arXiv subjects

Entong He

Publications and source records attributed to Entong He.

7 recordsLinked to original sources

arXiv2026

unitaryQIP = unitaryPSPACE

Unitary synthesis complexity studies the computational cost of applying a target unitary to an unknown quantum state, extending complexity theory beyond its traditional focus on problems with classical inputs and outputs. Rosenthal and Yuen (ITCS 2022) introduced two complexity classes for unitary synthesis: $\mathsf{unitaryQIP}$ and $\mathsf{unitaryPSPACE}$ for the unitary families implementable via interactive proofs and in polynomial space, respectively. In this work, we prove the equality $\mathsf{unitaryQIP}=\mathsf{unitaryPSPACE}$ and thereby establish a unitary-complexity analogue of $\mathsf{QIP} = \mathsf{PSPACE}$ (Jain, Ji, Upadhyay, and Watrous, J. ACM 2011) and $\mathsf{stateQIP}=\mathsf{statePSPACE}$ (Rosenthal and Yuen, ITCS 2022; Metger and Yuen, FOCS 2023). To prove $\mathsf{unitaryQIP} \subseteq \mathsf{unitaryPSPACE}$, we use an acceptance rigidity lemma derived from the soundness condition to show that the polynomial-space prover constructed for a fixed input in state synthesis (Metger and Yuen, FOCS 2023) implements the target unitary on every input, leading to a polynomial-space simulation of the protocol. For the reverse inclusion, we build on OpenAI's recently announced solution to the unitary synthesis problem (Aaronson and Kuperberg, Theory Comput. 2007), and show that $\mathsf{unitaryPSPACE}$ families can be synthesized in polynomial time with a $\mathsf{PSPACE}$ oracle. We then implement the oracle queries using auxiliary states prepared via the $\mathsf{statePSPACE} \subseteq \mathsf{stateQIP}$ protocol (Rosenthal and Yuen, ITCS 2022). Beyond the equality, we show that our protocol for $\mathsf{unitaryPSPACE}$ can be parallelized to constant rounds when the verifier receives polynomially many copies of the input, and we also obtain a complexity-theoretic barrier to proving the existence of $\mathsf{EFI}$ pairs.

quant-ph↗

arXiv2026

Optimal classical shadow estimation of unitary channels at Heisenberg limit

Full tomography of an unknown quantum evolution is resource-intensive and often unnecessary when the goal is only to predict selected properties. This motivates the study of classical shadow estimation of unitary channels (CSEU), a task in which one queries an unknown $d$-dimensional unitary $U$ and stores classical data that can later be used to predict expectation values $\mathrm{tr}[O UρU^\dagger]$ for arbitrary input states $ρ$ and observables $O$. Here we propose a parallel and non-adaptive CSEU protocol that uses $\mathcal{O}(\min\{d\varepsilon^{-2},d^{3/2}\varepsilon^{-1}\})$ queries to $U$ when the observables have constant effective size. This achieves Heisenberg scaling with respect to the additive error $\varepsilon$ and is query-optimal, as we prove a matching lower bound $Ω(\min\{d\varepsilon^{-2},d^{3/2}\varepsilon^{-1}\})$ for the query complexity, which remains valid even when stronger access to the unknown unitary is available. Our CSEU protocol is a versatile primitive with applications to several quantum learning tasks. In particular, it yields a near-optimal algorithm for learning an arbitrary Hamiltonian from its real-time evolution in the high-precision regime and recovers the best-known bounds for several tasks in a unified way.

quant-ph↗

arXiv2026

Query-optimal unitary channel tomography in diamond distance with parallel access

In the study of quantum process tomography, it has remained open how to learn a unitary channel in diamond distance with strictly parallel queries as efficiently as with sequential queries. Sequential queries allow one to exploit adaptivity to refine the estimate and adjust the learning strategy accordingly, whereas such adjustments are impossible for parallel queries. From the perspective of higher-order quantum operations, any parallel learning strategy can be simulated by a sequential one, whereas the converse does not hold in general, suggesting that sequential learning strategies are potentially more powerful. Contrary to this intuition, we present a new protocol for learning an unknown $d$-dimensional unitary channel to within $\varepsilon$ in diamond distance using $\mathcal{O}(d^2/\varepsilon)$ parallel queries, matching the lower bound presented in [Haah, Kothari, O'Donnell, and Tang, FOCS '23]. Our protocol thus closes the gap between parallel and sequential strategies for unitary channel tomography. As applications, it achieves optimal query complexity for boundary-regime quantum channel tomography and improves the query efficiency of the best-known protocol for tomography of fermionic linear optics.

