Distributed Quantum Inner Product Estimation with Low-Depth Circuits

• URL: http://arxiv.org/abs/2506.19574v2
• Date: Sat, 19 Jul 2025 04:36:23 GMT
• Title: Distributed Quantum Inner Product Estimation with Low-Depth Circuits
• Authors: Congcong Zheng, Kun Wang, Xutao Yu, Ping Xu, Zaichen Zhang,
• Abstract summary: This work explores DIPE with low-depth quantum circuits.<n>We first establish that DIPE with an arbitrary unitary $2$-design ensemble achieves an average sample complexity of $Theta(sqrt2n)$.<n>We then analyze ensembles below unitary $2$-designs showing average sample complexities of $O(sqrt2.18n)$ and $O(sqrt2.5n)$.
• Score: 14.494830101269677
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Distributed inner product estimation (DIPE) is a fundamental task in quantum information, aiming to estimate the inner product between two unknown quantum states prepared on distributed quantum platforms. Existing rigorous sample complexity analyses are limited to unitary $4$-designs, which present practical challenges for near-term quantum devices. This work addresses this challenge by exploring DIPE with low-depth quantum circuits. We first establish that DIPE with an arbitrary unitary $2$-design ensemble achieves an average sample complexity of $\Theta(\sqrt{2^n})$, where $n$ is the number of qubits. We then analyze ensembles below unitary $2$-designs -- specifically, the brickwork and local unitary $2$-design ensembles -- showing average sample complexities of $O(\sqrt{2.18^n})$ and $O(\sqrt{2.5^n})$, respectively. Furthermore, we analyze the state-dependent variance for the brickwork and Clifford ensembles. Remarkably, we find that DIPE with the global Clifford ensemble requires $\Theta(\sqrt{2^n})$ copies for arbitrary state pairs, with its efficiency further enhanced by the nonstabilizerness of the state pairs. Numerical simulations with GHZ states and Haar random states up to $26$ qubits show that low-depth circuit ensembles can match the performance of unitary $4$-designs in practice. Our findings offer theoretically guaranteed methods for implementing DIPE with experimentally feasible unitary ensembles.

Related papers

• Non-Iterative Disentangled Unitary Coupled-Cluster based on Lie-algebraic structure [0.0]
  Fixed Unitary Coupled-Cluster (UCC) ans"atze are attractive for performing quantum chemistry Variational Quantumsolver (VQE) computations.<n>We introduce $k$-NI-DUCC, a fixed and Non-iterative Disentangled Unitary Coupled-Cluster compact ansatz.
  arXiv  Detail & Related papers  (2024-08-26T14:19:53Z)
• Dividing quantum circuits for time evolution of stochastic processes by orthogonal series density estimation [0.0]
  Quantum Monte Carlo integration (QMCI) is a quantum algorithm to estimate expectations of random variables.<n>In this paper, we propose a method to divide $U_X(t)$ based on orthogonal series density estimation.<n>Our method achieves the circuit depth and total query complexity scaling as $O(sqrtN)$ and $O(N3/2)$, respectively.
  arXiv  Detail & Related papers  (2024-06-04T01:50:21Z)
• Accurate and precise quantum computation of valence two-neutron systems [0.0]
  We introduce a quantum algorithm to accurately and precisely compute the ground state of two-neutron systems. Our experiments using real quantum devices also show the pivotal role of the circuit layout design, attuned to the connectivity of the qubits.
  arXiv  Detail & Related papers  (2024-04-02T06:54:13Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Simulation of IBM's kicked Ising experiment with Projected Entangled Pair Operator [71.10376783074766]
  We perform classical simulations of the 127-qubit kicked Ising model, which was recently emulated using a quantum circuit with error mitigation. Our approach is based on the projected entangled pair operator (PEPO) in the Heisenberg picture. We develop a Clifford expansion theory to compute exact expectation values and use them to evaluate algorithms.
  arXiv  Detail & Related papers  (2023-08-06T10:24:23Z)
• On sampling determinantal and Pfaffian point processes on a quantum computer [49.1574468325115]
  DPPs were introduced by Macchi as a model in quantum optics the 1970s. Most applications require sampling from a DPP, and given their quantum origin, it is natural to wonder whether sampling a DPP on a classical computer is easier than on a classical one. Vanilla sampling consists in two steps, of respective costs $mathcalO(N3)$ and $mathcalO(Nr2)$ operations on a classical computer, where $r$ is the rank of the kernel matrix.
  arXiv  Detail & Related papers  (2023-05-25T08:43:11Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• Distributed quantum inner product estimation [14.222887950206658]
  A benchmarking task known as cross-platform verification has been proposed that aims to estimate the fidelity of states prepared on two quantum computers. No quantum communication can be performed between the two physical platforms due to hardware constraints. We show that the sample complexity must be at least $Omega(max1/varepsilon2,sqrtd/varepsilon)$, even in the strongest setting.
  arXiv  Detail & Related papers  (2021-11-05T05:35:03Z)
• Halving the cost of quantum multiplexed rotations [0.0]
  We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls. Our results roughly halve the cost of state-of-art electronic structure simulations based on qubitization of double-factorized or tensor-hypercontracted representations.
  arXiv  Detail & Related papers  (2021-10-26T06:49:44Z)
• Under-bagging Nearest Neighbors for Imbalanced Classification [63.026765294759876]
  We propose an ensemble learning algorithm called textitunder-bagging $k$-NN (textitunder-bagging $k$-NN) for imbalanced classification problems.
  arXiv  Detail & Related papers  (2021-09-01T14:10:38Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.