Flow conditions for continuous variable measurement-based quantum computing

• URL: http://arxiv.org/abs/2104.00572v3
• Date: Wed, 13 Jul 2022 13:01:15 GMT
• Title: Flow conditions for continuous variable measurement-based quantum computing
• Authors: Robert I. Booth and Damian Markham
• Abstract summary: We introduce flow-based methods for quantum computation with continuous-variable graph states. We show that an MBQC with CV-flow approximates a unitary arbitrarily well in the infinite-squeezing limit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In measurement-based quantum computing (MBQC), computation is carried out by a sequence of measurements and corrections on an entangled state. Flow, and related concepts, are powerful techniques for characterising the dependence of the corrections on previous measurement results. We introduce flow-based methods for quantum computation with continuous-variable graph states, which we call CV-flow. These are inspired by, but not equivalent to, the notions of causal flow and g-flow for qubit MBQC. We also show that an MBQC with CV-flow approximates a unitary arbitrarily well in the infinite-squeezing limit, addressing issues of convergence which are unavoidable in the infinite-dimensional setting. In developing our proofs, we provide a method for converting a CV-MBQC computation into a circuit form, analogous to the circuit extraction method of Miyazaki et al, and an efficient algorithm for finding CV-flow when it exists based on the qubit version by Mhalla and Perdrix. Our results and techniques naturally extend to the cases of MBQC for quantum computation with qudits of prime local dimension.

Related papers

• Two quantum algorithms for solving the one-dimensional advection-diffusion equation [0.0]
  Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection-diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other.
  arXiv  Detail & Related papers  (2023-12-30T21:23:15Z)
• Deterministic Ans\"atze for the Measurement-based Variational Quantum Eigensolver [0.0]
  This study introduces MBVQE-ans"atze that respect determinism and resemble the widely used problem-agnostic hardware-efficient VQE ansatz. We find that ensuring determinism works better via postselection than by adaptive measurements at the expense of increased sampling cost. We propose an efficient MBQC-inspired method to prepare the resource state, specifically the cluster state, on hardware with heavy-hex connectivity.
  arXiv  Detail & Related papers  (2023-12-20T18:08:25Z)
• Mapping quantum circuits to shallow-depth measurement patterns based on graph states [0.0]
  We create a hybrid simulation technique for measurement-based quantum computing. We show that groups of fully commuting operators can be implemented using fully-parallel, i.e., non-adaptive, measurements. We discuss how such circuits can be implemented in constant quantum depths by employing quantum teleportation.
  arXiv  Detail & Related papers  (2023-11-27T19:00:00Z)
• Real-time error mitigation for variational optimization on quantum hardware [45.935798913942904]
  We define a Real Time Quantum Error Mitigation (RTQEM) algorithm to assist in fitting functions on quantum chips with VQCs. Our RTQEM routine can enhance VQCs' trainability by reducing the corruption of the loss function.
  arXiv  Detail & Related papers  (2023-11-09T19:00:01Z)
• Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr\"odinger Equation [56.9919517199927]
  "Wasserstein Quantum Monte Carlo" (WQMC) uses the gradient flow induced by the Wasserstein metric, rather than Fisher-Rao metric, and corresponds to transporting the probability mass, rather than teleporting it. We demonstrate empirically that the dynamics of WQMC results in faster convergence to the ground state of molecular systems.
  arXiv  Detail & Related papers  (2023-07-06T17:54:08Z)
• Graphix: optimizing and simulating measurement-based quantum computation on local-Clifford decorated graph [0.0]
  We introduce an open-source software library Graphix, which optimize and simulates measurement-based quantum computation (MBQC) By combining the measurement calculus with an efficient graph state simulator, Graphix allows the classical preprocessing of Pauli measurements in the measurement patterns.
  arXiv  Detail & Related papers  (2022-12-22T18:58:20Z)
• End-to-end resource analysis for quantum interior point methods and portfolio optimization [63.4863637315163]
  We provide a complete quantum circuit-level description of the algorithm from problem input to problem output. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm.
  arXiv  Detail & Related papers  (2022-11-22T18:54:48Z)
• Compilation of algorithm-specific graph states for quantum circuits [55.90903601048249]
  We present a quantum circuit compiler that prepares an algorithm-specific graph state from quantum circuits described in high level languages. The computation can then be implemented using a series of non-Pauli measurements on this graph state.
  arXiv  Detail & Related papers  (2022-09-15T14:52:31Z)
• Outcome determinism in measurement-based quantum computation with qudits [0.0]
  In measurement-based quantum computing, computation is carried out by a sequence of measurements and corrections on an entangled state. We introduce flow-based methods for MBQC with qudit graph states, which we call Zd-flow, when the local dimension is an odd prime. Our main results are that Zd-flow is a necessary and sufficient condition for a strong form of outcome determinism.
  arXiv  Detail & Related papers  (2021-09-28T15:36:36Z)
• Q-Match: Iterative Shape Matching via Quantum Annealing [64.74942589569596]
  Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) This paper proposes Q-Match, a new iterative quantum method for QAPs inspired by the alpha-expansion algorithm. Q-Match can be applied for shape matching problems iteratively, on a subset of well-chosen correspondences, allowing us to scale to real-world problems.
  arXiv  Detail & Related papers  (2021-05-06T17:59:38Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)

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.