Reducing Depth and Measurement Weights in Pauli-based Computation

• URL: http://arxiv.org/abs/2408.04007v1
• Date: Wed, 7 Aug 2024 18:00:11 GMT
• Title: Reducing Depth and Measurement Weights in Pauli-based Computation
• Authors: Filipa C. R. Peres, Ernesto F. Galvão,
• Abstract summary: Pauli-based computation (PBC) is a universal measurement-based quantum computation model steered by an adaptive sequence of independent and compatible Pauli measurements on magic-state qubits. Here, we propose several new ways of decreasing the weight of the Pauli measurements and their associated textsccnot complexity. We also demonstrate how to reduce this model's computational depth.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Pauli-based computation (PBC) is a universal measurement-based quantum computation model steered by an adaptive sequence of independent and compatible Pauli measurements on separable magic-state qubits. Here, we propose several new ways of decreasing the weight of the Pauli measurements and their associated \textsc{cnot} complexity; we also demonstrate how to reduce this model's computational depth. Inspired by known state-transfer methods, we introduce incPBC, a universal model for quantum computation requiring a larger number of (now incompatible) Pauli measurements of weight at most 2. For usual PBC, we prove new upper bounds on the required weights and computational depth, obtained via a pre-compilation step. We also propose a heuristic algorithm that can contribute reductions of over 30\% to the average weight of Pauli measurements (and associated \textsc{cnot} count) when simulating and compiling Clifford-dominated random quantum circuits with up to 22 $T$ gates and over 20\% for instances with larger $T$ counts.

Related papers

• Reducing the sampling complexity of energy estimation in quantum many-body systems using empirical variance information [45.18582668677648]
  We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition. We construct an adaptive estimator using the state's actual variance.
  arXiv  Detail & Related papers  (2025-02-03T19:00:01Z)
• An access model for quantum encoded data [0.0]
  We introduce and investigate a data access model (approximate sample and query) that is satisfiable by the preparation and measurement of block encoded states. We illustrate that this is compositional and has some computational power. We apply these results to obtain improvements over the state of the art in the sample and computational complexity of distributed inner product estimation.
  arXiv  Detail & Related papers  (2024-12-02T19:00:00Z)
• Pyramid Vector Quantization for LLMs [8.779688608449902]
  Pyramid Vector Quantization (PVQ) for large language models. PVQ uses a fixed integer lattice on the sphere by projecting points onto the 1-sphere, which allows for efficient encoding and decoding without requiring an explicit codebook in memory. We achieve state-of-the-art quantization performance with pareto-optimal trade-off between performance and bits per weight and bits per activation, compared to compared methods.
  arXiv  Detail & Related papers  (2024-10-22T11:57:32Z)
• On the Constant Depth Implementation of Pauli Exponentials [49.48516314472825]
  We decompose arbitrary exponentials into circuits of constant depth using $mathcalO(n)$ ancillae and two-body XX and ZZ interactions. We prove the correctness of our approach, after introducing novel rewrite rules for circuits which benefit from qubit recycling.
  arXiv  Detail & Related papers  (2024-08-15T17:09:08Z)
• Quantum Circuit Optimisation and MBQC Scheduling with a Pauli Tracking Library [0.0]
  Pauli tracking allows one to reduce the number of Pauli gates that must be executed on quantum hardware. This is relevant for measurement-based quantum computing and for error-corrected circuits that are implemented through Clifford circuits.
  arXiv  Detail & Related papers  (2024-05-07T03:00:57Z)
• A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method [39.671915199737846]
  We introduce a multiple-circuit algorithm for a quantum lattice Boltzmann method (QLBM) solve of the incompressible Navier--Stokes equations. The presented method is validated and demonstrated for 2D lid-driven cavity flow.
  arXiv  Detail & Related papers  (2024-01-20T15:32:01Z)
• QuIP: 2-Bit Quantization of Large Language Models With Guarantees [44.212441764241]
  This work studies post-training parameter quantization in large language models (LLMs) We introduce quantization with incoherence processing (QuIP), a new method based on the insight that quantization benefits from $textitincoherent$ weight and Hessian matrices.
  arXiv  Detail & Related papers  (2023-07-25T07:44:06Z)
• 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)
• Iterative Qubit Coupled Cluster using only Clifford circuits [36.136619420474766]
  An ideal state preparation protocol can be characterized by being easily generated classically. We propose a method that meets these requirements by introducing a variant of the iterative qubit coupled cluster (iQCC) We demonstrate the algorithm's correctness in ground-state simulations and extend our study to complex systems like the titanium-based compound Ti(C5H5)(CH3)3 with a (20, 20) active space.
  arXiv  Detail & Related papers  (2022-11-18T20:31:10Z)
• Pauli String Partitioning Algorithm with the Ising Model for Simultaneous Measurement [0.0]
  We propose an efficient algorithm for partitioning Pauli strings into subgroups, which can be simultaneously measured in a single quantum circuit. Our partitioning algorithm drastically reduces the total number of measurements in a variational quantum eigensolver for a quantum chemistry.
  arXiv  Detail & Related papers  (2022-05-09T01:49:21Z)
• Quantum circuit compilation and hybrid computation using Pauli-based computation [0.0]
  Pauli-based computation (PBC) is driven by a sequence of adaptively chosen, non-destructive measurements of Pauli observables. We propose practical ways of implementing PBC as adaptive quantum circuits and provide code to do the required classical side-processing.
  arXiv  Detail & Related papers  (2022-03-03T16:01:55Z)

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.