before\, is favourable because the g
enerality of the sheaf approach allows for the uncovering of connections t
o other fields\, and also because theoretical developments in the active f
ield of sheaf theory can be directly applied to the context of quantum inf
ormation. One such theoretical development\, the application to contextual
ity of which was first discussed in [1]\, is Vorob'ev's theorem. In the co
ntext of quantum information\, it allows us to identify which setups can n
ever exhibit contextuality. In this sense\, and by negation\, we know that
for observation of non-classical behaviour attention must be focused on t
he measurement setups which do not fall into this category. Besides explai
ning this theorem\, I will discuss some of the other results contained wit
hin [1]\, such as using such principles to derive monogamy of entanglement
. I will moreover explain why and how we might hope to extend such results
to more general setups\, such as setups where some measurements occur bef
ore others so that there is a temporal ordering on the measurement set.\n\
n[1] Soares Barbosa\, Rui 2015\, 'Contextuality in Quantum Mechanics and B
eyond'\, PhD thesis\, University of Oxford.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arne Heimendahl (University of Cologne)
DTSTART:20220912T130000Z
DTEND:20220912T140000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/7
DESCRIPTION:Title: Wigner’s theorem of stabilizer states\nby Arne Heimen
dahl (University of Cologne) as part of Bilkent Quantum Computing Seminar\
n\n\nAbstract\nStabilizer states are one of the main components for quantu
m computation with magic states and the basis for the design of quantum er
ror correcting codes.\n\nIn this talk\, I will describe the symmetry group
of the set of stabilizer states for any number of qubits or qudits with d
being an odd prime.\nPreviously\, the group was understood only in the qu
bit case\, where it coincides with the linear and anti-linear Clifford ope
rations.\nHowever\, for qudits\, the structure is somewhat richer and depe
nds on whether one or more than one qudit is considered. \n\nFurthermore\,
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 joint wo
rk with Valentin Obst and David Gross.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20221104T113000Z
DTEND:20221104T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/8
DESCRIPTION:Title: Introduction to Measurement-Based Quantum Computing\nby
Selman Ipek (Bilkent University) as part of Bilkent Quantum Computing Sem
inar\n\nLecture held in SA 141.\n\nAbstract\nQuantum teleportation is a ba
sic protocol in quantum information science that harnesses many quintessen
tial features of quantum theory. Here we introduce MBQC by making connecti
ons to quantum teleportation. We will show how basic quantum gates familia
r from the so-called circuit model of quantum computation are performed in
the measurement-based framework. \nReferences: arXiv:quant-ph/0508124\nAd
ditional sources: arXiv:quant-ph/0504097\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20221111T113000Z
DTEND:20221111T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/9
DESCRIPTION:Title: Nonlocal correlations as an information-theoretic resource
(2005)\nby Selman Ipek (Bilkent University) as part of Bilkent Quantum
Computing Seminar\n\nLecture held in SA 141.\n\nAbstract\nThe statistics
of measurement outcomes coming from quantum theory satisfy a principle kno
wn as no-signaling which prevents faster than light information transfer.
It is possible to study statistical models that satisfy this principle ind
ependently of quantum theory. Here we introduce the notion of nonsignaling
distributions and the implications of such models for information process
ing. \nReferences: arXiv:quant-ph/0404097\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aziz Kharoof (Bilkent University)
DTSTART:20221202T113000Z
DTEND:20221202T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/11
DESCRIPTION:Title: The Sheaf-Theoretic Structure of Definite Causality\nb
y Aziz Kharoof (Bilkent University) as part of Bilkent Quantum Computing S
eminar\n\nLecture held in SA 141.\n\nAbstract\nIn its full generality MBQC
is adaptive: the outcomes of a prior measurement determine the measuremen
t bases of a subsequent measurement. One possible way to incorporate this
adaptivity is by introducing the notion of a causal order. This can be don
e by introducing the notion of partially ordered sets (posets) as a bookke
eping device which takes this causal ordering into account. Here the notio
n of causal sheaves is introduced\, which in one sense generalizes the she
af-theoretic approach to include causal order\, but at the same time consi
ders a more restricted set of measurement scenarios dealing only with spac
e-like separated parties.\nReferences: arXiv:1701.01888\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehmet Kırtışoğlu (Bilkent University)
DTSTART:20221209T113000Z
DTEND:20221209T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/12
DESCRIPTION:Title: Simplicial quantum contextuality\nby Mehmet Kırtışo
ğlu (Bilkent University) as part of Bilkent Quantum Computing Seminar\n\n
Lecture 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 simpl
icial approach to contextuality generalizes the sheaf-theoretic approach o
f Abramsky and Brandenberger. Many standard results like the theorems of F
ine\, Kochen and Specker\, and Gleason can be established from this perspe
ctive. Owing to its generality\, the simplicial approach is a good candida
te for modeling adaptive MBQC.\nReferences: arXiv:2204.06648\nAdditional S
ources: arXiv:0809.4221\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20221216T113000Z
DTEND:20221216T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/13
DESCRIPTION:Title: Nonclassical correlations as a resource for computation\nby Selman Ipek (Bilkent University) as part of Bilkent Quantum Computin
