arXiv subjects

Ning Bao

Publications and source records attributed to Ning Bao.

At least 37 records · Page 2Linked to original sources

arXiv2024

Exploiting recursive structures for the design of novel quantum primitives

The advent of fault-tolerant quantum computers marks a significant milestone, yet the development of practical quantum algorithms remains a critical challenge. Effective quantum algorithms are essential for leveraging the power of quantum computers, and their design is often non-intuitive. This paper addresses the issue of generating novel quantum primitives by focusing on recursive circuits. We explore the recursive circuit structures prevalent in existing quantum algorithms and demonstrate how these structures can be exploited to design new, potentially advantageous quantum algorithms. We base our discussion on the quantum Fourier transform (QFT), which is a primitive that is widely used in quantum algorithms. We show that the recursive structure in well-established fast classical transforms forms a fruitful bridge with quantum algorithms, enabling the design of novel quantum primitives and the discovery of new discrete numerical transforms. The discussion is split into two complementary parts, the forward and the reverse direction, in which existing classical transforms are implemented using polynomial-time quantum circuits and recursive circuits are used to find novel non-sparse classical transforms with guaranteed quantum speedup, respectively. We comment on the potential impact on quantum algorithms, numerical analysis, and signal processing.

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arXiv2024

Properties of the contraction map for holographic entanglement entropy inequalities

We present a deterministic way of finding contraction maps for candidate holographic entanglement entropy inequalities modulo choices due to actual degeneracy. We characterize its complexity and give an argument for the completeness of the contraction map proof method as a necessary and sufficient condition for the validity of an entropy inequality for holographic entanglement.

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arXiv2024

Bootstrapping shallow circuits

Recently, a polynomial time classical algorithm has been found for learning the shallow representation of a unitary $U$ acting on $n$-qubits, by learning local inversions and then sewing them back together with ancilla qubits and SWAP gates. In this work, we bootstrap local inversion learning (LIL) to optimize quantum circuit depth by learning shallow representations for its sub-unitaries. We recursively cut circuits and apply the LIL algorithm to replace sub-circuits with their shallow representations, if it can be found by the algorithm. If not, we keep cutting until the optimization terminates, either by finding shallow representations or by reaching constant-depth sub-circuits. By replacing sub-circuits with their shallow representations, we hope to obtain some compression of the quantum circuit. Due to the binary search structure, the optimization algorithm has time complexity logarithmic in the depth of the original given circuit.

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arXiv2024

Optimal twirling depths for shadow tomography in the presence of noise

The classical shadows protocol is an efficient strategy for estimating properties of an unknown state $ρ$ using a small number of state copies and measurements. In its original form, it involves twirling the state with unitaries from some ensemble and measuring the twirled state in a fixed basis. It was recently shown that for computing local properties, optimal sample complexity (copies of the state required) is remarkably achieved for unitaries drawn from shallow depth circuits composed of local entangling gates, as opposed to purely local (zero depth) or global twirling (infinite depth) ensembles. Here we consider the sample complexity as a function of the depth of the circuit, in the presence of noise. We find that this noise has important implications for determining the optimal twirling ensemble. Under fairly general conditions, we i) show that any single-site noise can be accounted for using a depolarizing noise channel with an appropriate damping parameter $f$; ii) compute thresholds $f_{\text{th}}$ at which optimal twirling reduces to local twirling for arbitrary operators and iii) $n^{\text{th}}$ order Renyi entropies ($n \ge 2$); and iv) provide a meaningful upper bound $t_{\text{max}}$ on the optimal circuit depth for any finite noise strength $f$, which applies to all operators and entanglement entropy measurements. These thresholds strongly constrain the search for optimal strategies to implement shadow tomography and can be easily tailored to the experimental system at hand.

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arXiv2024

Holographic Entanglement Distillation from the Surface State Correspondence

We study correlations between geometric subfactors living on the Ryu-Takayanagi surface that bounds the entanglement wedge. Using the surface-state correspondence and the bit threads program, we are able to calculate mutual information and conditional mutual information between subfactors. This enables us to count the shared Bell pairs between subfactors, and we propose an entanglement distillation procedure over these subsystems via a SWAP gate protocol. We comment on extending to multipartite entanglement.

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arXiv2023

A Rubik's Cube inspired approach to Clifford synthesis

The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's Cube problem, we develop a machine learning approach for Clifford synthesis based on learning an approximation to the distance to the identity. This approach is probabilistic and computationally intensive. However, when a decomposition is successfully found, it often involves fewer gates than existing synthesis algorithms. Additionally, our approach is much more flexible than existing algorithms in that arbitrary gate sets, device topologies, and gate fidelities may incorporated, thus allowing for the approach to be tailored to a specific device.

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arXiv2023

Superselection Rules, Quantum Error Correction, and Quantum Chromodynamics

We investigate the relationship between superselection rules and quantum error correcting codes. We demonstrate that the existence of a superselection rule implies the Knill-Laflamme condition in quantum error correction. As an example, we examine quantum chromodynamics through the lens of quantum error correction, where the proton and neutron states in the model are explored as different superselection sectors that protect logical information. Finally we comment on topological quantum error correcting codes and supersymmetric quantum field theory within this framework.

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arXiv2023

Variational quantum simulation of critical Ising model with symmetry averaging

Here, we investigate the use of deep multi-scale entanglement renormalization (DMERA) circuits as a variational ansatz for ground states of gapless systems. We use the exactly-solvable one-dimensional critical transverse-field Ising model as a testbed. Numerically exact simulation of the ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, DMERA strongly outperforms a standard QAOA-style ansatz, and that a major source of systematic error in correlation functions approximated using DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. We propose that this technique for mitigating systematic error could be applied to NISQ simulations of physical systems with other symmetries.

