arXiv subjects

Brian Barch

Publications and source records attributed to Brian Barch.

5 recordsLinked to original sources

arXiv2026

Analog-Digital Quantum Computing with Quantum Annealing Processors

Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing annealing QPUs to scale to much larger sizes than gate-based systems, but constraining the class of available operations. Here we expand the class by performing analog-digital quantum computing in a highly-multiplexed, superconducting quantum annealing processor. This involves evolution under a fixed many-body Hamiltonian that, in the weak-coupling regime, is well-described by an effective XY model, together with arbitrary-basis initialization and measurement via auxiliary qubits. Operationally, this is equivalent to implementing single-qubit gates at the beginning and end of an analog quantum evolution. We demonstrate this capability with several foundational applications: single-qubit and two-qubit coherent oscillations with varying initialization and measurement bases, a multi-qubit quantum walk with fermionic dispersion in line with theory, and Anderson localization in a disordered chain. These experiments open the door to a wide range of new possibilities in quantum computation and simulation, greatly expanding the applications of commercially available quantum annealing processors.

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arXiv2025

Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics

Non-Hermitian (NH) quantum systems demonstrate striking differences from their Hermitian counterparts, leading to claims of NH advantage in areas ranging from metrology to entanglement generation. We show that in the context of quantum computation, any such NH advantage is unlikely to be scalable as an efficient computational resource: if coherent normalized non-unitary evolution could be realized with only polynomial overhead, then the resulting model could implement postselection, implying implausibly strong complexity-theoretic power under standard assumptions. We define NHBQP(U) as the computational power of poly-size quantum circuits that, in addition to a standard universal unitary gate set, may apply a fixed gate U on $O(1)$ qubits that is not proportional to a unitary, with the state renormalized after each use of U. We prove this model is powerful enough to decide PostBQP. In the standard uniform circuit-family model this characterization is tight: for any fixed such U, NHBQP(U)=PostBQP=PP. PostBQP is believed intractable, so this suggests that any scalable NH computational advantage must come with a cost limiting its efficiency. Additionally, we study locality-preserving purifications of restricted classes of non-unitary systems. Using this framework, we show that unitary gates with postselection can simulate not only evolution under NH Hamiltonians but arbitrary quantum trajectories. Any NH model whose purification lies in a strongly simulable unitary family (e.g., Clifford, matchgate, or low-bond-dimension tensor-network circuits) remains efficiently classically simulable, provided the relevant postselected events occur with probability $\Omega(2^{-\text{poly}(n)})$. Thus adding non-Hermiticity to a universal unitary system makes it infeasibly computationally powerful, while adding it to a strongly simulable system adds no computational power in this setting.

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arXiv2024

Locality, Correlations, Information, and non-Hermitian Quantum Systems

Local non-Hermitian (NH) quantum systems generically exhibit breakdown of Lieb-Robinson (LR) bounds, motivating study of whether new locality measures might shed light not seen by existing measures. In this paper we extend the standard connected correlation function (CC) to NH systems in a form that recovers locality. Additionally, we use the metric formalism to derive a modified CC which recovers not just locality but even LR bounds in local $PT$-Symmetric systems, and discuss extensions of both CCs to the $n$-partite case. We show that in Hermitian systems $\delta\rho = \rho-\rho_A\otimes\rho_B$ can be written as a linear combination of CCs, allowing us to place an LR bound on $\Vert\delta\rho\Vert_2$. We show this generically extends to an LR bound on mutual information as well. We then extend this to NH systems, where we show its violations can be used to place a necessary condition on which NH Hamiltonians are capable of nonlocal entanglement generation. Numerical simulations are provided by means of exact diagonalization for the NH Transverse-Field Ising Model, demonstrating both breakdown and recovery of LR bounds.

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arXiv2023

Scrambling and operator entanglement in local non-Hermitian quantum systems

The breakdown of Lieb-Robinson bounds in local, non-Hermitian quantum systems opens up the possibility for a rich landscape of quantum many-body phenomenology. We elucidate this by studying information scrambling and quantum chaos in non-Hermitian variants of paradigmatic local quantum spin-chain models. We utilize a mixture of exact diagonalization and tensor network techniques for our numerical results and focus on three dynamical quantities: (i) out-of-time-ordered correlators (OTOCs), (ii) operator entanglement of the dynamics, and (iii) entanglement growth following a quench from product initial states. We show that while OTOCs fail to capture information scrambling in a simple, local, non-Hermitian transverse-field Ising model, the closely related operator entanglement is a robust measure of dynamical properties of interest. Moreover, we show that the short-time growth of operator entanglement can generically detect ``entanglement phase transitions'' in these systems while its long-time average is shown to be a reliable indicator of quantum chaos and entanglement phases. This allows us to extend operator entanglement based diagnostics from previous works on closed and open quantum systems, to the new arena of monitored quantum dynamics. Finally, we remark on the efficacy of these dynamical quantities in detecting integrability/chaos in the presence of continuous monitoring.

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arXiv2021

Low overhead universality and quantum supremacy using only $Z$-control

We consider a model of quantum computation we call "Varying-$Z$" (V$Z$), defined by applying controllable $Z$-diagonal Hamiltonians in the presence of a uniform and constant external $X$-field, and prove that it is universal, even in 1D. Universality is demonstrated by construction of a universal gate set with $O(1)$ depth overhead. We then use this construction to describe a circuit whose output distribution cannot be classically simulated unless the polynomial hierarchy collapses, with the goal of providing a low-resource method of demonstrating quantum supremacy. The V$Z$ model can achieve quantum supremacy in $O(n)$ depth, equivalent to the random circuit sampling models despite a higher degree of homogeneity: it requires no individually addressed $X$-control.

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