2,734 research outputs found
Quantum Random Access Codes with Shared Randomness
We consider a communication method, where the sender encodes n classical bits
into 1 qubit and sends it to the receiver who performs a certain measurement
depending on which of the initial bits must be recovered. This procedure is
called (n,1,p) quantum random access code (QRAC) where p > 1/2 is its success
probability. It is known that (2,1,0.85) and (3,1,0.79) QRACs (with no
classical counterparts) exist and that (4,1,p) QRAC with p > 1/2 is not
possible.
We extend this model with shared randomness (SR) that is accessible to both
parties. Then (n,1,p) QRAC with SR and p > 1/2 exists for any n > 0. We give an
upper bound on its success probability (the known (2,1,0.85) and (3,1,0.79)
QRACs match this upper bound). We discuss some particular constructions for
several small values of n.
We also study the classical counterpart of this model where n bits are
encoded into 1 bit instead of 1 qubit and SR is used. We give an optimal
construction for such codes and find their success probability exactly--it is
less than in the quantum case.
Interactive 3D quantum random access codes are available on-line at
http://home.lanet.lv/~sd20008/racs .Comment: 51 pages, 33 figures. New sections added: 1.2, 3.5, 3.8.2, 5.4 (paper
appears to be shorter because of smaller margins). Submitted as M.Math thesis
at University of Waterloo by M
Simulating Large Quantum Circuits on a Small Quantum Computer
Limited quantum memory is one of the most important constraints for near-term
quantum devices. Understanding whether a small quantum computer can simulate a
larger quantum system, or execute an algorithm requiring more qubits than
available, is both of theoretical and practical importance. In this Letter, we
introduce cluster parameters and of a quantum circuit. The tensor
network of such a circuit can be decomposed into clusters of size at most
with at most qubits of inter-cluster quantum communication. We propose a
cluster simulation scheme that can simulate any -clustered quantum
circuit on a -qubit machine in time roughly , with further
speedups possible when taking more fine-grained circuit structure into account.
We show how our scheme can be used to simulate clustered quantum systems --
such as large molecules -- that can be partitioned into multiple significantly
smaller clusters with weak interactions among them. By using a suitable
clustered ansatz, we also experimentally demonstrate that a quantum variational
eigensolver can still achieve the desired performance for estimating the energy
of the BeH molecule while running on a physical quantum device with half
the number of required qubits.Comment: Codes are available at https://github.com/TianyiPeng/Partiton_VQ
Zoom In, Class Out: An Event Study on Publicly Traded Ed Tech Firm Valuations During COVID-19
This paper examines how publicly traded Ed Tech firms reacted to negative announcements regarding COVID-19. Using an event study method, I document how an international portfolio of Ed Tech firms react across multiple event windows. The results show that Ed Tech firms reacted positively to the announcement of the first US death and negatively to the World Health Organization’s declaration that COVID-19 was a pandemic. Additionally, differences in geographical location did not impact cumulative abnormal returns across event windows. Finally, firm-specific characteristics such as volatility and financial leverage had little or no significance on stock returns
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