Name: Quantum Connections in Sweden-10 Summer School
Start: 2022-06-12T07:00:00+02:00
End: 2022-06-25T12:00:00+02:00
Location: Högberga Gård

Monday, 6 June 2022
Tuesday, 7 June 2022
Wednesday, 8 June 2022
Thursday, 9 June 2022
Friday, 10 June 2022
Saturday, 11 June 2022
Sunday, 12 June 2022

07:00 Check-in (for participants from abroad and lecturers)
Check-in (for participants from abroad and lecturers)
07:00 - 19:00

Monday, 13 June 2022

08:00 Registration
Registration
08:00 - 09:15
Room: Fåhraeus salen

09:15 Opening Session and information from organizers
Opening Session and information from organizers
09:15 - 09:30
Room: Fåhraeus salen
09:30 New physics with superconductor-semiconductor hybrids - Charles Marcus (Niels Bohr Institute, University of Copenhagen)
New physics with superconductor-semiconductor hybrids
- Charles Marcus (Niels Bohr Institute, University of Copenhagen)
09:30 - 10:30
Room: Fåhraeus salen In these lectures, I will discuss the consequences of a recent breakthrough in material science, the growth of heterostructures containing superconductors and semiconductors. This includes studies of basic condensed matter physics, such as the superconductor-insulator transition and the so-called anomalous metal phase, to Majorana zero modes and gatemon qubits. In keeping with the theme of the workshop, I will emphasize resent results and opportunities in creating “designer networks” of Josephson junctions.
10:30 Coffee Break
Coffee Break
10:30 - 10:45
Room: Fåhraeus salen
10:45 New physics with superconductor-semiconductor hybrids - Charles Marcus (Niels Bohr Institute, University of Copenhagen)
New physics with superconductor-semiconductor hybrids
- Charles Marcus (Niels Bohr Institute, University of Copenhagen)
10:45 - 11:45
Room: Fåhraeus salen In these lectures, I will discuss the consequences of a recent breakthrough in material science, the growth of heterostructures containing superconductors and semiconductors. This includes studies of basic condensed matter physics, such as the superconductor-insulator transition and the so-called anomalous metal phase, to Majorana zero modes and gatemon qubits. In keeping with the theme of the workshop, I will emphasize resent results and opportunities in creating “designer networks” of Josephson junctions.
11:45 Lunch Break
Lunch Break
11:45 - 13:00
Room: Dining hall
13:00 Superconducting Qubits - Martinis John (University of California, Santa Barbara)
Superconducting Qubits
- Martinis John (University of California, Santa Barbara)
13:00 - 13:50
Room: Fåhraeus salen I will describe the basic physics of superconducting qubits, from a practical and intuitive point of view describing them as non-linear oscillators. I will also review the theory of the surface code, which is a good way to understand how fault-tolerant error correction works. All of this is put together in a review of the quantum supremacy experiment, where high-fidelity qubit operations are possible in a scalable system.
13:50 Break
Break
13:50 - 14:10
Room: Fåhraeus salen
14:10 Superconducting Qubits - John Martinis (University of California, Santa Barbara)
Superconducting Qubits
- John Martinis (University of California, Santa Barbara)
14:10 - 15:00
Room: Fåhraeus salen I will describe the basic physics of superconducting qubits, from a practical and intuitive point of view describing them as non-linear oscillators. I will also review the theory of the surface code, which is a good way to understand how fault-tolerant error correction works. All of this is put together in a review of the quantum supremacy experiment, where high-fidelity qubit operations are possible in a scalable system.
15:00 Coffee Break
Coffee Break
15:00 - 15:30
Room: Fåhraeus salen
15:30 BEC-BCS Crossover and the Unitary Fermi Gas - Zwierlein Martin (Massachusetts Institute of Technology)
BEC-BCS Crossover and the Unitary Fermi Gas
- Zwierlein Martin (Massachusetts Institute of Technology)
15:30 - 16:20
Room: Fåhraeus salen ?
16:20 Break
Break
16:20 - 16:40
Room: Fåhraeus salen
16:40 Realization of the Fermi-Hubbard Model with Quantum Gases - Zwierlein Martin (Massachusetts Institute of Technology)
Realization of the Fermi-Hubbard Model with Quantum Gases
- Zwierlein Martin (Massachusetts Institute of Technology)
16:40 - 17:30
Room: Fåhraeus salen ?
17:30 Break
Break
17:30 - 17:45
Room: Fåhraeus salen

