An entanglement-aware quantum computer simulation algorithm

• URL: http://arxiv.org/abs/2307.16870v1
• Date: Mon, 31 Jul 2023 17:27:04 GMT
• Title: An entanglement-aware quantum computer simulation algorithm
• Authors: Maxime Oliva
• Abstract summary: I propose a method for inferring the fidelity of an approximate quantum state without direct comparison to its exact counterpart. I show that this algorithm far surpasses standard fixed bond dimension truncation schemes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The advent of quantum computers promises exponential speed ups in the execution of various computational tasks. While their capabilities are hindered by quantum decoherence, they can be exactly simulated on classical hardware at the cost of an exponential scaling in terms of number of qubits. To circumvent this, quantum states can be represented as matrix product states (MPS), a product of tensors separated by so-called bond dimensions. Limiting bond dimensions growth approximates the state, but also limits its ability to represent entanglement. Methods based on this representation have been the most popular tool at simulating large quantum systems. But how to trust resulting approximate quantum states for such intractable systems sizes ? I propose here a method for inferring the fidelity of an approximate quantum state without direct comparison to its exact counterpart, and use it to design an ``entanglement-aware'' (EA) algorithm for both pure and mixed states. As opposed to state of the art methods which limit bond dimensions up to an arbitrary maximum value, this algorithm receives as input a fidelity, and adapts dynamically its bond dimensions to both local entanglement and noise such that the final quantum state fidelity at least reaches the input fidelity. I show that this algorithm far surpasses standard fixed bond dimension truncation schemes. In particular, a noiseless random circuit of 300 qubits and depth 75 simulated using MPS methods takes one week of computation time, while EA-MPS only needs 2 hours to reach similar quantum state fidelity.

Related papers

• Estimating quantum amplitudes can be exponentially improved [11.282486674587236]
  Estimating quantum amplitudes is a fundamental task in quantum computing. We present a novel framework for estimating quantum amplitudes by transforming pure states into their matrix forms. Our framework achieves the standard quantum limit $epsilon-2$ and the Heisenberg limit $epsilon-1$, respectively.
  arXiv  Detail & Related papers  (2024-08-25T04:35:53Z)
• Mixed-Dimensional Qudit State Preparation Using Edge-Weighted Decision Diagrams [3.393749500700096]
  Quantum computers have the potential to solve intractable problems. One key element to exploiting this potential is the capability to efficiently prepare quantum states for multi-valued, or qudit, systems. In this paper, we investigate quantum state preparation with a focus on mixed-dimensional systems.
  arXiv  Detail & Related papers  (2024-06-05T18:00:01Z)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• A quantum implementation of high-order power method for estimating geometric entanglement of pure states [39.58317527488534]
  This work presents a quantum adaptation of the iterative higher-order power method for estimating the geometric measure of entanglement of multi-qubit pure states. It is executable on current (hybrid) quantum hardware and does not depend on quantum memory. We study the effect of noise on the algorithm using a simple theoretical model based on the standard depolarising channel.
  arXiv  Detail & Related papers  (2024-05-29T14:40:24Z)
• 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)
• Sequential quantum simulation of spin chains with a single circuit QED device [5.841833052422423]
  Quantum simulation of many-body systems in materials science and chemistry are promising application areas for quantum computers. We show how a single-circuit quantum electrodynamics device can be used to simulate the ground state of a highly-entangled quantum many-body spin chain. We demonstrate that the large state space of the cavity can be used to replace multiple qubits in a qubit-only architecture, and could therefore simplify the design of quantum processors for materials simulation.
  arXiv  Detail & Related papers  (2023-08-30T18:00:03Z)
• Quantum State Tomography for Matrix Product Density Operators [28.799576051288888]
  Reconstruction of quantum states from experimental measurements is crucial for the verification and benchmarking of quantum devices. Many physical quantum states, such as states generated by noisy, intermediate-scale quantum computers, are usually structured. We establish theoretical guarantees for the stable recovery of MPOs using tools from compressive sensing and the theory of empirical processes.
  arXiv  Detail & Related papers  (2023-06-15T18:23:55Z)
• Combining Matrix Product States and Noisy Quantum Computers for Quantum Simulation [0.0]
  Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems. We show that using classical knowledge in the form of tensor networks provides a way to better use limited quantum resources.
  arXiv  Detail & Related papers  (2023-05-30T17:21:52Z)
• Calculating the many-body density of states on a digital quantum computer [58.720142291102135]
  We implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer. We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18bits.
  arXiv  Detail & Related papers  (2023-03-23T17:46:28Z)
• Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
  We design, implement, and evaluate three hybrid quantum k-Means algorithms. We exploit quantum phenomena to speed up the computation of distances. We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
  arXiv  Detail & Related papers  (2022-12-13T16:04:16Z)
• Optimal quantum control via genetic algorithms for quantum state engineering in driven-resonator mediated networks [68.8204255655161]
  We employ a machine learning-enabled approach to quantum state engineering based on evolutionary algorithms. We consider a network of qubits -- encoded in the states of artificial atoms with no direct coupling -- interacting via a common single-mode driven microwave resonator. We observe high quantum fidelities and resilience to noise, despite the algorithm being trained in the ideal noise-free setting.
  arXiv  Detail & Related papers  (2022-06-29T14:34:00Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• A quantum processor based on coherent transport of entangled atom arrays [44.62475518267084]
  We show a quantum processor with dynamic, nonlocal connectivity, in which entangled qubits are coherently transported in a highly parallel manner. We use this architecture to realize programmable generation of entangled graph states such as cluster states and a 7-qubit Steane code state.
  arXiv  Detail & Related papers  (2021-12-07T19:00:00Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

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.