g Seminar\n\nLecture held in SA 141.\n\nAbstract\nComputational power in M
BQC resides in the correlations between measurement outcomes. Here we cons
ider an MBQC scheme that is fully adaptive (feedforward of measurement out
comes is allowed)\, but where the classical side processing only performs
linear operations (mod 2 arithmetic). Although such a model is not even un
iversal for classical computation\, once supplied with a nonclassical reso
urce (e.g.\, quantum state\, PR box\, etc.)\, it is possible to compute no
nlinear functions within this computational model\, thus promoting the mod
el to classical universality.\nReferences: Anders/Browne (2008): arXiv:090
7.5449\nReferences: Raussendorf (2013): arXiv:0805.1002\nBackground materi
al: arXiv:0712.0921\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20221223T113000Z
DTEND:20221223T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/14
DESCRIPTION:Title: Generalized Bell Inequality Experiments and Computation\nby Selman Ipek (Bilkent University) as part of Bilkent Quantum Computin
g Seminar\n\nLecture held in SA 141.\n\nAbstract\nIn the simplified settin
g of non-adaptive MBQC the choice of measurement basis for one local syste
m (e.g.\, qubit) does not depend on the outcomes of any previous measureme
nts. Thus non-adaptive MBQC is similar in spirit to Bell-type experiments
consisting of distant parties that do not communicate. Following Hoban\, e
t al. we consider such Bell-type experiments and study the convex geometry
of the corresponding local and nonlocal regions. Experimental setups with
classical statistics that are explained by local hidden variable models (
LVH) are found to have limited computational power\, which is related to B
ell-type inequalities.\nReferences: arXiv:1009.5213\nReferences: arXiv:110
8.4798\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ho Yiu Chung (Bilkent University)
DTSTART:20221230T113000Z
DTEND:20221230T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/15
DESCRIPTION:Title: Contextuality as a resource for measurement-based quantum
computation beyond qubits\nby Ho Yiu Chung (Bilkent University) as par
t of Bilkent Quantum Computing Seminar\n\nLecture held in SA 141.\n\nAbstr
act\nWhen dealing with an MBQC with binary outcome measurements the follow
ing is true: a nonlinear function is computed if and only if the resource
is strongly contextual. However\, this tidy result does not remain true wh
en the set of outcomes is 𝑑>2. Frembs\, et al. consider the more genera
l case of 𝑑-outcome measurements and establish that strong contextualit
y is needed to compute functions (i.e.\, polynomials) of a certain degree
not possible for the classical side-processor.\n\nReferences: arXiv:1804.0
7364\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Sikora (Bilkent University)
DTSTART:20230210T113000Z
DTEND:20230210T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/16
DESCRIPTION:Title: Cohomological framework for contextual quantum computation
\nby Igor Sikora (Bilkent University) as part of Bilkent Quantum Compu
ting Seminar\n\nLecture held in SA 141.\n\nAbstract\nCohomological framewo
rk for contextual quantum computation (2019) (Igor)\nIn a previous talk th
e topological approach to contextuality was introduced based on chain comp
lexes and cohomology theory. Here many aspects of this framework are carri
ed over with the explicit goal of studying (temporally flat) MBQC more car
efully. Within this framework two types of topological invariants are iden
tified\; one relevant for the deterministic case\, while the other for the
probabilistic case. An essential takeaway is that the outputs of a comput
ation within this formalism are directly related to these topological inva
riants\, thus the “hardness” of the computation is characterized by eq
uivalence classes related to topology.\n\nReferences: arXiv:1602.04155\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20230217T113000Z
DTEND:20230217T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/17
DESCRIPTION:Title: Putting paradoxes to work: contextuality in measurement-ba
sed quantum computation\nby Selman Ipek (Bilkent University) as part o
f Bilkent Quantum Computing Seminar\n\nLecture held in SA 141.\n\nAbstract
\nThe topological approach to MBQC based on arXiv:1701.01888 and arXiv:160
2.04155 deals with the temporally flat case. One possible avenue to accomm
odating adaptivity is discussed using a so-called “iffy” proof.\n\nRef
erences: arXiv:2208.06624\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ho Yiu Chung (Bilkent University)
DTSTART:20230203T113000Z
DTEND:20230203T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/18
DESCRIPTION:Title: Contextuality as a resource for measurement-based quantum
computation beyond qubits\nby Ho Yiu Chung (Bilkent University) as par
t of Bilkent Quantum Computing Seminar\n\nLecture held in SA 141.\n\nAbstr
act\nWhen dealing with an MBQC with binary outcome measurements the follow
ing is true: a nonlinear function is computed if and only if the resource
is strongly contextual. However\, this tidy result does not remain true wh
en the set of outcomes is $d>2$. Frembs\, et al. consider the more general
case of $d$-outcome measurements and establish that strong contextuality
is needed to compute functions (i.e.\, polynomials) of a certain degree no
t possible for the classical side-processor.\n\nReferences: arXiv:1804.073
64\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20230303T113000Z
DTEND:20230303T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/19
DESCRIPTION:Title: Introduction to the Stabilizer Formalism\nby Selman Ip
ek (Bilkent University) as part of Bilkent Quantum Computing Seminar\n\nLe
cture held in SA 141.\n\nAbstract\nIn the finite-dimensional regime certai
n pure quantum states can be completely characterized by maximal abelian (
i.e.\, commuting) subgroups of the Pauli group. These are called stabilize