17:45 with Marcus, Martinis, Zwierlein.
with Marcus, Martinis, Zwierlein.
17:45 - 18:30
Room: Fåhraeus salen

18:40 Welcome Drinks followed by Dinner
Welcome Drinks followed by Dinner
18:40 - 20:40
Tuesday, 14 June 2022
09:30 New physics with superconductor-semiconductor hybrids - Charles Marcus (University of Copenhagen)
New physics with superconductor-semiconductor hybrids
- Charles Marcus (University of Copenhagen)
09:30 - 10:30
Room: Fåhraeus salen In these lectures, I will discuss the consequences of a recent breakthrough in material science, the growth of heterostructures containing superconductors and semiconductors. This includes studies of basic condensed matter physics, such as the superconductor-insulator transition and the so-called anomalous metal phase, to Majorana zero modes and gatemon qubits. In keeping with the theme of the workshop, I will emphasize resent results and opportunities in creating “designer networks” of Josephson junctions.
10:30 Coffee Break
Coffee Break
10:30 - 10:45
Room: Fåhraeus salen
10:45 New physics with superconductor-semiconductor hybrids - Charles Marcus (University of Copenhagen)
New physics with superconductor-semiconductor hybrids
- Charles Marcus (University of Copenhagen)
10:45 - 11:45
Room: Fåhraeus salen In these lectures, I will discuss the consequences of a recent breakthrough in material science, the growth of heterostructures containing superconductors and semiconductors. This includes studies of basic condensed matter physics, such as the superconductor-insulator transition and the so-called anomalous metal phase, to Majorana zero modes and gatemon qubits. In keeping with the theme of the workshop, I will emphasize resent results and opportunities in creating “designer networks” of Josephson junctions.
11:45 Lunch Break
Lunch Break
11:45 - 13:00
Room: Dining hall
13:00 Superconducting Qubits - John Martinis (University of California, Santa Barbara)
Superconducting Qubits
- John Martinis (University of California, Santa Barbara)
13:00 - 13:50
Room: Fåhraeus salen I will describe the basic physics of superconducting qubits, from a practical and intuitive point of view describing them as non-linear oscillators. I will also review the theory of the surface code, which is a good way to understand how fault-tolerant error correction works. All of this is put together in a review of the quantum supremacy experiment, where high-fidelity qubit operations are possible in a scalable system.
13:50 Break
Break
13:50 - 14:10
Room: Fåhraeus salen
14:10 Superconducting Qubits - John Martinis (University of California, Santa Barbara)
Superconducting Qubits
- John Martinis (University of California, Santa Barbara)
14:10 - 15:00
Room: Fåhraeus salen I will describe the basic physics of superconducting qubits, from a practical and intuitive point of view describing them as non-linear oscillators. I will also review the theory of the surface code, which is a good way to understand how fault-tolerant error correction works. All of this is put together in a review of the quantum supremacy experiment, where high-fidelity qubit operations are possible in a scalable system.
15:00 Coffee Break
Coffee Break
15:00 - 15:30
Room: Fåhraeus salen
15:30 Fractionalization of charge and statistics in two dimensions - Michael Manfra (Purdue University)
Fractionalization of charge and statistics in two dimensions
- Michael Manfra (Purdue University)
15:30 - 16:20
Room: Fåhraeus salen A basic tenet of quantum mechanics is that all elementary particles are either bosons or fermions. Ensembles of bosons and fermions may act differently due to differences in their underlying statistical properties. For example, much of the electronic structure of ordinary solids may be explained by symmetry and noting electrons are fermions and obey the Pauli exclusion principle – fermions cannot exist in the same quantum state simultaneously. On the other hand, integral spin atoms and photons are bosons and are not constrained by the Pauli principle. Bose-Einstein condensation and superfluidity are some of the most spectacular properties of bosons. Starting in the early 1980’s it was theoretically conjectured that excitations that are neither bosons nor fermions may exist under special conditions in two dimensional systems. These unusual excitations were dubbed “anyons” by Frank Wilczek. Anyons may have fractional charge and fractional statistics, however directly probing these properties presents experimental challenges. My lectures will focus on experiments that demonstrate fractional statistics have observable consequences for the two-dimensional electron gas in the fractional quantum Hall regime. While theory indicated the necessity of anyons from the earliest days of the fractional quantum Hall effect, experimental verification has required many advances in materials, experimental probes, and understanding of the operation of electronic Fabry-Perot interferometers in the quantum Hall regime in real devices. I hope to describe how these challenges were met through the work of many groups over the last few decades and outline the physics that remains to be explored in future generations of experiments.
16:20 Break
Break
16:20 - 16:40
Room: Fåhraeus salen
16:40 Fractionalization of charge and statistics in two dimensions - Michael Manfra (Purdue University)
Fractionalization of charge and statistics in two dimensions
- Michael Manfra (Purdue University)
16:40 - 17:30
Room: Fåhraeus salen A basic tenet of quantum mechanics is that all elementary particles are either bosons or fermions. Ensembles of bosons and fermions may act differently due to differences in their underlying statistical properties. For example, much of the electronic structure of ordinary solids may be explained by symmetry and noting electrons are fermions and obey the Pauli exclusion principle – fermions cannot exist in the same quantum state simultaneously. On the other hand, integral spin atoms and photons are bosons and are not constrained by the Pauli principle. Bose-Einstein condensation and superfluidity are some of the most spectacular properties of bosons. Starting in the early 1980’s it was theoretically conjectured that excitations that are neither bosons nor fermions may exist under special conditions in two dimensional systems. These unusual excitations were dubbed “anyons” by Frank Wilczek. Anyons may have fractional charge and fractional statistics, however directly probing these properties presents experimental challenges. My lectures will focus on experiments that demonstrate fractional statistics have observable consequences for the two-dimensional electron gas in the fractional quantum Hall regime. While theory indicated the necessity of anyons from the earliest days of the fractional quantum Hall effect, experimental verification has required many advances in materials, experimental probes, and understanding of the operation of electronic Fabry-Perot interferometers in the quantum Hall regime in real devices. I hope to describe how these challenges were met through the work of many groups over the last few decades and outline the physics that remains to be explored in future generations of experiments.
17:30 Break
Break
17:30 - 17:45
Room: Fåhraeus salen

