A quantum hamiltonian simulation benchmark

• URL: http://arxiv.org/abs/2108.03747v2
• Date: Fri, 12 May 2023 10:05:58 GMT
• Title: A quantum hamiltonian simulation benchmark
• Authors: Yulong Dong, K. Birgitta Whaley, Lin Lin
• Abstract summary: Hamiltonian simulation is one of the most important problems in quantum computation. We propose a drastically simplified quantum circuit that uses only one ancilla qubit and no multi-qubit controlled gates.
• Score: 1.5301252700705212
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hamiltonian simulation is one of the most important problems in quantum computation, and quantum singular value transformation (QSVT) is an efficient way to simulate a general class of Hamiltonians. However, the QSVT circuit typically involves multiple ancilla qubits and multi-qubit control gates. In order to simulate a certain class of $n$-qubit random Hamiltonians, we propose a drastically simplified quantum circuit that we refer to as the minimal QSVT circuit, which uses only one ancilla qubit and no multi-qubit controlled gates. We formulate a simple metric called the quantum unitary evolution score (QUES), which is a scalable quantum benchmark and can be verified without any need for classical computation. Under the globally depolarized noise model, we demonstrate that QUES is directly related to the circuit fidelity, and the potential classical hardness of an associated quantum circuit sampling problem. Under the same assumption, theoretical analysis suggests there exists an `optimal' simulation time $t^{\text{opt}}\approx 4.81$, at which even a noisy quantum device may be sufficient to demonstrate the potential classical hardness.

Related papers

• 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)
• Enhancing Quantum Field Theory Simulations on NISQ Devices with Hamiltonian Truncation [0.0]
  This paper presents an alternative to traditional methods for simulating the real-time evolution in Quantum Field Theories (QFTs) by leveraging Hamiltonian Truncation (HT) We study the Schwinger model, systematically reducing the complexity of the Hamiltonian via HT while preserving essential physical properties. For the observables studied in this paper, the HT approach converges quickly with the number of qubits, allowing for the interesting physics processes to be captured without needing many qubits.
  arXiv  Detail & Related papers  (2024-07-26T18:03:20Z)
• Polynomial-Time Classical Simulation of Noisy IQP Circuits with Constant Depth [0.5188841610098435]
  We show that for an arbitrary IQP circuit undergoing dephasing or depolarizing noise, the output distribution can be efficiently sampled by a classical computer. We take advantage of the fact that IQP circuits have deep sections of diagonal gates, which allows the noise to build up predictably and induce a large-scale breakdown of entanglement within the circuit.
  arXiv  Detail & Related papers  (2024-03-21T17:55:26Z)
• 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)
• Quantum Simulations for Strong-Field QED [0.0]
  We perform quantum simulations of strong-field QED (SFQED) in $3+1$ dimensions. The interactions relevant for Breit-Wheeler pair-production are transformed into a quantum circuit. Quantum simulations of a "null double slit" experiment are found to agree well with classical simulations.
  arXiv  Detail & Related papers  (2023-11-30T03:05:26Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation [1.433758865948252]
  We show how to design MPFs that do not amplify the hardware and sampling errors, and demonstrate their performance. We observe an error reduction of up to an order of magnitude when compared to a product formula approach by suppressing hardware noise with Pauli Twirling, pulse efficient transpilation, and a novel zero-noise extrapolation based on scaled cross-resonance pulses.
  arXiv  Detail & Related papers  (2022-07-22T18:00:05Z)
• Variational Adiabatic Gauge Transformation on real quantum hardware for effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
  We introduce the Variational Adiabatic Gauge Transformation (VAGT) VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit. The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
  arXiv  Detail & Related papers  (2021-11-16T20:50:08Z)
• 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 Eigensolver with Reduced Circuit Complexity [3.1158760235626946]
  We present a novel approach to reduce quantum circuit complexity in VQE for electronic structure calculations. Our algorithm, called ClusterVQE, splits the initial qubit space into subspaces (qubit clusters) which are further distributed on individual quantum circuits. The new algorithm simultaneously reduces the number of qubits and circuit depth, making it a potential leader for quantum chemistry simulations on NISQ devices.
  arXiv  Detail & Related papers  (2021-06-14T17:23:46Z)
• 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.