r states and well-known examples include Bell as well as Greenberger\, Hor
ne\, Zeilinger states. The stabilizer formalism is a subtheory of finite-d
imensional quantum mechanics consisting of stabilizer states\, Clifford un
itaries (i.e.\, unitaries that map one Pauli operator to another)\, and me
asurement of Pauli observables. The ability to fully describe such quantum
states in group theoretic terms makes their analysis extremely convenient
and they play an important role in quantum information processing and als
o quantum error correction. A key result for our purposes in this seminar
is the celebrated Gottesman-Knill theorem which establishes that any quant
um circuit built out of stabilizer states\, Clifford unitaries\, and Pauli
measurements (called stabilizer circuits) can be efficiently simulated on
a classical computer.\n\nReferences: arXiv:quant-ph/9807006\n\nReferences
: Nielsen/Chuang: QCQI (Ch. 10)\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20230317T113000Z
DTEND:20230317T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/20
DESCRIPTION:Title: Improved Simulation of Stabilizer Circuits\nby Selman
Ipek (Bilkent University) as part of Bilkent Quantum Computing Seminar\n\n
Lecture held in SA 141.\n\nAbstract\nThe Gottesman-Knill theorem establish
es that stabilizer circuits (defined previously) can be simulated efficien
tly on a classical computer. In arXiv:quant-ph/0406196 Aaronson and Gottes
man improve the efficiency of the classical simulation and demonstrate tha
t stabilizer circuits are (most likely) not universal for classical comput
ation. Circuits that are otherwise stabilizer with the exception of a smal
l number of non-Clifford gates are also considered and the complexity of s
uch circuits scales exponentially with the number of non-Clifford gates.\n
\nReferences: arXiv:quant-ph/0406196\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20230324T113000Z
DTEND:20230324T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/21
DESCRIPTION:Title: Universal Quantum Computation with ideal Clifford gates an
d noisy ancillas\nby Selman Ipek (Bilkent University) as part of Bilke
nt Quantum Computing Seminar\n\nLecture held in SA 141.\n\nAbstract\nIn st
udying the resources necessary to achieve a quantum speedup it is useful t
o distinguish between operations that are (a) free\, or (b) costly. The fa
ct that stabilizer circuits can be efficiently classically simulated sugge
sts that stabilizer operations be designated as free. This begs the questi
on of whether it is possible to augment the free stabilizer operations wit
h an additional costly resource (to be consumed) which promotes stabilizer
circuits to quantum universality. Bravyi and Kitaev (arXiv:quant-ph/04030
25) demonstrate that there are certain quantum states (deemed “magic”)
which achieve precisely this. They also detail a protocol for distilling
such magic states from a collection of noisy ancilla states.\n\nReferences
: arXiv:quant-ph/0403025\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20230331T113000Z
DTEND:20230331T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/22
DESCRIPTION:Title: Quantum universality and magic state distillation\nby
Selman Ipek (Bilkent University) as part of Bilkent Quantum Computing Semi
nar\n\nLecture held in SA 141.\n\nAbstract\nStabilizer circuits can be pro
moted to quantum universality via the injection of magic states. An open q
uestion is the determination of precisely which non-stabilizer quantum sta
tes can be considered “magic”. Following Reichardt\, we discuss magic
state distillation protocols that tighten the boundary between the classic
ally efficiently simulatable regime and that of full universal quantum com
putation.\n\nReferences: arXiv:0608085\n\nReferences: https://core.ac.uk/d
ownload/pdf/44132852.pdf\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20230414T113000Z
DTEND:20230414T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/23
DESCRIPTION:Title: Trading classical and quantum resources\nby Selman Ipe
k (Bilkent University) as part of Bilkent Quantum Computing Seminar\n\nLec
ture held in SA 141.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20230522T103000Z
DTEND:20230522T120000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/24
DESCRIPTION:Title: Quasiprobability methods in classical simulation (I)\n
by Selman Ipek (Bilkent University) as part of Bilkent Quantum Computing S
eminar\n\nLecture held in SA 141.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Howard (University of Galway)
DTSTART:20230407T113000Z
DTEND:20230407T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/25
DESCRIPTION:Title: Topics in Stabilizer Quantum Computation\nby Mark Howa
rd (University of Galway) as part of Bilkent Quantum Computing Seminar\n\n
Lecture held in SA 141.\n\nAbstract\nThe central question in quantum infor
mation theory is to delineate the operational capabilities achievable unde
r the rules of quantum mechanics but not achievable with classical physics
. As such\, it can be useful to tinker with hypothetical theories having d
ifferent sets of allowed state preparations\, transformations and measurem
ents\; different combinations can give us theories that are less powerful
than\, equal to\, or more powerful than quantum mechanics. When we attempt
to understand the computational power of circuits\, so-called stabilizer
circuits comprise a restricted class that are provably weaker than a gener
al (“universal”) quantum computer. For stabilizer circuits\, the descr
iption of the achievable states and their updates is efficient leading to
a classical simulation algorithm that is polynomial in the number of qubit
s. Remarkably\, it is easy to boost the power of stabilizer circuits to th
at of a universal quantum computer by adding access to non-stabilizer stat
es or operations. When error-correction is used these additional states or
operations are typically very costly. All of the above naturally suggests