17:45 with Marcus, Martinis, Manfra.
with Marcus, Martinis, Manfra.
17:45 - 18:30
Room: Fåhraeus salen

19:00 Dinner
Dinner
19:00 - 20:00
Room: Dining hall
Wednesday, 15 June 2022
09:30 Exploring the gravity-quantum interface at low energies - Igor Pikovski (Stockholm University)
Exploring the gravity-quantum interface at low energies
- Igor Pikovski (Stockholm University)
09:30 - 10:30
Room: Fåhraeus salen The search for a quantum theory of gravity is one of the main challenges of modern physics. One major challenge is the lack of observable signatures that can guide theoretical developments. But in recent years, the interplay between quantum physics and general relativity at low energies has emerged as a promising new cross-disciplinary research field. The rapid progress in experimental control of quantum systems at novel scales, and a fresh quantum information perspective, have opened new opportunities for table-top tests to shine some light on this mostly unexplored regime of physics. In this lecture series, I will discuss some examples of this new field, from tests of Post-Newtonian quantum dynamics to quantum gravity phenomenology.
10:30 Coffee Break
Coffee Break
10:30 - 10:45
Room: Fåhraeus salen
10:45 Exploring the gravity-quantum interface at low energies - Igor Pikovski (Stockholm University)
Exploring the gravity-quantum interface at low energies
- Igor Pikovski (Stockholm University)
10:45 - 11:45
Room: Fåhraeus salen The search for a quantum theory of gravity is one of the main challenges of modern physics. One major challenge is the lack of observable signatures that can guide theoretical developments. But in recent years, the interplay between quantum physics and general relativity at low energies has emerged as a promising new cross-disciplinary research field. The rapid progress in experimental control of quantum systems at novel scales, and a fresh quantum information perspective, have opened new opportunities for table-top tests to shine some light on this mostly unexplored regime of physics. In this lecture series, I will discuss some examples of this new field, from tests of Post-Newtonian quantum dynamics to quantum gravity phenomenology.
11:45 Lunch Break
Lunch Break
11:45 - 13:00
Room: Dining hall
13:00 Fractional statistics - Martin Greiter (Julius-Maximilians-Universität)
Fractional statistics
- Martin Greiter (Julius-Maximilians-Universität)
13:00 - 13:50
Room: Fåhraeus salen In two and one spatial dimensions, we have the possibility of anyon statistics, that is, quantum statistics of identical particles which interpolates between the canonical choices of fermions and bosons. The mathematical reason is that in a path integral formulation, the group describing interchanges is not the permutation, but the braid group, which, in two dimensions, has a continuum of one-dimensional representation labeled by a U(1) phase parameter θ. Physically, this statistical parameter describes the phase acquired by the wave function as we interchange two anyons by winding them counterclockwise around each other. This phase leads to a fractional shift in the allowed values for the relative angular momenta. Anyons can be realized by composites consisting of electric charge and infinitesimally thin magnetic ﬂux tubes. Restrictions for fractional statistics on closed surfaces can be traced back to Dirac’s monopole condition. In ﬁeld theory, statistical transmutations, and in particular anyon statistics, can be implemented very naturally by a Chern-Simons term in a ﬁctitious gauge ﬁeld, which attaches both charge and ﬂux tubes to the particles. The quasi particle excitations of fractionally quantized Hall states obey anyon statistics. In one dimension, the crossings of anyons on a ring are always uni-directional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. In non-Abelian generalizations, anyons span an internal space of (degenerate) states and transform under higher dimensional representations of the braid group as we wind them around each other. Since the internal state vector is insensitive to local perturbations, non-Abelian anyons may prove instrumental in the construction of fault-tolerant quantum computers.
13:50 Break
Break
13:50 - 14:10
Room: Fåhraeus salen
14:10 Fractional statistics - Martin Greiter (Julius-Maximilians-Universität)
Fractional statistics
- Martin Greiter (Julius-Maximilians-Universität)
14:10 - 15:00
