Deterministic Ans\"atze for the Measurement-based Variational Quantum Eigensolver

• URL: http://arxiv.org/abs/2312.13241v1
• Date: Wed, 20 Dec 2023 18:08:25 GMT
• Title: Deterministic Ans\"atze for the Measurement-based Variational Quantum Eigensolver
• Authors: Anna Schroeder, Matthias Heller, Mariami Gachechiladze
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Measurement-based quantum computing (MBQC) is a promising approach to reducing circuit depth in noisy intermediate-scale quantum algorithms such as the Variational Quantum Eigensolver (VQE). Unlike gate-based computing, MBQC employs local measurements on a preprepared resource state, offering a trade-off between circuit depth and qubit count. Ensuring determinism is crucial to MBQC, particularly in the VQE context, as a lack of flow in measurement patterns leads to evaluating the cost function at irrelevant locations. This study introduces MBVQE-ans\"atze that respect determinism and resemble the widely used problem-agnostic hardware-efficient VQE ansatz. We evaluate our approach using ideal simulations on the Schwinger Hamiltonian and $XY$-model and perform experiments on IBM hardware with an adaptive measurement capability. In our use case, we find that ensuring determinism works better via postselection than by adaptive measurements at the expense of increased sampling cost. Additionally, we propose an efficient MBQC-inspired method to prepare the resource state, specifically the cluster state, on hardware with heavy-hex connectivity, requiring a single measurement round, and implement this scheme on quantum computers with $27$ and $127$ qubits. We observe notable improvements for larger cluster states, although direct gate-based implementation achieves higher fidelity for smaller instances.

Related papers

• Benchmarking Quantum Annealers with Near-Optimal Minor-Embedded Instances [0.0]
  This paper establishes a new protocol to generate graph instances with their associated near-optimal minor-embedding mappings to D-Wave Quantum Annealers. We use this method to benchmark QA on large instances of unconstrained and constrained optimization problems and compare the performance of the QPU with efficient classical solvers.
  arXiv  Detail & Related papers  (2024-05-02T15:19:39Z)
• Measurement-Based Quantum Approximate Optimization [0.24861619769660645]
  We focus on measurement-based quantum computing protocols for approximate optimization. We derive measurement patterns for applying QAOA to the broad and important class of QUBO problems. We discuss the resource requirements and tradeoffs of our approach to that of more traditional quantum circuits.
  arXiv  Detail & Related papers  (2024-03-18T06:59:23Z)
• 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)
• Robust and efficient verification of graph states in blind measurement-based quantum computation [52.70359447203418]
  Blind quantum computation (BQC) is a secure quantum computation method that protects the privacy of clients. It is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension.
  arXiv  Detail & Related papers  (2023-05-18T06:24:45Z)
• Applications and resource reductions in measurement-based variational quantum eigensolvers [0.0]
  We present three different problems which are solved by employing a measurement-based implementation of the variational quantum eigensolver algorithm (MBVQE) We show that by utilising native measurement-based gates rather than standard gates, such as the standard CNOT, MBQCs may be obtained that are both shallow and have simple connectivity while simultaneously exhibiting a large expressibility.
  arXiv  Detail & Related papers  (2023-02-01T22:58:12Z)
• 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)
• QSAN: A Near-term Achievable Quantum Self-Attention Network [73.15524926159702]
  Self-Attention Mechanism (SAM) is good at capturing the internal connections of features. A novel Quantum Self-Attention Network (QSAN) is proposed for image classification tasks on near-term quantum devices.
  arXiv  Detail & Related papers  (2022-07-14T12:22:51Z)
• Adiabatic Quantum Computing for Multi Object Tracking [170.8716555363907]
  Multi-Object Tracking (MOT) is most often approached in the tracking-by-detection paradigm, where object detections are associated through time. As these optimization problems are often NP-hard, they can only be solved exactly for small instances on current hardware. We show that our approach is competitive compared with state-of-the-art optimization-based approaches, even when using of-the-shelf integer programming solvers.
  arXiv  Detail & Related papers  (2022-02-17T18:59:20Z)
• Scaling Quantum Approximate Optimization on Near-term Hardware [49.94954584453379]
  We quantify scaling of the expected resource requirements by optimized circuits for hardware architectures with varying levels of connectivity. We show the number of measurements, and hence total time to synthesizing solution, grows exponentially in problem size and problem graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.
  arXiv  Detail & Related papers  (2022-01-06T21:02:30Z)
• 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.