a few questions that I will address:\n\n1) How should we classically simu
late stabilizer circuits interspersed with a few non-stabilizer gates\, an
d how does the runtime scale?\n\n2) How can we minimize the use of costly
non-stabilizer operations?\n\n3) What quantum mechanical property is missi
ng from stabilizer circuits but present in universal quantum computers?\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hakop Pashayan (Freie Universität Berlin)
DTSTART:20230526T113000Z
DTEND:20230526T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/26
DESCRIPTION:Title: Classical simulation of quantum circuits\nby Hakop Pas
hayan (Freie Universität Berlin) as part of Bilkent Quantum Computing Sem
inar\n\nLecture held in SA 141.\n\nAbstract\nI will give some background o
n classical simulation then I will present a general framework for simulat
ing quantum circuits using quasiprobabilistic methods. Through examples\,
I will demonstrate the strengths of this approach in its runtime performan
ce\, flexibility and generality.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Seddon (Phasecraft)
DTSTART:20230512T113000Z
DTEND:20230512T130000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/27
DESCRIPTION:Title: Stabilizer simulation methods for mixed magic states and n
oisy channels\nby James Seddon (Phasecraft) as part of Bilkent Quantum
Computing Seminar\n\nLecture held in SA 141.\n\nAbstract\nIt has been kno
wn since the early days of the stabilizer formalism that while Clifford ci
rcuits with stabilizer state inputs can be simulated efficiently in the nu
mber of qubits and operations\, more general circuits can be simulated wit
h an overhead growing exponentially with\, for example\, the number of T g
ates\, or some other "magic" resource. Quantifiers of magic resource known
as magic monotones formalize the notion that some states/operations are h
arder to simulate than others\, and various classical simulation algorithm
s have been proposed where performance guarantees depend explicitly on som
e magic monotone. A sequence of works on stabilizer rank culminated in the
powerful simulator of Ref. [1]\, which reduces runtime by replacing an ex
act stabilizer decomposition with a sparsified approximation\, but is larg
ely restricted to simulating pure state evolution. Meanwhile\, a parallel
avenue of research developed links between quasiprobability simulation met
hods and robustness-type monotones [2\, 3]\, yielding the insight that noi
sier circuits can be easier to simulate. Simulators of this type admit mix
ed initial states and more general quantum channels\, but tend to be slowe
r than stabilizer rank-based methods. In this seminar I will outline how s
tabilizer rank methods can be extended to deal with mixed magic states [4]
and noisy non-Clifford operations [5]\, in the process improving on the r
untime bounds of Ref. [1]. I will also discuss how this method (and the ot
hers introduced in Ref. [4]) can be situated within a broader framework of
simulators for general quantum circuits on qubits\, each with an associat
ed magic monotone\, showing that stabilizer rank and quasiprobability meth
ods are more closely related than they first appear.\n\n[1] Bravyi\, Brown
e\, Calpin\, Campbell\, Gosset & Howard (2019) arxiv:1808.00128\n\n[2] Pas
hayan\, Wallman & Bartlett (2015) arxiv:1503.07525\n\n[3] Howard & Campbel
l (2017) arxiv:1609.07488\n\n[4] Seddon\, Regula\, Pashayan\, Ouyang and C
ampbell (2021) arxiv:2002.06181\n\n[5] Seddon (2022) https://discovery.ucl
.ac.uk/id/eprint/10146361/\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240209T110000Z
DTEND:20240209T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/28
DESCRIPTION:Title: Introduction to Category Theory\nby Walker Stern (Bilk
ent University) as part of Bilkent Quantum Computing Seminar\n\nLecture he
ld in SA 141.\n\nAbstract\nThough category theory often feels abstruse whe
n first encountered\, it rests upon a few simple definitions which draw on
commonalities in mathematical arguments. In this preliminary talk\, we pr
esent some of the basic definitions of category theory\, and illustrate th
em through numerous examples. To wit\, we will discuss categories\, functo
rs\, natural transformations. The talk will conclude with a discussion of
universal properties and (co)limits\, with a particular emphasis on (co)pr
oducts.\n\nReferences:\n\n1. Emily Riehl. Category theory in Context. Dove
r\, 2016. Chapters 1 & 2\n\n2. Tom Leinster. Basic Category Theory. Cambri
dge\, 2014. Chapter 1\n\n3. Saunders Mac Lane. Categories for the Working
Mathematician. Springer GTM volume 5\, 1978.\nChapter\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20240216T110000Z
DTEND:20240216T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/29
DESCRIPTION:Title: Motivating Categorical Quantum Mechanics\nby Selman Ip
ek (Bilkent University) as part of Bilkent Quantum Computing Seminar\n\nLe
cture held in SA 141.\n\nAbstract\nCircuit diagrams\, such as those that i
mplement quantum protocols have long been a useful tool in the\nfield of q
uantum information and computation. Such diagrams\, in fact\, have a marke
d similarity to string\ndiagrams appearing in category theory\, an analogy
that was made precise by the seminal work of Abramsky\nand Coecke [1]. He
re we illustrate the naturalness of the categorical setting for describing
quantum protocols\nusing the example of quantum teleportation [1\, §2.1]
and motivate the kind of structures that will be needed\nto faithfully re
alize such quantum processes. Key notions in quantum theory\, such as stat
e\, transformation\,\nand measurement will be stated in a fully categorica
l language [1\, §6] whose precise meaning will be unpacked\nin subsequent
talks.\n\nReferences:\n\n1. Abramsky\, Samson\, and Bob Coecke. “Catego
rical quantum mechanics.” Handbook of quantum logic\nand quantum structu
res 2 (2009): 261-325. Section 2.\n\n2. Heunen\, Chris\, and Jamie Vicary.