Room: Fåhraeus salen In two and one spatial dimensions, we have the possibility of anyon statistics, that is, quantum statistics of identical particles which interpolates between the canonical choices of fermions and bosons. The mathematical reason is that in a path integral formulation, the group describing interchanges is not the permutation, but the braid group, which, in two dimensions, has a continuum of one-dimensional representation labeled by a U(1) phase parameter θ. Physically, this statistical parameter describes the phase acquired by the wave function as we interchange two anyons by winding them counterclockwise around each other. This phase leads to a fractional shift in the allowed values for the relative angular momenta. Anyons can be realized by composites consisting of electric charge and infinitesimally thin magnetic ﬂux tubes. Restrictions for fractional statistics on closed surfaces can be traced back to Dirac’s monopole condition. In ﬁeld theory, statistical transmutations, and in particular anyon statistics, can be implemented very naturally by a Chern-Simons term in a ﬁctitious gauge ﬁeld, which attaches both charge and ﬂux tubes to the particles. The quasi particle excitations of fractionally quantized Hall states obey anyon statistics. In one dimension, the crossings of anyons on a ring are always uni-directional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. In non-Abelian generalizations, anyons span an internal space of (degenerate) states and transform under higher dimensional representations of the braid group as we wind them around each other. Since the internal state vector is insensitive to local perturbations, non-Abelian anyons may prove instrumental in the construction of fault-tolerant quantum computers.
15:00 Coffee Break
Coffee Break
15:00 - 15:30
Room: Fåhraeus salen
15:30 Quantum thermodynamics - Nicole Yunger Halpern (University of Maryland - College Park)
Quantum thermodynamics
- Nicole Yunger Halpern (University of Maryland - College Park)
15:30 - 16:20
Room: Fåhraeus salen Thermodynamics has shed light on engines, efficiency, and time’s arrow since the Industrial Revolution. But the steam engines that powered the Industrial Revolution were large and classical. Much of today’s technology and experiments are small-scale, quantum, far from equilibrium, and processing information. Nineteenth-century thermodynamics needs re-envisioning for the 21st century. Guidance has come from the mathematical toolkit of quantum information theory. Applying quantum information theory to thermodynamics sheds light on fundamental questions (e.g., how does entanglement spread during quantum thermalization? How can we distinguish quantum heat from quantum work?) and practicalities (e.g., quantum engines and the thermodynamic value of coherences). I will overview how quantum information theory is being used to revolutionize thermodynamics. Recommended reading: Yunger Halpern, Quantum Steampunk: The Physics of Yesterday’s Tomorrow, Johns Hopkins U. Press (2022).
16:20 Break
Break
16:20 - 16:40
Room: Fåhraeus salen
16:40 Quantum thermodynamics - Nicole Yunger Halpern (University of Maryland - College Park)
Quantum thermodynamics
- Nicole Yunger Halpern (University of Maryland - College Park)
16:40 - 17:30
Room: Fåhraeus salen Thermodynamics has shed light on engines, efficiency, and time’s arrow since the Industrial Revolution. But the steam engines that powered the Industrial Revolution were large and classical. Much of today’s technology and experiments are small-scale, quantum, far from equilibrium, and processing information. Nineteenth-century thermodynamics needs re-envisioning for the 21st century. Guidance has come from the mathematical toolkit of quantum information theory. Applying quantum information theory to thermodynamics sheds light on fundamental questions (e.g., how does entanglement spread during quantum thermalization? How can we distinguish quantum heat from quantum work?) and practicalities (e.g., quantum engines and the thermodynamic value of coherences). I will overview how quantum information theory is being used to revolutionize thermodynamics. Recommended reading: Yunger Halpern, Quantum Steampunk: The Physics of Yesterday’s Tomorrow, Johns Hopkins U. Press (2022).
17:30 Break
Break
17:30 - 17:45
Room: Fåhraeus salen
17:45 Quantum-optical topological states in arrays of qubits - Maxim Gorlach
Quantum-optical topological states in arrays of qubits
- Maxim Gorlach
17:45 - 18:15
Room: Fåhraeus salen
18:15 with Greiter, Yunger-Halpern, Gorlach
with Greiter, Yunger-Halpern, Gorlach
18:15 - 19:00
Room: Fåhraeus salen

