Quantum Simulation via Stochastic Combination of Unitaries
arXiv:2407.21095 · doi:10.1038/s41534-025-01168-w
Abstract
Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit dilations. This naturally enables simulations of open systems, which we demonstrate by preparing damped many-qubit GHZ states on ibm_hanoi. The technique further inspires two Hamiltonian simulation algorithms with gate counts that are asymptotically independent of the spectral precision target, reducing resource requirements by several orders of magnitude for a benchmark system.
16 pages, 7 figures
References in corpus (35)
- Adiabatic Quantum Computing
- Simulated Quantum Computation of Molecular Energies
- Quantum Amplitude Amplification and Estimation
- Hamiltonian Simulation by Qubitization
- Quantum algorithms for quantum chemistry and quantum materials science
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- Simulating Hamiltonian dynamics with a truncated Taylor series
- Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
- Toward the first quantum simulation with quantum speedup
- A random compiler for fast Hamiltonian simulation
- A review of progress in the physics of open quantum systems: theory and experiment
- Exponential improvement in precision for simulating sparse Hamiltonians
- Nearly optimal lattice simulation by product formulas
- Digital quantum simulation of open quantum systems using quantum imaginary time evolution
- Relating out-of-time-order correlations to entanglement via multiple-quantum coherences
- Ground state preparation and energy estimation on early fault-tolerant quantum computers via quantum eigenvalue transformation of unitary matrices
- Verifying Multipartite Entangled GHZ States via Multiple Quantum Coherences
- Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
- Quantum networks with neutral atom processing nodes
- A randomized quantum algorithm for statistical phase estimation
- Distributing Graph States Over Arbitrary Quantum Networks
- Generation and verification of 27-qubit Greenberger-Horne-Zeilinger states in a superconducting quantum computer
- Simulating Quantum Dynamics On A Quantum Computer
- Linear combination of Hamiltonian simulation for nonunitary dynamics with optimal state preparation cost
- Analysis of Multipartite Entanglement Distribution using a Central Quantum-Network Node
- Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision
- Entanglement generation in a quantum network at distance-independent rate
- Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
- Randomizing multi-product formulas for Hamiltonian simulation
- Implementing any Linear Combination of Unitaries on Intermediate-term Quantum Computers
- Composite Quantum Simulations
- Importance sampling for stochastic quantum simulations
- Block-encoding dense and full-rank kernels using hierarchical matrices: applications in quantum numerical linear algebra
- Simulation of open quantum systems via low-depth convex unitary evolutions
- Realistic simulation of quantum computation using unitary and measurement channels