Categories for Quantum Theory: an introduction. Oxford University\nPress\
, 2019. Chapter 0.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240223T110000Z
DTEND:20240223T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/30
DESCRIPTION:Title: Symmetric Monoidal Categories (I)\nby Walker Stern (Bi
lkent University) as part of Bilkent Quantum Computing Seminar\n\nLecture
held in SA 141.\n\nAbstract\nWe will introduce monoidal categories and sym
metric monoidal categories (SMCs) as well as the string\ndiagrams which pr
ovide graphical calculi for computations in SMCs (Primary reference: [1\,C
h. 1]\, secondary\nreferences: [2\, §3.1\, §3.3]\, [5\, Ch. XI]\, [3\, C
h. 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 categ
ories of vector spaces\, categories of finite dimensional Hilbert\nspaces\
, and several others.\n\nReferences:\n\n1. Heunen\, Chris\, and Jamie Vica
ry. Categories for Quantum Theory: an introduction. Oxford University\nPre
ss\, 2019.\n\n2. Samson Abramsky and Bob Coecke. Categorical Quantum Mecha
nics. arXiv:0808.1023\n\n3. Peter Selinger. A survey of graphical language
s for monoidal categories. arXiv:0908.3347\n\n4. John Baez. Quantum Gravit
y Seminar - Fall 2000. online notes\n\n5. Saunders Mac Lane. Categories fo
r the Working Mathematician. Springer GTM volume 5\, 1978.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20240301T110000Z
DTEND:20240301T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/31
DESCRIPTION:Title: Symmetric Monoidal Categories (II)\nby Redi Haderi (Bi
lkent University) as part of Bilkent Quantum Computing Seminar\n\nLecture
held in SA 141.\n\nAbstract\nThe structure involved in a symmetric monoida
l category is very broad\, which is of benefit to the general\ntheory. How
ever\, quantum mechanics\, which is typically formulated using Hilbert spa
ces\, requires substantially more structure than is present in an arbitra
ry SMC. In particular\, the notions of conjugation and transpose are of ke
y import in the study of quantum mechanics. In this talk\, we introduce da
gger structures\non categories\, and dagger SMCs\, which axiomatize some o
f the necessary structure (Primary reference: [1\,\n§4.3]\, secondary ref
erence: [2\,§2.3.1]). We then discuss internal mapping objects and compac
t closed categories (Primary reference: [1.§4.3]\, secondary references:
[2\,§3.4]\, [3]). We motivate these definitions for the\nfeatures of the
category of finite dimensional Hilbert Spaces\, and provide other example
s throughout.\n\nReferences:\n\n1. Abramsky\, Samson\, and Bob Coecke. Cat
egorical quantum mechanics. Handbook of quantum logic\nand quantum structu
res 2 (2009): 261-325.\n\n2. Heunen\, Chris\, and Jamie Vicary. Categories
for Quantum Theory: an introduction. Oxford University\nPress\, 2019.\n\n
3. Brian Day Note on compact closed categories. (doi: 10.1017/S14467887000
20334).\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker Stern (Bilkent University)
DTSTART:20240315T110000Z
DTEND:20240315T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/32
DESCRIPTION:Title: Symmetric Monoidal Categories (III)\nby Walker Stern (
Bilkent University) as part of Bilkent Quantum Computing Seminar\n\nLectur
e held in SA 141.\n\nAbstract\nIn a symmetric monoidal category\, the set
of maps from the monoidal unit to itself inherits additional\nstructure. T
hese scalars in the category are inspired by\, for instance\, the isomorph
ism between linear maps\nfrom $\\mathbb{C}$ to itself and the field $\\mat
hbb{C}$. However\, the additive structure and the notion of traces which a
re key to\nthe computation of quantum probabilities require some developme
nt. In this talk\, we describe biproducts\nand distributivity in (symmetri
c monoidal) category\, and the concomitant structures induced on scalars i
n\na symmetric monoidal category (Primary reference: [1\, §5]\, secondary
references: [2\,§2.2.3]). We introduce\ncategorical definitions of trace
s and partial traces\, the latter familiar in quantum information theory a
s\na procedure for obtaining information about a subsystem (Primary refere
nce: [2\, §4.6\, §5.1]\, secondary\nreference: [1\, §2.1\, §2.2]\, [3]
).\n\nReferences:\n\n1. Abramsky\, Samson\, and Bob Coecke. Categorical qu
antum mechanics. Handbook of quantum logic\nand quantum structures 2 (2009
): 261-325.\n\n2. Heunen\, Chris\, and Jamie Vicary. Categories for Quantu
m Theory: an introduction. Oxford University\nPress\, 2019.\n\n3. Andre Jo
yal\, Ross Street\, and Dominic Verity. Traced Monoidal Categories. (doi:1
0.1017/S0305004100074338).\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20240322T110000Z
DTEND:20240322T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/33
DESCRIPTION:Title: Categorical Quantum Mechanics\nby Selman Ipek (Bilkent
University) as part of Bilkent Quantum Computing Seminar\n\nLecture held
in SA 141.\n\nAbstract\nHaving built up the machinery of dagger SMCs\, we
revisit the motivating discussion and restate the\naxioms of quantum mecha
nics in a categorical language [1\, §6]. The Born rule for computing prob
abilities\ncan be derived from this point of view [1\, §6.1]. A number of
quantum protocols can also be described within\nthis formalism (e.g.\, lo
