Tower: Data Structures in Quantum Superposition

@article{Yuan2022TowerDS,
  title={Tower: Data Structures in Quantum Superposition},
  author={Charles Yuan and Michael Carbin},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.10255}
}
Emerging quantum algorithms for problems such as element distinctness, subset sum, and closest pair demonstrate computational advantages by relying on abstract data structures . Practically realizing such an algorithm as a program for a quantum computer requires an efficient implementation of the data structure whose operations correspond to unitary operators that manipulate quantum superpositions of data. To correctly operate in superposition, an implementation must satisfy three properties… 

References

SHOWING 1-10 OF 58 REFERENCES
SQUARE: Strategic Quantum Ancilla Reuse for Modular Quantum Programs via Cost-Effective Uncomputation
TLDR
This paper presents SQUARE (Strategic QUantum Ancilla REuse), a compilation infrastructure that tackles allocation and reclamation of scratch qubits in modular quantum programs, and proposes an improved metric, the “active quantum volume,” and uses this metric to evaluate the effectiveness of the algorithm.
LIQUi|>: A Software Design Architecture and Domain-Specific Language for Quantum Computing
Languages, compilers, and computer-aided design tools will be essential for scalable quantum computing, which promises an exponential leap in our ability to execute complex tasks. LIQUi|> is a
Parallelizing the queries in a bucket-brigade quantum random access memory
TLDR
It is concluded that, in theory, fault-tolerant bucket- Brigade quantum RAM queries can be performed approximately with the speed of classical RAM, and the exponentially many ancillas from the bucket-brigade addressing scheme are a tradeoff cost for achieving exponential query speedup compared to quantum read-only memories whose queries are sequential by design.
Graph comparison via nonlinear quantum search
TLDR
An efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for a pair of arbitrary graphs and thus provides a meaningful measure of graph similarity and demonstrates the power of nonlinear quantum search techniques to solve a subset of NP-hard problems.
Toward the first quantum simulation with quantum speedup
TLDR
It is argued that simulating the time evolution of spin systems is a classically hard problem of practical interest that is among the easiest to address with early quantum devices, and develops optimized implementations and performs detailed resource analyses for several leading quantum algorithms for this problem.
Quipper: a scalable quantum programming language
TLDR
Quipper, a scalable, expressive, functional, higher-order quantum programming language, which is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware.
A functional quantum programming language
  • Jonathan Grattage
  • Computer Science
    20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05)
  • 2005
TLDR
QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings explicit, and preserves superpositions and entanglement -which is essential for quantum parallelism.
Silq: a high-level quantum language with safe uncomputation and intuitive semantics
TLDR
This work presents Silq, the first quantum language that addresses this challenge by supporting safe, automatic uncomputation, and enables an intuitive semantics that implicitly drops temporary values, as in classical computation.
Quantum Programming with Inductive Datatypes: Causality and Affine Type Theory
TLDR
This paper constructs a sound categorical model for the quantum programming language QPL and provides the first detailed semantic treatment of user-defined inductive datatypes in quantum programming, and shows the denotational interpretation is invariant with respect to big-step reduction.
Limits of quantum speed-ups for computational geometry and other problems: Fine-grained complexity via quantum walks
TLDR
The theory of fine-grained complexity is extended to the quantum setting, and new lower-bounds on the time complexity of quantum algorithms for several computational problems are shown, implying tight limits on the quantum speedup that is possible for these problems.
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