19:00 Dinner
Dinner
19:00 - 20:00
Room: Dining hall
Thursday, 16 June 2022
09:30 Quantum Simulations and Quantum Error Correction with Bosonic Modes - Steve Girvin (Yale University)
Quantum Simulations and Quantum Error Correction with Bosonic Modes
- Steve Girvin (Yale University)
09:30 - 10:30
Room: Fåhraeus salen It is well-known that fermions are difficult to simulate with qubits because of their odd symmetry under exchange. It is less widely appreciated that bosons, despite their even symmetry under exchange, are also difficult to simulate with qubits. I will discuss how quantum hardware containing bosonic modes (microwave resonators) offers great hardware efficiency for simulation of many-body and lattice gauge models containing bosons. Time permitting, I will also discuss recent experimental success in quantum error correction beyond the break-even point using the GKP bosonic code.
10:30 Break
Break
10:30 - 10:45
Room: Fåhraeus salen
10:45 Quantum Simulations and Quantum Error Correction with Bosonic Modes - Steve Girvin (Yale University)
Quantum Simulations and Quantum Error Correction with Bosonic Modes
- Steve Girvin (Yale University)
10:45 - 11:45
Room: Fåhraeus salen It is well-known that fermions are difficult to simulate with qubits because of their odd symmetry under exchange. It is less widely appreciated that bosons, despite their even symmetry under exchange, are also difficult to simulate with qubits. I will discuss how quantum hardware containing bosonic modes (microwave resonators) offers great hardware efficiency for simulation of many-body and lattice gauge models containing bosons. Time permitting, I will also discuss recent experimental success in quantum error correction beyond the break-even point using the GKP bosonic code.
11:45 Lunch Break
Lunch Break
11:45 - 13:00
Room: Dining hall
13:00 Fractionalization of charge and statistics in two dimensions - Michael Manfra (Purdue University)
Fractionalization of charge and statistics in two dimensions
- Michael Manfra (Purdue University)
13:00 - 13:50
Room: Fåhraeus salen A basic tenet of quantum mechanics is that all elementary particles are either bosons or fermions. Ensembles of bosons and fermions may act differently due to differences in their underlying statistical properties. For example, much of the electronic structure of ordinary solids may be explained by symmetry and noting electrons are fermions and obey the Pauli exclusion principle – fermions cannot exist in the same quantum state simultaneously. On the other hand, integral spin atoms and photons are bosons and are not constrained by the Pauli principle. Bose-Einstein condensation and superfluidity are some of the most spectacular properties of bosons. Starting in the early 1980’s it was theoretically conjectured that excitations that are neither bosons nor fermions may exist under special conditions in two dimensional systems. These unusual excitations were dubbed “anyons” by Frank Wilczek. Anyons may have fractional charge and fractional statistics, however directly probing these properties presents experimental challenges. My lectures will focus on experiments that demonstrate fractional statistics have observable consequences for the two-dimensional electron gas in the fractional quantum Hall regime. While theory indicated the necessity of anyons from the earliest days of the fractional quantum Hall effect, experimental verification has required many advances in materials, experimental probes, and understanding of the operation of electronic Fabry-Perot interferometers in the quantum Hall regime in real devices. I hope to describe how these challenges were met through the work of many groups over the last few decades and outline the physics that remains to be explored in future generations of experiments.
13:50 Break
Break
13:50 - 14:10
Room: Fåhraeus salen
14:10 Fractionalization of charge and statistics in two dimensions - Michael Manfra (Purdue University)
Fractionalization of charge and statistics in two dimensions
- Michael Manfra (Purdue University)
14:10 - 15:00
