6 research outputs found
Architecture and protocols for all-photonic quantum repeaters
An all-photonic repeater scheme based on a type of graph state called a
repeater graph state (RGS) promises tolerance to photon losses as well as
operational errors, and offers a fast Bell pair generation rate, limited only
by the RGS creation time (rather than enforced round-trip waits). Prior
research on the topic has focused on the RGS generation and analyzing the
secret key sharing rate, but there is a need to extend to use cases such as
distributed computation or teleportation as will be used in a general-purpose
Quantum Internet. Here, we propose a protocol and architecture that consider
how end nodes participate in the connection; the capabilities and
responsibilities of each node; the classical communications between nodes; and
the Pauli frame correction information per end-to-end Bell pair. We give
graphical reasoning on the correctness of the protocol via graph state
manipulation rules. We then show that the RGS scheme is well suited to use in a
link architecture connecting memory-based repeaters and end nodes for
applications beyond secret sharing. Finally, we discuss the practicality of
implementing our proposed protocol on quantum network simulators and how it can
be integrated into an existing proposed quantum network architecture.Comment: 10 pages, 8 figures, comments welcom
Lower Bounds on Number of QAOA Rounds Required for Guaranteed Approximation Ratios
The quantum alternating operator ansatz (QAOA) is a heuristic hybrid
quantum-classical algorithm for finding high-quality approximate solutions to
combinatorial optimization problems, such as Maximum Satisfiability. While QAOA
is well-studied, theoretical results as to its runtime or approximation ratio
guarantees are still relatively sparse. We provide some of the first lower
bounds for the number of rounds (the dominant component of QAOA runtimes)
required for QAOA. For our main result, (i) we leverage a connection between
quantum annealing times and the angles of QAOA to derive a lower bound on the
number of rounds of QAOA with respect to the guaranteed approximation ratio. We
apply and calculate this bound with Grover-style mixing unitaries and (ii) show
that this type of QAOA requires at least a polynomial number of rounds to
guarantee any constant approximation ratios for most problems. We also (iii)
show that the bound depends only on the statistical values of the objective
functions, and when the problem can be modeled as a -local Hamiltonian, can
be easily estimated from the coefficients of the Hamiltonians. For the
conventional transverse field mixer, (iv) our framework gives a trivial lower
bound to all bounded occurrence local cost problems and all strictly -local
cost Hamiltonians matching known results that constant approximation ratio is
obtainable with constant round QAOA for a few optimization problems from these
classes. Using our novel proof framework, (v) we recover the Grover lower bound
for unstructured search and -- with small modification -- show that our bound
applies to any QAOA-style search protocol that starts in the ground state of
the mixing unitaries.Comment: 24 pages, comments welcome, v3: correct some phrasing; results stay
unchange
A Substrate Scheduler for Compiling Arbitrary Fault-tolerant Graph States
Graph states are useful computational resources in quantum computing,
particularly in measurement-based quantum computing models. However, compiling
arbitrary graph states into executable form for fault-tolerant surface code
execution and accurately estimating the compilation cost and the run-time
resource cost remains an open problem. We introduce the Substrate Scheduler, a
compiler module designed for fault-tolerant graph state compilation. The
Substrate Scheduler aims to minimize the space-time volume cost of generating
graph states. We show that Substrate Scheduler can efficiently compile graph
states with thousands of vertices for "A Game of Surface Codes"-style
patch-based surface code systems. Our results show that our module generates
graph states with the lowest execution time complexity to date, achieving graph
state generation time complexity that is at or below linear in the number of
vertices and demonstrating specific types of graphs to have constant generation
time complexity. Moreover, it provides a solid foundation for developing
compilers that can handle a larger number of vertices, up to the millions or
billions needed to accommodate a wide range of post-classical quantum computing
applications.Comment: 11 pages, 11 figure
A Quantum Internet Architecture
Entangled quantum communication is advancing rapidly, with laboratory and
metropolitan testbeds under development, but to date there is no unifying
Quantum Internet architecture. We propose a Quantum Internet architecture
centered around the Quantum Recursive Network Architecture (QRNA), using
RuleSet-based connections established using a two-pass connection setup.
Scalability and internetworking (for both technological and administrative
boundaries) are achieved using recursion in naming and connection control. In
the near term, this architecture will support end-to-end, two-party
entanglement on minimal hardware, and it will extend smoothly to multi-party
entanglement and the use of quantum error correction on advanced hardware in
the future. For a network internal gateway protocol, we recommend (but do not
require) qDijkstra with seconds per Bell pair as link cost for routing; the
external gateway protocol is designed to build recursively. The strength of our
architecture is shown by assessing extensibility and demonstrating how robust
protocol operation can be confirmed using the RuleSet paradigm.Comment: 17 pages, 7 numbered figure
QuISP: a Quantum Internet Simulation Package
We present an event-driven simulation package called QuISP for large-scale
quantum networks built on top of the OMNeT++ discrete event simulation
framework. Although the behavior of quantum networking devices have been
revealed by recent research, it is still an open question how they will work in
networks of a practical size. QuISP is designed to simulate large-scale quantum
networks to investigate their behavior under realistic, noisy and heterogeneous
configurations. The protocol architecture we propose enables studies of
different choices for error management and other key decisions. Our confidence
in the simulator is supported by comparing its output to analytic results for a
small network. A key reason for simulation is to look for emergent behavior
when large numbers of individually characterized devices are combined. QuISP
can handle thousands of qubits in dozens of nodes on a laptop computer,
preparing for full Quantum Internet simulation. This simulator promotes the
development of protocols for larger and more complex quantum networks.Comment: 17 pages, 12 figure
Amplitude Amplification for Optimization via Subdivided Phase Oracle
We propose an algorithm using a modified variant of amplitude amplification
to solve combinatorial optimization problems via the use of a subdivided phase
oracle. Instead of dividing input states into two groups and shifting the phase
equally for all states within the same group, the subdivided phase oracle
changes the phase of each input state uniquely in proportion to their objective
value. We provide visualization of how amplitudes change after each iteration
of applying the subdivided phase oracle followed by conventional Grover
diffusion in the complex plane. We then show via numerical simulation that for
normal, skew normal, and exponential distribution of objective values, the
algorithm can be used to amplify the probability of measuring the optimal
solution to a significant degree independent of the search space size. In the
case of skew normal and exponential distributions, this probability can be
amplified to be close to unity, making our algorithm near deterministic. We
then modify our algorithm in order to demonstrate how it can be extended to a
broader set of objective value distributions. Finally, we discuss the speedup
compared to classical schemes using the query complexity model, and show that
our algorithm offers a significant advantage over these classical approaches.Comment: 9 pages, 7 figures, comments welcom