Unbounded loops in quantum programs: categories and weak while loops

• URL: http://arxiv.org/abs/2212.05371v1
• Date: Sat, 10 Dec 2022 22:03:51 GMT
• Title: Unbounded loops in quantum programs: categories and weak while loops
• Authors: Pablo Andr\'es-Mart\'inez
• Abstract summary: dissertation has two main contributions: (i) a categorical study of coherent quantum iteration and (ii) the introduction of weak while loops. The objective is to endow categories of quantum processes with a traced monoidal structure capable of modelling iterative quantum loops. A weak while loop is a classical control flow primitive that offers a trade-off between the collapse caused on each iteration and the amount of information gained.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Control flow of quantum programs is often divided into two different classes: classical and quantum. Quantum programs with classical control flow have their conditional branching determined by the classical outcome of measurements, and these collapse quantum data. Conversely, quantum control flow is coherent, i.e. it does not perturb quantum data; quantum walk-based algorithms are practical examples where coherent quantum feedback plays a major role. This dissertation has two main contributions: (i) a categorical study of coherent quantum iteration and (ii) the introduction of weak while loops. (i) The objective is to endow categories of quantum processes with a traced monoidal structure capable of modelling iterative quantum loops. To this end, the trace of a morphism is calculated via the execution formula, which adds up the contribution of all possible paths of the control flow. Haghverdi's unique decomposition categories are generalised to admit additive inverses and equipped with convergence criteria using basic topology. In this setting, it is possible to prove the validity of the execution formula as a categorical trace on certain categories of quantum processes. (ii) A weak while loop is a classical control flow primitive that offers a trade-off between the collapse caused on each iteration and the amount of information gained. The trade-off may be adjusted by tuning a parameter and, in certain situations, it is possible to set its value so that we may control the algorithm without sacrificing its quantum speed-up. As an example, it is shown that Grover's search problem can be implemented using a weak while loop, maintaining the same time complexity as the standard Grover's algorithm (as previously shown by Mizel).

Related papers

• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Quantum Algorithm for Querying Causality of Multiloop Scattering Amplitudes [0.0]
  The first application of a quantum algorithm to Feynman loop integrals is reviewed. The two on-shell states of a Feynman propagator are naturally encoded in a qubit. The problem to be addressed is the identification of the causal singular configurations of multiloop Feynman diagrams.
  arXiv  Detail & Related papers  (2022-11-10T11:12:10Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• Equivalence Checking of Dynamic Quantum Circuits [7.835264621634824]
  State-of-the-art quantum devices still contain only a very limited number of qubits. One possible way to execute more realistic algorithms in near-term quantum devices is to employ dynamic quantum circuits. This technique can help to significantly reduce the resources required to achieve a given accuracy of a quantum algorithm.
  arXiv  Detail & Related papers  (2021-06-03T08:03:22Z)
• Handling Non-Unitaries in Quantum Circuit Equivalence Checking [4.265279817927261]
  Quantum computers are reaching a level where interactions between classical and quantum computations can happen in real-time. This marks the advent of a new, broader class of quantum circuits: dynamic quantum circuits. They offer a broader range of available computing primitives that lead to new challenges for design tasks such as simulation, compilation, and verification.
  arXiv  Detail & Related papers  (2021-06-02T12:04:56Z)
• Exploiting dynamic quantum circuits in a quantum algorithm with superconducting qubits [0.207811670193148]
  We build dynamic quantum circuits on a superconducting-based quantum system. We exploit one of the most fundamental quantum algorithms, quantum phase estimation, in its adaptive version. We demonstrate that the version of real-time quantum computing with dynamic circuits can offer a substantial and tangible advantage.
  arXiv  Detail & Related papers  (2021-02-02T18:51:23Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum circuits with classical versus quantum control of causal order [0.0]
  It is known that quantum supermaps which respect a definite, predefined causal order between their input operations correspond to fixed-order quantum circuits. Here we identify two new types of circuits that naturally generalise the fixed-order case. We show that quantum circuits with quantum control of causal order can only generate "causal" correlations, compatible with a well-defined causal order.
  arXiv  Detail & Related papers  (2021-01-21T19:00:06Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.