Room: Fåhraeus salen A basic tenet of quantum mechanics is that all elementary particles are either bosons or fermions. Ensembles of bosons and fermions may act differently due to differences in their underlying statistical properties. For example, much of the electronic structure of ordinary solids may be explained by symmetry and noting electrons are fermions and obey the Pauli exclusion principle – fermions cannot exist in the same quantum state simultaneously. On the other hand, integral spin atoms and photons are bosons and are not constrained by the Pauli principle. Bose-Einstein condensation and superfluidity are some of the most spectacular properties of bosons. Starting in the early 1980’s it was theoretically conjectured that excitations that are neither bosons nor fermions may exist under special conditions in two dimensional systems. These unusual excitations were dubbed “anyons” by Frank Wilczek. Anyons may have fractional charge and fractional statistics, however directly probing these properties presents experimental challenges. My lectures will focus on experiments that demonstrate fractional statistics have observable consequences for the two-dimensional electron gas in the fractional quantum Hall regime. While theory indicated the necessity of anyons from the earliest days of the fractional quantum Hall effect, experimental verification has required many advances in materials, experimental probes, and understanding of the operation of electronic Fabry-Perot interferometers in the quantum Hall regime in real devices. I hope to describe how these challenges were met through the work of many groups over the last few decades and outline the physics that remains to be explored in future generations of experiments.
15:00 Coffee Break
Coffee Break
15:00 - 15:30
Room: Fåhraeus salen
15:30 Topological superconductivity - Annica Black-Schaffer (Uppsala University)
Topological superconductivity
- Annica Black-Schaffer (Uppsala University)
15:30 - 16:20
Room: Fåhraeus salen Topological states of matter have emerged in the last decade as one of the absolute most vibrant areas of condensed matter physics. These range from topological insulators and Weyl semimetals but also an abundance of different topological states in superconductors. The defining property for all these phases of matter is a global non-trivial topology of their electronic structure. This is fundamentally different from the traditional Landau paradigm traditionally used to classify matter, where local order parameters appearing due to spontaneous symmetry breaking play the key role. Topological superconductors are particularly interesting as they automatically join these two fundamentally different views of matter having both a global topological order and a local superconducting order parameter. Combining this with the distinctive particle-hole mixing in superconductors gives rise to emergent Majorana fermion states, that can be viewed as half electron quasiparticles offering unique possibilities to realize robust quantum computation. In these lectures I will cover the basic theory of topological superconductivity. Starting from an elementary understanding of conventional BCS superconductivity and topological insulators, I will discuss several different topological superconducting states, as well as focusing on how and why Majorana fermions appear as topological protected edge states.
16:20 Break
Break
16:20 - 16:40
Room: Fåhraeus salen
16:40 Topological superconductivity - Annica Black-Schaffer (Uppsala University)
Topological superconductivity
- Annica Black-Schaffer (Uppsala University)
16:40 - 17:30
Room: Fåhraeus salen Topological states of matter have emerged in the last decade as one of the absolute most vibrant areas of condensed matter physics. These range from topological insulators and Weyl semimetals but also an abundance of different topological states in superconductors. The defining property for all these phases of matter is a global non-trivial topology of their electronic structure. This is fundamentally different from the traditional Landau paradigm traditionally used to classify matter, where local order parameters appearing due to spontaneous symmetry breaking play the key role. Topological superconductors are particularly interesting as they automatically join these two fundamentally different views of matter having both a global topological order and a local superconducting order parameter. Combining this with the distinctive particle-hole mixing in superconductors gives rise to emergent Majorana fermion states, that can be viewed as half electron quasiparticles offering unique possibilities to realize robust quantum computation. In these lectures I will cover the basic theory of topological superconductivity. Starting from an elementary understanding of conventional BCS superconductivity and topological insulators, I will discuss several different topological superconducting states, as well as focusing on how and why Majorana fermions appear as topological protected edge states.
17:30 Break
Break
17:30 - 17:45
Room: Fåhraeus salen

