Quantum flow algorithms for simulating many-body systems on quantum computers

• URL: http://arxiv.org/abs/2305.05168v2
• Date: Tue, 8 Aug 2023 16:29:57 GMT
• Title: Quantum flow algorithms for simulating many-body systems on quantum computers
• Authors: Karol Kowalski, Nicholas P. Bauman
• Abstract summary: We conduct quantum simulations of strongly correlated systems using the quantum flow (QFlow) approach. Our QFlow algorithms significantly reduce circuit complexity and pave the way for scalable and constant-circuit-depth quantum computing.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We conducted quantum simulations of strongly correlated systems using the quantum flow (QFlow) approach, which enables sampling large sub-spaces of the Hilbert space through coupled eigenvalue problems in reduced dimensionality active spaces. Our QFlow algorithms significantly reduce circuit complexity and pave the way for scalable and constant-circuit-depth quantum computing. Our simulations show that QFlow can optimize the collective number of wave function parameters without increasing the required qubits using active spaces having an order of magnitude fewer number of parameters.

Related papers

• Resource-adaptive quantum flow algorithms for quantum simulations of many-body systems: sub-flow embedding procedures [0.20462238493547852]
  We utilize the quantum flow (QFlow) method to perform quantum simulations of correlated systems. Our research demonstrates that the circuits for evaluating the low dimensionality subproblems are significantly less complex than the parent problem. Our findings shed light on the potential of QFlow in efficiently handling correlated systems via quantum simulations.
  arXiv  Detail & Related papers  (2024-10-15T19:00:33Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach [5.193557673127421]
  We present a general framework to calculate the lower bound for simulating a broad class of quantum Markov semigroups. Our framework can be applied to both unital and non-unital quantum dynamics.
  arXiv  Detail & Related papers  (2024-07-22T03:57:41Z)
• 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)
• Overhead-constrained circuit knitting for variational quantum dynamics [0.0]
  We use circuit knitting to partition a large quantum system into smaller subsystems that can each be simulated on a separate device. We show that the same method can be used to reduce the circuit depth by cutting long-ranged gates.
  arXiv  Detail & Related papers  (2023-09-14T17:01:06Z)
• Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms [0.0]
  We propose several quantum Krylov fast-forwarding (QKFF) algorithms capable of predicting long-time dynamics well beyond the coherence time of current quantum hardware. Our algorithms use real-time evolved Krylov basis states prepared on the quantum computer and a multi-reference subspace method to ensure convergence towards high-fidelity, long-time dynamics.
  arXiv  Detail & Related papers  (2022-08-01T16:00:20Z)
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation [55.41644538483948]
  Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates. We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
  arXiv  Detail & Related papers  (2021-08-06T19:38:03Z)
• Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
  We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions. Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
  arXiv  Detail & Related papers  (2021-06-24T20:16:02Z)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Optimal quantum simulation of open quantum systems [1.9551668880584971]
  Digital quantum simulation on quantum systems require algorithms that can be implemented using finite quantum resources. Recent studies have demonstrated digital quantum simulation of open quantum systems on Noisy Intermediate-Scale Quantum (NISQ) devices. We develop quantum circuits for optimal simulation of Markovian and Non-Markovian open quantum systems.
  arXiv  Detail & Related papers  (2020-12-14T14:00:36Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)

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.