gic gate teleportation and entanglement swapping) with the aid of the diag
ramatic\ncalculus.\n\nReferences:\n\n1. Abramsky\, Samson\, and Bob Coecke
. Categorical quantum mechanics. Handbook of quantum logic\nand quantum st
ructures 2 (2009): 261-325. Section 6.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20240329T110000Z
DTEND:20240329T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/34
DESCRIPTION:Title: No-cloning theorem in categorical quantum mechanics\nb
y Redi Haderi (Bilkent University) as part of Bilkent Quantum Computing Se
minar\n\nLecture held in SA 141.\n\nAbstract\nAs with many algebraic struc
tures\, the conditions and data which define a monoid structure on a set c
an\nbe reframed diagrammatically\, leading to the notion of a monoid objec
t in a monoidal category. Dualizing this\ndefinition provides the notion o
f a comonoid. In this talk\, we introduce and discuss monoids and comonoid
s\nin SMCs. These structures can be used to prove that any category with a
notion of uniform deleting or\nuniform copying (or cloning) cannot descri
be quantum theory.\n\nReferences:\n\n1. Heunen\, Chris\, and Jamie Vicary.
Categories for Quantum Theory: an introduction. Oxford University\nPress\
, 2019. Chapter 4.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Torres Castillo (Bilkent University)
DTSTART:20240405T110000Z
DTEND:20240405T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/35
DESCRIPTION:Title: Frobenius algebras and complementarity\nby Victor Torr
es Castillo (Bilkent University) as part of Bilkent Quantum Computing Semi
nar\n\nLecture held in SA 141.\n\nAbstract\nIn quantum theory observables
that do not commute are considered incompatible. Maximally incompatible\,
or complementary\, observables are such that measurement of one destroys a
ll information about the\nother. This property is modeled in CQM using the
notion of Frobenius algebras. These Frobenius algebras\nmay be seen as an
enhancement of the monoids discussed in the previous talk using the theor
y of duality in\nsymmetric monoidal categories. We will additionally discu
ss extra properties and structures on Frobenius\nalgebras\, in particular\
, dagger Frobenius algebras. Frobenius algebras are also of substantial im
portance in\nthe study of topological quantum field theory (TQFT).\n\nRefe
rences:\n\n1. Heunen\, Chris\, and Jamie Vicary. Categories for Quantum Th
eory: an introduction. Oxford University\nPress\, 2019. Chapter 5\, Chapte
r 6.\n\n2. Joachim Kock. Frobenius algebras and 2D topological quantum fie
ld theories. Cambridge\, 2010.\nSection 3.6.\n\n3. Bob Coecke\, Dusko Pavl
ovic and Jamie Vicary. A new description of orthogonal bases. Mathematical
\nStructures in Computer Science (2012).\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20240503T110000Z
DTEND:20240503T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/37
DESCRIPTION:Title: Complete positivity\nby Selman Ipek (Bilkent Universit
y) as part of Bilkent Quantum Computing Seminar\n\nLecture held in SA 141.
\n\nAbstract\nTo handle a theory of mixed states — essential to the stud
y of quantum mechanics — it is necessary to\nconsider completely positiv
e maps in a compact closed dagger monoidal category $\\mathcal{C}$. We wil
l define mixed\nstates and completely positive maps\, and show how this le
ads to the construction of a category $\\text{CP}(\\mathcal{C})$\, whose\n
objects are certain Frobenius algebras in $\\mathcal{C}$\, and whose morph
isms are completely positive morphisms. We\nwill then discuss how both cla
ssical statistical mechanics and quantum mechanics can be expressed in the
\ncategory $\\text{CP}(\\mathcal{C})$.\n\nReferences:\n\n1. Heunen\, Chris
\, and Jamie Vicary. Categories for Quantum Theory: an introduction. Oxfor
d University\nPress\, 2019. Chapter 7\n\n2. Selinger\, Peter. Dagger Compa
ct Closed Categories and Completely Positive Maps. Electronic Notes\nin Th
eoretical Computer Science 170 (2007) 139–163\n\n3. Coecke\, Bob and Heu
nen\, Chris. Pictures of complete positivity in arbitrary dimension. Infor
mation\nand Computation 250 (2016) 50–58\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Redi Haderi (Bilkent University)
DTSTART:20240510T110000Z
DTEND:20240510T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/38
DESCRIPTION:Title: Bicategories and monoidal bicategories\nby Redi Haderi
(Bilkent University) as part of Bilkent Quantum Computing Seminar\n\nLect
ure held in SA 141.\n\nAbstract\nTo study categorifications of Hilbert spa
ces\, it is necessary to consider higher categories. In this talk we will\
ndevelop the idea of bicategories and monoidal bicategories\, 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\nd
iscussing oriented structures and oriented duals.\n\nReferences:\n\n1. Heu
nen\, Chris\, and Jamie Vicary. Categories for Quantum Theory: an introduc
tion. Oxford University\nPress\, 2019. Chapter 8\n\n2. Leinster\, Tom. Hig
her Operads\, Higher Categories. Cambridge University Press\, 2010. Sectio
n 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://stable.researchseminars.org/talk/BilkentMathGrad/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Walker H. Stern (Bilkent University)
DTSTART:20240517T110000Z
DTEND:20240517T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/39