quant-ph↗

arXiv2026

Resource quantification for programming low-depth quantum circuits

Noisy intermediate-scale quantum (NISQ) devices pave the way for implementing quantum algorithms that offer quantum advantages over their classical counterparts. Due to the intrinsic noise and decoherence in the physical system, NISQ machines are naturally modeled as large-scale, low-depth quantum circuits. In practice, executing such circuits requires sending program states that encode the relevant instructions to a programmable quantum computer, typically through a cloud service. Existing programming approaches designed for generic unitary transformations are computationally inefficient in the low-depth setting, and therefore remain unsatisfactory. As such, to realize NISQ algorithms, it is crucial to find an efficient way to program low-depth circuits as the number of qubits $N$ increases. Here, we investigate the circuit complexity and the size of quantum memory, known as the program cost, required to program low-depth brickwork circuits. We establish a tight worst-case program cost of $Θ(N \mathrm{polylog} N)$ for universally programming low-depth brickwork circuits in the large-$N$ regime. Moreover, we analyze the trade-off between the cost of describing the layout of local gates and the cost of programming them to implement the target unitaries via the light-cone argument. Our findings suggest that faithful gate-wise programming is essentially optimal in the low-depth regime.

quant-ph↗

arXiv2024

Topics in Non-local Games: Synchronous Algebras, Algebraic Graph Identities, and Quantum NP-hardness Reductions

We review the correspondence between synchronous games and their associated $*$-algebra. Building upon the work of (Helton et al., New York J. Math. 2017), we propose results on algebraic and locally commuting graph identities. Based on the noncommutative Nullstellensätze (Watts, Helton and Klep, Annales Henri Poincaré 2023), we build computational tools that check the non-existence of perfect $C^*$ and algebraic strategies of synchronous games using Gröbner basis methods and semidefinite programming. We prove the equivalence between the hereditary and $C^*$ models questioned in (Helton et al., New York J. Math. 2017). We also extend the quantum-version NP-hardness reduction $\texttt{3-SAT}^* \leq_p \texttt{3-Coloring}^*$ due to (Ji, arXiv 2013) by exhibiting another instance of such reduction $\texttt{3-SAT}^* \leq_p \texttt{Clique}^*$.

quant-ph↗

arXiv2024

QuERLoc: Towards Next-Generation Localization with Quantum-Enhanced Ranging

Remarkable advances have been achieved in localization techniques in past decades, rendering it one of the most important technologies indispensable to our daily lives. In this paper, we investigate a novel localization approach for future computing by presenting QuERLoc, the first study on localization using quantum-enhanced ranging. By fine-tuning the evolution of an entangled quantum probe, quantum ranging can output the information integrated in the probe as a specific mapping of distance-related parameters. QuERLoc is inspired by this unique property to measure a special combination of distances between a target sensor and multiple anchors within one single physical measurement. Leveraging this capability, QuERLoc settles two drawbacks of classical localization approaches: (i) the target-anchor distances must be measured individually and sequentially, and (ii) the resulting optimization problems are non-convex and are sensitive to noise. We first present the theoretical formulation of preparing the probing quantum state and controlling its dynamic to induce a convexified localization problem, and then solve it efficiently via optimization. We conduct extensive numerical analysis of QuERLoc under various settings. The results show that QuERLoc consistently outperforms classical approaches in accuracy and closely follows the theoretical lowerbound, while maintaining low time complexity. It achieves a minimum reduction of 73% in RMSE and 97.6% in time consumption compared to baselines. By introducing range-based quantum localization to the mobile computing community and showing its superior performance, QuERLoc sheds light on next-generation localization technologies and opens up new directions for future research.

cs.ET↗

arXiv2024

Quantum Ranging Enhanced TDoA Localization

Localization is critical to numerous applications. The performance of classical localization protocols is limited by the specific form of distance information and suffer from considerable ranging errors. This paper foresees a new opportunity by utilizing the exceptional property of entangled quantum states to measure a linear combination of target-anchor distances. Specifically, we consider localization with quantum-based TDoA measurements. Classical TDoA ranging takes the difference of two separate measurements. Instead, quantum ranging allows TDoA estimation within a single measurement, thereby reducing the ranging errors. Numerical simulations demonstrate that the new quantum-based localization significantly outperforms conventional algorithms based on classical ranging, with over 50% gains on average.

cs.ET↗