Qubit-efficient entanglement spectroscopy using qubit resets

Journal Article · 01 September 2021 · Quantum

DOI: https://doi.org/10.22331/q-2021-09-02-535 · OSTI ID:1818586

Yirka, Justin  ^[1]; Subaşı, Yiğit  ^[2]

---

1. Department of Computer Science, The University of Texas at Austin, Austin, TX 78712, USA
2. Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

One strategy to fit larger problems on NISQ devices is to exploit a tradeoff between circuit width and circuit depth. Unfortunately, this tradeoff still limits the size of tractable problems since the increased depth is often not realizable before noise dominates. Here, we develop $\text{qubit-efficient}$ quantum algorithms for entanglement spectroscopy which avoid this tradeoff. In particular, we develop algorithms for computing the trace of the $n$ -th power of the density operator of a quantum system, $Tr\left({\rho }^n\right)$ , (related to the Rényi entropy of order $n$ ) that use fewer qubits than any previous efficient algorithm while achieving similar performance in the presence of noise, thus enabling spectroscopy of larger quantum systems on NISQ devices. Our algorithms, which require a number of qubits independent of $n$ , are variants of previous algorithms with width proportional to $n$ , an asymptotic difference. The crucial ingredient in these new algorithms is the ability to measure and reinitialize subsets of qubits in the course of the computation, allowing us to reuse qubits and increase the circuit depth without suffering the usual noisy consequences. We also introduce the notion of $\text{effective circuit depth}$ as a generalization of standard circuit depth suitable for circuits with qubit resets. This tool helps explain the noise-resilience of our qubit-efficient algorithms and should aid in designing future algorithms. We perform numerical simulations to compare our algorithms to the original variants and show they perform similarly when subjected to noise. Additionally, we experimentally implement one of our qubit-efficient algorithms on the Honeywell System Model H0, estimating $Tr\left({\rho }^n\right)$ for larger n than possible with previous algorithms.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1818586
• Report Number(s): LA-UR-20-25416; 535
• Journal Information: Quantum, Journal Name: Quantum Vol. 5; ISSN 2521-327X
• Publisher: Verein zur Forderung des Open Access Publizierens in den QuantenwissenschaftenCopyright Statement
• Country of Publication: Austria
• Language: English