17:45 with Girvin, Manfra, Black-Shaffer
with Girvin, Manfra, Black-Shaffer
17:45 - 18:30
Room: Fåhraeus salen

19:00 Conference Dinner
Conference Dinner
19:00 - 20:00
Room: Dining hall
Friday, 17 June 2022
09:30 Topological superconductors and Majorana fermions Or Odd-frequency superconductivity - Annica Black-Schaffer (Uppsala University)
Topological superconductors and Majorana fermions Or Odd-frequency superconductivity
- Annica Black-Schaffer (Uppsala University)
09:30 - 10:30
Room: Fåhraeus salen
10:30 Coffee Break
Coffee Break
10:30 - 10:45
Room: Fåhraeus salen
10:45 Topological superconductors and Majorana fermions Or Odd-frequency superconductivity - Annica Black-Schaffer (Uppsala University)
Topological superconductors and Majorana fermions Or Odd-frequency superconductivity
- Annica Black-Schaffer (Uppsala University)
10:45 - 11:45
Room: Fåhraeus salen
11:45 Lunch Break
Lunch Break
11:45 - 13:00
Room: Dining hall
13:00 Quantum Simulations and Quantum Error Correction with Bosonic Modes - Steve Girvin (Yale University)
Quantum Simulations and Quantum Error Correction with Bosonic Modes
- Steve Girvin (Yale University)
13:00 - 13:50
Room: Fåhraeus salen It is well-known that fermions are difficult to simulate with qubits because of their odd symmetry under exchange. It is less widely appreciated that bosons, despite their even symmetry under exchange, are also difficult to simulate with qubits. I will discuss how quantum hardware containing bosonic modes (microwave resonators) offers great hardware efficiency for simulation of many-body and lattice gauge models containing bosons. Time permitting, I will also discuss recent experimental success in quantum error correction beyond the break-even point using the GKP bosonic code.
13:50 Break
Break
13:50 - 14:10
Room: Fåhraeus salen
14:10 Quantum Simulations and Quantum Error Correction with Bosonic Modes - Steve Girvin (Yale University)
Quantum Simulations and Quantum Error Correction with Bosonic Modes
- Steve Girvin (Yale University)
14:10 - 15:00
Room: Fåhraeus salen It is well-known that fermions are difficult to simulate with qubits because of their odd symmetry under exchange. It is less widely appreciated that bosons, despite their even symmetry under exchange, are also difficult to simulate with qubits. I will discuss how quantum hardware containing bosonic modes (microwave resonators) offers great hardware efficiency for simulation of many-body and lattice gauge models containing bosons. Time permitting, I will also discuss recent experimental success in quantum error correction beyond the break-even point using the GKP bosonic code.
15:00 Coffee Break
Coffee Break
15:00 - 15:30
Room: Fåhraeus salen
15:30 Exceptional Topology of Non-Hermitian Systems - Emil Bergholtz (Stockholm University)
Exceptional Topology of Non-Hermitian Systems
- Emil Bergholtz (Stockholm University)
15:30 - 16:20
Room: Fåhraeus salen Non-Hermitian “Hamiltonians” occur in the effective description of various physical settings ranging from classical photonics to quantum materials. Using simple examples, I will discuss topological aspects of such systems related to the non-Hermitian concept of exceptional degeneracies at which both eigenvalues and eigenvectors coalesce. I will also discuss how the bulk-boundary correspondence is modified in non-Hermitian systems and how this might be harnessed in novel sensor devices.
16:20 Break
Break
16:20 - 16:40
Room: Fåhraeus salen
16:40 Exceptional Topology of Non-Hermitian Systems - Emil Bergholtz (Stockholm University)
Exceptional Topology of Non-Hermitian Systems
- Emil Bergholtz (Stockholm University)
16:40 - 17:30
Room: Fåhraeus salen Non-Hermitian “Hamiltonians” occur in the effective description of various physical settings ranging from classical photonics to quantum materials. Using simple examples, I will discuss topological aspects of such systems related to the non-Hermitian concept of exceptional degeneracies at which both eigenvalues and eigenvectors coalesce. I will also discuss how the bulk-boundary correspondence is modified in non-Hermitian systems and how this might be harnessed in novel sensor devices.
17:30 Break
Break
17:30 - 17:45
Room: Fåhraeus salen

