# 3rd QSC General Assembly

On the 4th of December we will be organizing the third QSC General Assembly.

**Date and Time**

Wednesday, December 4, 2019. The technical program starts as 10:30 h (walk-in as of 10:00h).

**Location**

Public library OBA (”Openbare Bibliotheek Amsterdam''), OBA Forum, 6^{th} floor,

Oosterdokskade 143, Amsterdam.

OBA is located next to the Amsterdam Central Station, a 10 minutes walk from the train station.

**Program**

10:00 - 10:30 Welcome and coffee

10:30 - 11:15 Tom O'Brien (Leiden):

*Nearly optimal measurement scheduling for partial tomography of quantum states*

11:15 - 11:45 Yfke Dulek (Amsterdam):

*Secure multi-party quantum computation with a dishonest majority*

11:45 - 12:00 Harry Buhrman (Amsterdam) *- Developments in QSC*

12:00 - 13:30 Lunch / room to discuss

13:30 - 14:15 Barbara Kraus (Innsbruck): *From compressible to universal quantum computation*

14:15 - 14:45 Alex Grilo (Amsterdam):

*Recent advances in Zero-knowledge protocols in the quantum setting*

14:45 - 15:15 Tea / Coffee

15:15 - 16:00 Wolfgang Tittel (Delft): *Towards quantum repeaters*

16:00 - 16:45 Panel by Joris van Hoboken (Amsterdam):

*Legal and ethical perspectives on quantum computing*

17:00 - 19:30 Walking Dinner

**Registration**

Registration is **free but required. Please register by wednesday November 27.**

Organisers: Ronald de Wolf, Harry Buhrman, Doutzen Abma and Susanne van Dam (Secretary)

**Abstracts: **

**Tom O'Brien (Leiden):** *Nearly optimal measurement scheduling for partial tomography of quantum states*

Many applications of quantum simulation require to prepare and then characterize quantum states by performing an efficient partial tomography to estimate observables corresponding to k-body reduced density matrices (k-RDMs). For instance, variational algorithms for the quantum simulation of chemistry usually require that one measure the fermionic 2-RDM. While such marginals provide a tractable description of quantum states from which many important properties can be computed, their determination often requires a prohibitively large number of circuit repetitions. Here we describe a method by which all elements of k-body qubit RDMs acting on N qubits can be directly measured with a number of circuits scaling as O(3klog^(k−1)N), an exponential improvement in N over prior art. Next, we show that if one is able to implement a linear depth circuit on a linear array prior to measurement,

then one can directly measure all elements of the fermionic 2-RDM using only O(N^2) circuits. We prove that this result is asymptotically optimal, thus establishing an exponential separation between the number of circuits required to directly measure all elements of qubit versus fermion RDMs. We further demonstrate a technique to estimate the expectation value of any linear combination of fermionic 2-RDM elements using O(N^4/ω) circuits, each with only O(ω) gates on a linear array where ω≤N is a free parameter. We expect these results will improve the viability of many proposals for near-term quantum simulation.

**Yfke Dulek (Amsterdam):** *Secure multi-party quantum computation with a dishonest majority*

Suppose that multiple people, each with their own quantum computer and connected through quantum channels, want to perform a joint computation. They do not trust each other, so they want to ensure that their inputs to the computation remain private, and that whatever outcome comes out is the correct output. This problem is known as multi-party quantum computation. Until recently, secure protocols were only known for settings where either the number of honest parties outweighs the number of dishonest parties, or only two parties are involved in total. We extend ideas for the two-party setting to devise an efficient protocol for multi-party quantum computation, that is secure even if all-but-one parties are colluding adversaries. In this talk, I will give an overview of the protocol, and hightlight its key ingredients. This talk is based on joint work with Alex Grilo, Stacey Jeffery, Christian Majenz, and Christian Schaffner.

**Barbara Kraus (Innsbruck)**: *From compressible to universal quantum computation*

Quantum algorithms which are composed of so-called matchgates can be compressed into an exponentially smaller quantum computation. The the usage of an additional resource, the so-called magic states, elevates the computational power to universal quantum computation, while maintaining the same gate set. I will present the characterization of these magic states and discuss the consequences of these results in the context of quantum computation.

**Alex Grilo (Amsterdam): ***Recent advances in Zero-knowledge protocols in the quantum setting*

Zero-knowledge proofs are a fundamental building block in classical Cryptography, having far-reaching applications. Recently, there has been some effort in improving our understanding of Zero-knowledge protocols in the quantum setting, hopefully leading to striking objects as in classical case. In this talk, I will give an overview of such results, highlighting some tools that could be also used in different contexts. This talk is based on a joint work with William Slofstra and Henry Yuen, and on a joint work with Anne Broadbent.

**Wolfgang Tittel (Leiden):** *Towards quantum repeaters*

Exploiting the non-classical properties of entangled states as well as quantum memory for light, quantum repeaters allow quantum communication in theory over arbitrarily long distances. I will describe a quantum repeater architecture based on spectral multiplexing and briefly discuss a specific realization of quantum memory for light using rare-earth-ion doped crystals.