TY - JOUR T1 - Estimation of Hamiltonian parameters from thermal states Y1 - 2024 A1 - Luis Pedro García-Pintos A1 - Kishor Bharti A1 - Jacob Bringewatt A1 - Hossein Dehghani A1 - Adam Ehrenberg A1 - Nicole Yunger Halpern A1 - Alexey V. Gorshkov AB -

We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term that contains the parameter and on the term's degree of noncommutativity with the full Hamiltonian: higher uncertainty and commuting operators lead to better precision. We apply the bounds to show that there exist entangled thermal states such that the parameter can be estimated with an error that decreases faster than 1/n−−√, beating the standard quantum limit. This result governs Hamiltonians where an unknown scalar parameter (e.g. a component of a magnetic field) is coupled locally and identically to n qubit sensors. In the high-temperature regime, our bounds allow for pinpointing the optimal estimation error, up to a constant prefactor. Our bounds generalize to joint estimations of multiple parameters. In this setting, we recover the high-temperature sample scaling derived previously via techniques based on quantum state discrimination and coding theory. In an application, we show that noncommuting conserved quantities hinder the estimation of chemical potentials.

UR - https://arxiv.org/abs/2401.10343 ER - TY - JOUR T1 - Fault-tolerant hyperbolic Floquet quantum error correcting codes Y1 - 2023 A1 - Ali Fahimniya A1 - Hossein Dehghani A1 - Kishor Bharti A1 - Sheryl Mathew A1 - Alicia J. Kollár A1 - Alexey V. Gorshkov A1 - Michael J. Gullans AB -

A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call "hyperbolic Floquet codes." These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for n qubits that, according to our prescription that defines the code, provably achieve a finite encoding rate (1/8+2/n) and have a depth-3 syndrome extraction circuit. Similar to hyperbolic surface codes, the distance of the code at each time-step scales at most logarithmically in n. The family of lattices we choose indicates that this scaling is achievable in practice. We develop and benchmark an efficient matching-based decoder that provides evidence of a threshold near 0.1% in a phenomenological noise model. Utilizing weight-two check operators and a qubit connectivity of 3, one of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a [[400,52,8]] code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.

UR - https://arxiv.org/abs/2309.10033 ER - TY - JOUR T1 - Entanglement entropy scaling transition under competing monitoring protocols Y1 - 2020 A1 - Mathias Van Regemortel A1 - Ze-Pei Cian A1 - Alireza Seif A1 - Hossein Dehghani A1 - Mohammad Hafezi AB -

Dissipation generally leads to the decoherence of a quantum state. In contrast, numerous recent proposals have illustrated that dissipation can also be tailored to stabilize many-body entangled quantum states. While the focus of these works has been primarily on engineering the non-equilibrium steady state, we investigate the build-up of entanglement in the quantum trajectories. Specifically, we analyze the competition between two different dissipation channels arising from two incompatible continuous monitoring protocols. The first protocol locks the phase of neighboring sites upon registering a quantum jump, thereby generating a long-range entanglement through the system, while the second one destroys the coherence via dephasing mechanism. By studying the unraveling of stochastic quantum trajectories associated with the continuous monitoring protocols, we present a transition for the scaling of the averaged trajectory entanglement entropies, from critical scaling to area-law behavior. Our work provides novel insights into the occurrence of a measurement-induced phase transition within a continuous monitoring protocol.

UR - https://arxiv.org/abs/2008.08619 ER -