Esha Swaroop | Searcharxiv

arXiv2025

Quasiprobabilistic imaginary-time evolution on quantum computers

Imaginary-time evolution plays an important role in algorithms for computing ground-state and thermal equilibrium properties of quantum systems, but can be challenging to simulate on classical computers. Many quantum algorithms for imaginary-time evolution have resource requirements that are prohibitive for current quantum devices and face performance issues due to noise. Here, we propose a new algorithm for computing imaginary-time evolved expectation values on quantum computers, inspired by probabilistic error cancellation, an error-mitigation technique. Our algorithm works by decomposing a Trotterization of imaginary-time evolution into a probabilistic linear combination of operations, each of which is then implemented on a quantum computer. The measurement data is then classically post-processed to obtain the expectation value of the imaginary-time evolved state. Our algorithm requires no ancillary qubits and can be made noise-resilient without additional error mitigation. It is well-suited for estimating thermal expectation values by making use of the notion of a thermal pure quantum state. We demonstrate our algorithm by performing numerical simulations of thermal pure quantum state preparation for the 1D Heisenberg Hamiltonian on 8 qubits, and by using an IBM quantum computer to estimate the energy of the same Hamiltonian on 2 qubits. We observe promising results compared to the exact values, illustrating the potential of our algorithm for probing the physics of quantum many-body systems on current hardware.

quant-ph↗

arXiv2024

Universal adapters between quantum LDPC codes

We propose the repetition code adapter as a way to perform joint logical Pauli measurements within a quantum low-density parity check (LDPC) codeblock or between separate such codeblocks, thus providing a flexible tool for fault-tolerant computation with quantum LDPC codes. This adapter is universal in the sense that it works regardless of the LDPC codes involved and the logical Paulis being measured. The construction achieves joint logical Pauli measurement of $t$ weight $O(d)$ operators using $O(d)$ time and $\tilde O(td)$ additional qubits and checks, up to a factor polylogarithmic in $d$. As a special case, for some geometrically-local codes in fixed $D\ge2$ dimensions, only $O(td)$ additional qubits and checks are required instead. By extending the adapter in the case $t=2$, we also construct a toric code adapter that uses $O(d^2)$ additional qubits and checks to perform addressable logical CNOT gates on arbitrary LDPC codes via Dehn twists. To obtain these results, we develop a novel weaker form of graph edge expansion and the $\mathsf{SkipTree}$ algorithm, which ensures a sparse transformation between different weight-2 check bases for the classical repetition code.

quant-ph↗