17:45 with Black-Schaffer, Girvin, Bergholtz
with Black-Schaffer, Girvin, Bergholtz
17:45 - 18:30
Room: Fåhraeus salen

19:00 Dinner and social activities
Dinner and social activities
19:00 - 21:00
Saturday, 18 June 2022
09:15 In two and one spatial dimensions... - Martin Greiter (Julius-Maximilians-Universität)
In two and one spatial dimensions...
- Martin Greiter (Julius-Maximilians-Universität)
09:15 - 10:15
Room: Fåhraeus salen In two and one spatial dimensions, we have the possibility of anyon statistics, that is, quantum statistics of identical particles which interpolates between the canonical choices of fermions and bosons. The mathematical reason is that in a path integral formulation, the group describing interchanges is not the permutation, but the braid group, which, in two dimensions, has a continuum of one-dimensional representation labeled by a U(1) phase parameter θ. Physically, this statistical parameter describes the phase acquired by the wave function as we interchange two anyons by winding them counterclockwise around each other. This phase leads to a fractional shift in the allowed values for the relative angular momenta. Anyons can be realized by composites consisting of electric charge and infinitesimally thin magnetic ﬂux tubes. Restrictions for fractional statistics on closed surfaces can be traced back to Dirac’s monopole condition. In ﬁeld theory, statistical transmutations, and in particular anyon statistics, can be implemented very naturally by a Chern-Simons term in a ﬁctitious gauge ﬁeld, which attaches both charge and ﬂux tubes to the particles. The quasi particle excitations of fractionally quantized Hall states obey anyon statistics. In one dimension, the crossings of anyons on a ring are always uni-directional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. In non-Abelian generalizations, anyons span an internal space of (degenerate) states and transform under higher dimensional representations of the braid group as we wind them around each other. Since the internal state vector is insensitive to local perturbations, non-Abelian anyons may prove instrumental in the construction of fault-tolerant quantum computers.
10:15 Coffee Break
Coffee Break
10:15 - 10:30
Room: Fåhraeus salen
10:30 In two and one spatial dimensions... - Martin Greiter (Julius-Maximilians-Universität)
In two and one spatial dimensions...
- Martin Greiter (Julius-Maximilians-Universität)
10:30 - 11:30
Room: Fåhraeus salen In two and one spatial dimensions, we have the possibility of anyon statistics, that is, quantum statistics of identical particles which interpolates between the canonical choices of fermions and bosons. The mathematical reason is that in a path integral formulation, the group describing interchanges is not the permutation, but the braid group, which, in two dimensions, has a continuum of one-dimensional representation labeled by a U(1) phase parameter θ. Physically, this statistical parameter describes the phase acquired by the wave function as we interchange two anyons by winding them counterclockwise around each other. This phase leads to a fractional shift in the allowed values for the relative angular momenta. Anyons can be realized by composites consisting of electric charge and infinitesimally thin magnetic ﬂux tubes. Restrictions for fractional statistics on closed surfaces can be traced back to Dirac’s monopole condition. In ﬁeld theory, statistical transmutations, and in particular anyon statistics, can be implemented very naturally by a Chern-Simons term in a ﬁctitious gauge ﬁeld, which attaches both charge and ﬂux tubes to the particles. The quasi particle excitations of fractionally quantized Hall states obey anyon statistics. In one dimension, the crossings of anyons on a ring are always uni-directional, such that a fractional phase θ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. In non-Abelian generalizations, anyons span an internal space of (degenerate) states and transform under higher dimensional representations of the braid group as we wind them around each other. Since the internal state vector is insensitive to local perturbations, non-Abelian anyons may prove instrumental in the construction of fault-tolerant quantum computers.
11:45 Social activities - Excursion (please see the e-mail sent from us for the details)
Social activities - Excursion (please see the e-mail sent from us for the details)
11:45 - 19:45
Sunday, 19 June 2022

09:00 Free time (please see the notes for the details)
Free time (please see the notes for the details)
09:00 - 21:00