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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Hierarchical memories: Simulating quantum LDPC codes with local gates

Constant-rate low-density parity-check (LDPC) codes are promising candidates for constructing efficient fault-tolerant quantum memories. However, if physical gates are subject to geometric-locality constraints, it becomes challenging to realize these codes. In this paper, we construct a new family of [[N,K,D]] codes, referred to as hierarchical codes, that encode a number of logical qubits K=Ω(N/log(N) 2 ). The N th element of this code family is obtained by concatenating a constant-rate quantum LDPC code with a surface code; nearest-neighbor gates in two dimensions are sufficient to implement the corresponding syndrome-extraction circuit and achieve a threshold. Below threshold the logical failure rate vanishes superpolynomially as a function of the distance D(N). We present a bilayer architecture for implementing the syndrome-extraction circuit, and estimate the logical failure rate for this architecture. Under conservative assumptions, we find that the hierarchical code outperforms the basic encoding where all logical qubits are encoded in the surface code.

Pattison, Christopher A. [California Institute of ↗
DOE OSTI2024

Enhancing quantum utility: Simulating large-scale quantum spin chains on superconducting quantum computers

We present the quantum simulation of the frustrated quantum spin- 1 2 antiferromagnetic Heisenberg spin chain with competing nearest-neighbor ( J 1 ) and next-nearest-neighbor ( J 2 ) exchange interactions in the real superconducting quantum computer with qubits ranging up to 100. In particular, we implement the Hamiltonian with the next-nearest neighbor exchange interaction in conjunction with the nearest-neighbor interaction on IBM's superconducting quantum computer and carry out the time evolution of the spin chain by employing the first-order Trotterization. Furthermore, our implementation of the second-order Trotterization for the isotropic Heisenberg spin chain, involving only nearest-neighbor exchange interaction, enables precise measurement of the expectation values of staggered magnetization observable across a range of up to 100 qubits. Notably, in both cases, our approach results in a constant circuit depth in each Trotter step, independent of the number of qubits. Our demonstration of the accurate measurement of expectation values for the large-scale quantum system using superconducting quantum computers designates the quantum utility of these devices for investigating various properties of many-body quantum systems. This will be a stepping stone to achieving the quantum advantage over classical ones in simulating quantum systems before the fault tolerance quantum era. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2022

A Quantum Algorithm to Simulate Open Quantum Systems

Given the advent of quantum algorithms for a wide array of problems in linear algebra and machine learning, it is important to develop general methods for the simulation of arbitrary (ie non-unitary) operators on quantum hardware. In this talk, we present a novel quantum algorithm based on the quantum singular value transformation (QSVT) to apply an arbitrary operator K to some input state and subsequently estimate the expectation value of some observable. Our construction then immediately yields a route to estimating observables of states undergoing open quantum dynamics, whose effect is captured by a set of non-unitary Kraus operators. Our algorithm succeeds deterministically given the Sz-Nagy dilation, and we provide details on the algorithm's query and gate complexity, numerical verification, and comparisons with prior methods.

Quantum computing↗