Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
read the original abstract
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized implementations of Trotter-Suzuki-based product formulas. We show that low-order Trotter methods perform surprisingly well when used with phase estimation to compute relative precision quantities (e.g. energies per unit cell), as is often the goal for condensed-phase systems. In this context, simulations of the Hubbard and plane-wave electronic structure models with $N < 10^5$ fermionic modes can be performed with roughly $O(1)$ and $O(N^2)$ T complexities. We perform numerics revealing tradeoffs between the error and gate complexity of a Trotter step; e.g., we show that split-operator techniques have less Trotter error than popular alternatives. By compiling to surface code fault-tolerant gates and assuming error rates of one part per thousand, we show that one can error-correct quantum simulations of interesting, classically intractable instances with a few hundred thousand physical qubits.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
The Pinnacle Architecture: Reducing the cost of breaking RSA-2048 to 100 000 physical qubits using quantum LDPC codes
Pinnacle Architecture using QLDPC codes reduces physical qubits needed to factor RSA-2048 to under 100,000 at 10^{-3} error rate.
-
Phase estimation with randomized Hamiltonians
Generalizes iterative phase estimation to randomized Hamiltonians per step plus importance sampling, yielding fewer terms and sometimes fewer qubits for gapped chemical Hamiltonians.
-
Quantum Simulation of the Real-time Dynamics in the multi-flavor Gross-Neveu Model at the utility scale using Superconducting Quantum Computers
A scalable Trotterization and Localized Diagonal Operator Approximation enable real-time quantum simulation of the multi-flavor Gross-Neveu model on utility-scale superconducting hardware.
-
Tensor-based phase difference estimation on time series analysis
Tensor-network compression of nearest-neighbor circuits plus four-type measurements yields 0.4-4.7% error on 8-qubit Hubbard energy gaps and enables QPE-type runs on IBM devices up to 52 qubits with over 4000 two-qubit gates.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.