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arXiv2023

Reconstruction wedges in $AdS/CFT$ with boundary fractallike structures

In this work, we show the robustness of uberholography and its associated quantum error correcting code against the breakdown of entanglement wedge in the presence of highly entropic mixed states in the bulk. We show that for Cantor-set-like erasure in the boundary in $AdS_3/CFT_2$, the code distance is independent of the mixed-state entropy in the bulk in the $m\rightarrow\infty$ limit. We also show that for a Sierpinski triangle shaped boundary subregion with fractal boundary erasures in $AdS_4/CFT_3$, bulk reconstruction is possible in the presence of highly entropic mixed states in the bulk in the large $m$ regime.

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arXiv2022

Code Properties of the Holographic Sierpinski Triangle

We study the holographic quantum error correcting code properties of a Sierpinski Triangle-shaped boundary subregion in $AdS_4/CFT_3$. Due to existing no-go theorems in topological quantum error correction regarding fractal noise, this gives holographic codes a specific advantage over topological codes. We then further argue that a boundary subregion in the shape of the Sierpinski gasket in $AdS_5/CFT_4$ does not possess these holographic quantum error correction properties.

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arXiv2022

Entanglement area law for 1D gauge theories and bosonic systems

We prove an entanglement area law for a class of 1D quantum systems involving infinite-dimensional local Hilbert spaces. This class of quantum systems include bosonic models such as the Hubbard-Holstein model, and both U(1) and SU(2) lattice gauge theories in one spatial dimension. Our proof relies on new results concerning the robustness of the ground state and spectral gap to the truncation of Hilbert space, applied within the approximate ground state projector (AGSP) framework from previous work. In establishing this area law, we develop a system-size independent bound on the expectation value of local observables for Hamiltonians without translation symmetry, which may be of separate interest. Our result provides theoretical justification for using tensor network methods to study the ground state properties of quantum systems with infinite local degrees of freedom.

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arXiv2022

Deconfinement and Error Thresholds in Holography

We study the error threshold properties of holographic quantum error-correcting codes. We demonstrate that holographic CFTs admit an algebraic threshold, which is related to the confinement-deconfinement phase transition. We then apply geometric intuition from holography and the Hawking-Page phase transition to motivate the CFT result, and comment on potential extensions to other confining theories.

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arXiv2022

Topological Link Models of Multipartite Entanglement

We introduce a novel model of multipartite entanglement based on topological links, generalizing the graph/hypergraph entropy cone program. We demonstrate that there exist link representations of entropy vectors which provably cannot be represented by graphs or hypergraphs. Furthermore, we show that the contraction map proof method generalizes to the topological setting, though now requiring oracular solutions to well-known but difficult problems in knot theory.

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arXiv2022

On the importance of scalability and resource estimation of quantum algorithms for domain sciences

The quantum information science community has seen a surge in new algorithmic developments across scientific domains. These developments have demonstrated polynomial or better improvements in computational and space complexity, incentivizing further research in the field. However, despite recent progress, many works fail to provide quantitative estimates on algorithmic scalability or quantum resources required -- e.g., number of logical qubits, error thresholds, etc. -- to realize the highly sought "quantum advantage." In this paper, we discuss several quantum algorithms and motivate the importance of such estimates. By example and under simple scaling assumptions, we approximate the computational expectations of a future quantum device for a high energy physics simulation algorithm and how it compares to its classical analog. We assert that a standard candle is necessary for claims of quantum advantage.

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arXiv2022

Holevo Information of Black Hole Mesostates

We define a bulk wormhole geometry interpolating between horizons of differing size and determine characteristics of the HRT surface in these geometries. This construction is dual to black hole mesostates, an intermediate coarse-graining of states between black hole microstates and the full black hole state. We analyze the distinguishability of these objects using the recently derived holographic Holevo information techniques, demonstrating novel phase transition behavior for such systems.

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arXiv2021

A Gap Between the Hypergraph and Stabilizer Entropy Cones

It was recently found that the stabilizer and hypergraph entropy cones coincide for four parties, leading to a conjecture of their equivalence at higher party numbers. In this note, we show this conjecture to be false by proving new inequalities obeyed by all hypergraph entropy vectors that exclude particular stabilizer states on six qubits. By further leveraging this connection, we improve the characterization of stabilizer entropies and show that all linear rank inequalities at five parties, except for classical monotonicity, form facets of the stabilizer cone. Additionally, by studying minimum cuts on hypergraphs, we prove some structural properties of hypergraph representations of entanglement and generalize the notion of entanglement wedge nesting in holography.

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arXiv2021

Entanglement Wedge Cross Section Inequalities from Replicated Geometries

We generalize the constructions for the multipartite reflected entropy in order to construct spacetimes capable of representing multipartite entanglement wedge cross sections of differing party number as Ryu-Takayanagi surfaces on a single replicated geometry. We devise a general algorithm for such constructions for arbitrary party number and demonstrate how such methods can be used to derive novel inequalities constraining mulipartite entanglement wedge cross sections.

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arXiv2021

Magic State Distillation from Entangled States

Magic can be distributed non-locally in many-body entangled states, such as the low energy states of condensed matter systems. Using the Bravyi-Kitaev magic state distillation protocol, we find that non-local magic is distillable and can improve the distillation outcome. We analyze a few explicit examples and show that spin squeezing can be used to convert non-distillable states into distillable ones. Our analysis also suggests that the conventional product input states assumed by magic distillation protocols are extremely atypical among general states with distillable magic. It further justifies the need for studying a diverse range of entangled inputs that yield magic states with high probability.

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