DESCRIPTION:Title: Higher quantum theory and 2-Hilbert spaces\nby Walker
H. Stern (Bilkent University) as part of Bilkent Quantum Computing Seminar
\n\nLecture held in SA 141.\n\nAbstract\nIn this talk\, we will discuss ca
tegorifications of Hilbert spaces\, called $\\textit{2-Hilbert spaces}$. I
n much the same\nway as Hilbert spaces are sets with linear structures and
inner products satisfying a completeness condition\,\n2-Hilbert spaces ar
e categories with linear structures and inner products on their hom-sets\,
satisfying a\ncategorical completeness condition. We will develop the mon
oidal bicategory of 2-Hilbert spaces\, and discuss\nhow teleportation and
quantum dense coding manifest in this framework.\n\nReferences:\n\n1. Heun
en\, Chris\, and Jamie Vicary. Categories for Quantum Theory: an introduct
ion. Oxford University\nPress\, 2019. Chapter 8\n\n2. Baez\, John. Higher-
dimensional algebra II: 2-Hilbert spaces. Advances in Mathematics\, 127(2)
:125–189\,\n1997. Chapters 1-4\n\n3. Bartlett\, Bruce. On unitary 2-repr
esentations of finite groups and topological quantum field theory.\narXiv:
0901.3975. Sections 3.1\, 3.2\, & 3.3.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20240419T110000Z
DTEND:20240419T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/40
DESCRIPTION:Title: Categorical treatment of the Deutsch-Jozsa algorithm\n
by Selman Ipek (Bilkent University) as part of Bilkent Quantum Computing S
eminar\n\nLecture held in SA 141.\n\nAbstract\nThe Deutsch-Jozsa problem i
s a canonical example of a problem that can be solved by a quantum compute
r exponentially faster than a classical deterministic computer. Here we be
gin by describing the Deutsch-Jozsa problem and its solution according to
standard quantum theory [1\, §I.B]. We then describe how the solution wor
ks in categorical terms by building off of the notion of complementary str
uctures and Frobenius algebras built up in the previous talks.\n\nReferenc
es:\n\n1. Vicary\, Jamie. Topological structure of quantum algorithms. arX
iv preprint arXiv:1209.3917 (2013).\n\n2. Heunen\, Chris\, and Jamie Vicar
y. Categories for Quantum Theory: an introduction. Oxford University\nPres
s\, 2019. Chapter 6\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20240426T110000Z
DTEND:20240426T123000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/41
DESCRIPTION:Title: Applications of Categorical Quantum Mechanics to quantum c
omputation: ZX calculus\nby Selman Ipek (Bilkent University) as part o
f Bilkent Quantum Computing Seminar\n\nLecture held in SA 141.\n\nAbstract
\nSeveral quintessentially quantum notions\, such as no-cloning\, no-delet
ing\, as well as classical and complementary structures can be made precis
e in the categorical approach to quantum mechanics. The so-called ZX calcu
lus consists of two complementary classical structures on an underlying ob
ject in a compact dagger category. Many quantum gates used in quantum comp
utation have natural representations in the ZX-calculus. In this talk we w
ill give the main definition of the ZX-calculus and highlight interesting
aspects of the formalism\; e.g.\, ZX-calculus is sound and (approximately)
universal for quantum computation. Time permitting\, we will make connect
ions to the measurement-based model of quantum computation. \n\nReferences
:\n\n1. Heunen\, Chris\, and Jamie Vicary. Categories for Quantum Theory:
an introduction. Oxford University\nPress\, 2019. Chapter 6\n\n2. Coecke\,
Bob\, and Ross Duncan. Interacting quantum observables: categorical algeb
ra and diagrammatics. New J. Phys (13)\, 2011. arXiv: 0906.4725\n\n3. Dunc
an\, Ross. A graphical approach to measurement-based quantum computing. ar
Xiv preprint arXiv:1203.6242\, 2012.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Selman Ipek (Bilkent University)
DTSTART:20250401T143000Z
DTEND:20250401T153000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/42
DESCRIPTION:Title: Universal blind measurement-based quantum computations
\nby Selman Ipek (Bilkent University) as part of Bilkent Quantum Computing
Seminar\n\nLecture held in SA 141.\n\nAbstract\nWe consider a scenario in
which a client (Alice) with limited computational power\nwishes to perfor
m universal quantum computations via a server (Bob) without revealing thei
r\nunderlying computation. In this talk we discuss an interactive client-s
erver protocol due to\nBroadbent\, et al. [1]. This protocol requires no c
omputational assumptions and has perfect\nprivacy\, i.e.\, the server lear
ns nothing about the client'\;s inputs\, outputs\, or desired\ncomputat
ion. Furthermore\, the protocol is formulated using measurement-based quan
tum\ncomputing (MBQC)\, which is an alternative universal model of quantum
computation driven\nby single-qubit measurements on an entangled resource
state. For the purposes of private\nquantum computations\, a new universa
l resource for MBQC\, called the brickwork state\, is\nidentified and univ
ersality is established. Time permitting\, we also discuss variations of t
he\noriginal protocol with quantum inputs and quantum outputs\, as well as
a protocol for the\nclient to authenticate the results they receive from
the server.\n[1] A. Broadbent\, J. Fitzsimons\, E. Kashefi. Universal Blin
d Quantum Computation. 2009\n50th Annual IEEE Symp. on Found. of Comp. Sci
. DOI: 10.1109/FOCS.2009.36.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moises Bermejo Moran
DTSTART:20250408T143000Z
DTEND:20250408T153000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/43
DESCRIPTION:Title: Graph-theoretical contextuality II\nby Moises Bermejo
Moran as part of Bilkent Quantum Computing Seminar\n\nLecture held in SA 1
41.\n\nAbstract\nWe continue our review of “A combinatorial approach to
nonlocality and contextuality”\, by Acín\, Fritz\, Leverrier and Sainz
(2012). Classical and non-signalling correlations in contextuality scenari
os are described with two graph invariants of the graph capturing the comp
atibility between the outcomes. While quantum correlations can be approxim
ated with graph invariants\, a full characterisation requires the contextu
ality hypergraph. Remarkably\, such characterisation can be achieved with
a complete hierarchy of outer approximations corresponding with semidefini
te programs.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moises Bermejo Moran (Bilkent University)
DTSTART:20250422T143000Z
DTEND:20250422T153000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/44
DESCRIPTION:Title: Graph-theoretical contextuality III\nby Moises Bermejo
Moran (Bilkent University) as part of Bilkent Quantum Computing Seminar\n
\nLecture held in SA 141.\n\nAbstract\nWe will conclude our review of the
combinatorial approach to contextuality proposed in Acín-Fritz-Leverrier-
Sainz (2012) with the complete hierarchy of semidefinite programming appro
ximations to the set of quantum correlations. The first level of this hier
archy coincides with the Lovász approximation capturing almost quantum mo
dels that we discussed during the last session.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giacomo Nannicini (University of Southern California)
DTSTART:20250506T153000Z
DTEND:20250506T163000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/45
DESCRIPTION:Title: Quantum optimization: challenges and opportunities\nby
Giacomo Nannicini (University of Southern California) as part of Bilkent
Quantum Computing Seminar\n\nLecture held in SA 141.\n\nAbstract\nThis tal
k gives an optimizer's perspective on what is known\nabout the expected or
potential utility of quantum computers for\nmathematical optimization. We
will see that even if some of the\nexisting research trends require empir
ical validation and have escaped\nrigorous theoretical characterization of
potential advantage\, other\nareas of quantum optimization are supported
by well-established\nquantum subroutines\, which open up many interesting
possibilities in\nthe era of fault-tolerant quantum computation\, and poss
ibly even\nbefore.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Pironio (Université libre de Bruxelles)
DTSTART:20250527T143000Z
DTEND:20250527T153000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/48
DESCRIPTION:Title: Certification of quantum correlations at arbitrary distanc
es through routed Bell tests\nby Stefano Pironio (Université libre de
Bruxelles) as part of Bilkent Quantum Computing Seminar\n\nLecture held i
n SA 141.\n\nAbstract\nTransmission loss represents a major obstacle to th
e device-independent certification of quantum correlations over long dista
nces\, limiting applications such as device-independent quantum key distri
bution (DIQKD). In this talk\, I'll introduce the concept of routed Bell e
xperiments\, in which a particle sent to one side can be measured either n
ear or far from the source. I'll show how routed Bell tests involving only
entangled qubits can be used to certify quantum correlations even in the
presence of arbitrary loss on the channel to the distant device. This is a
chieved by adapting concepts from self-testing and quantum steering to the
routed Bell test framework. Finally\, as a natural extension of our appro
ach\, I'll outline a DIQKD protocol that\, in principle\, is secure over a
rbitrary distances.\nReference: arXiv:2502.12241\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sahil Imtiyaz (Basque Center for Applied Mathematics)
DTSTART:20251017T123000Z
DTEND:20251017T133000Z
DTSTAMP:20260404T110644Z
UID:BilkentMathGrad/49
DESCRIPTION:Title: Computation and Quantum Contextuality\nby Sahil Imtiya
z (Basque Center for Applied Mathematics) as part of Bilkent Quantum Compu
ting Seminar\n\nLecture held in SA 141.\n\nAbstract\nAbramsky and Brandenb
urger show that nonlocality and contextuality arise when locally compatibl
e data cannot be glued into a single global assignment. In a global topolo
gical data space\, interactions among locally defined maps can produce pat
terns that are consistent within each context yet incompatible globally—
the empirical hallmark of quantum contextuality. We make this concrete wit
h an evolving simplicial-bundle perspective and apply this framework to se
veral standard empirical models in quantum foundations. Finally\, we outli
ne a model of computation built on these structures that captures contextu
al behavior not natively handled by classical Turing-style interactive mod
els.\n
LOCATION:https://stable.researchseminars.org/talk/BilkentMathGrad/49/
END:VEVENT
END:VCALENDAR