Transition-Aware Decomposition of Single-Qudit Gates

• URL: http://arxiv.org/abs/2510.25561v2
• Date: Wed, 05 Nov 2025 07:24:59 GMT
• Title: Transition-Aware Decomposition of Single-Qudit Gates
• Authors: Denis A. Drozhzhin, Evgeniy O. Kiktenko, Aleksey K. Fedorov, Anastasiia S. Nikolaeva,
• Abstract summary: We propose a resource-efficient algorithm to decompose single-qudit operations into the sequence of pulses that are allowed by qudit selection rules.<n>We provide a comparison of qudit decompositions for several types of trapped ions, specifically $171textYb+$, $137textBa+$ and $40textCa+$ with different selection rules.
• Score: 0.19999259391104385
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum computation with $d$-level quantum systems, also known as qudits, benefits from the possibility to use a richer computational space compared to qubits. However, for arbitrary qudit-based hardware platform the issue is that a generic qudit operation has to be decomposed into the sequence of native operations $-$ pulses that are adjusted to the transitions between two levels in a qudit. Typically, not all levels in a qudit are simply connected to each other due to specific selection rules. Moreover, the number of pulses plays a significant role, since each pulse takes a certain execution time and may introduce error. In this paper, we propose a resource-efficient algorithm to decompose single-qudit operations into the sequence of pulses that are allowed by qudit selection rules. Using the developed algorithm, the number of pulses is at most $d(d{-}1)/2$ for an arbitrary single-qudit operation. For specific operations the algorithm could produce even fewer pulses. We provide a comparison of qudit decompositions for several types of trapped ions, specifically $^{171}\text{Yb}^+$, $^{137}\text{Ba}^+$ and $^{40}\text{Ca}^+$ with different selection rules, and also decomposition for superconducting qudits.

Related papers

• Block encoding of sparse matrices with a periodic diagonal structure [67.45502291821956]
  We provide an explicit quantum circuit for block encoding a sparse matrix with a periodic diagonal structure.<n>Various applications for the presented methodology are discussed in the context of solving differential problems.
  arXiv  Detail & Related papers  (2026-02-11T07:24:33Z)
• Qudit-based scalable quantum algorithm for solving the integer programming problem [0.0]
  programming (IP) is an NP-hard optimization problem that is widely used to represent a diverse set of real-world problems.<n>Most quantum algorithms for solving IP are highly resource inefficient because they encode integers into qubits.<n>In this work, a circuit-based scalable quantum algorithm is presented using multiple interacting qudits for which we show a quantum speed-up.
  arXiv  Detail & Related papers  (2025-08-19T15:06:49Z)
• Quantum and classical algorithms for SOCP based on the multiplicative weights update method [44.99833362998488]
  We give classical and quantum algorithms for approximately solving second-order cone programs (SOCPs)<n>Our approach follows the MW framework previously applied to semidefinite programs (SDPs)<n>We show that the additional structure of SOCPs can be exploited to give better runtime with SOCP-specific algorithms.
  arXiv  Detail & Related papers  (2025-07-18T17:55:58Z)
• Arbitrary state creation via controlled measurement [49.494595696663524]
  This algorithm creates an arbitrary $n$-qubit pure quantum superposition state with precision of $m$-decimals.<n>The algorithm uses one-qubit rotations, Hadamard transformations and C-NOT operations with multi-qubit controls.
  arXiv  Detail & Related papers  (2025-04-13T07:23:50Z)
• Simulation of Shor algorithm for discrete logarithm problems with comprehensive pairs of modulo p and order q [0.0]
  We simulate quantum circuits that operate on general pairs of modulo $p and order $q.<n>We show how much the strength of safe-prime groups and Schnorr groups is the same if $p$ is equal.<n>In particular, it was experimentally and theoretically shown that when a carryer is used in the addition circuit, the cryptographic strength of a Schnorr group with $p=$48$ bits under Shor's algorithm is almost equivalent to that of a safe-prime group with $p=$48$ bits.
  arXiv  Detail & Related papers  (2025-03-31T10:39:10Z)
• Space-Efficient Quantum Error Reduction without log Factors [50.10645865330582]
  We present a new highly simplified construction of a purifier, that can be understood as a weighted walk on a line similar to a random walk interpretation of majority voting.<n>Our purifier has exponentially better space complexity than the previous one, and quadratically better dependence on the soundness-completeness gap of the algorithm being purified.
  arXiv  Detail & Related papers  (2025-02-13T12:04:39Z)
• Efficient compilation of quantum circuits using multi-qubit gates [0.0]
  We present a compilation scheme which implements a general-circuit decomposition to a sequence of Ising-type, long-range, multi-qubit entangling gates.<n>We numerically test our compilation and show that, compared to conventional realizations with two-qubit gates, our compilations improves the logarithm of quantum volume by $20%$ to $25%$.
  arXiv  Detail & Related papers  (2025-01-28T19:08:13Z)
• Calculating response functions of coupled oscillators using quantum phase estimation [40.31060267062305]
  We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer.<n>Our proposed quantum algorithm operates in the standard $s-sparse, oracle-based query access model.<n>We show that a simple adaptation of our algorithm solves the random glued-trees problem in time.
  arXiv  Detail & Related papers  (2024-05-14T15:28:37Z)
• Pulse-controlled qubit in semiconductor double quantum dots [57.916342809977785]
  We present a numerically-optimized multipulse framework for the quantum control of a single-electron charge qubit. A novel control scheme manipulates the qubit adiabatically, while also retaining high speed and ability to perform a general single-qubit rotation.
  arXiv  Detail & Related papers  (2023-03-08T19:00:02Z)
• Efficient application of the factorized form of the unitary coupled-cluster ansatz for the variational quantum eigensolver algorithm by using linear combination of unitaries [0.0]
  The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons.
  arXiv  Detail & Related papers  (2023-02-17T04:03:06Z)
• Genetic algorithm for searching bipolar Single-Flux-Quantum pulse sequences for qubit control [0.0]
  We introduce a genetic algorithm for unipolar or bipolar SFQ control sequence search. In the future we will apply the developed approach to study a system of two qubits.
  arXiv  Detail & Related papers  (2022-09-20T15:24:02Z)
• Quantum Goemans-Williamson Algorithm with the Hadamard Test and Approximate Amplitude Constraints [62.72309460291971]
  We introduce a variational quantum algorithm for Goemans-Williamson algorithm that uses only $n+1$ qubits. Efficient optimization is achieved by encoding the objective matrix as a properly parameterized unitary conditioned on an auxilary qubit. We demonstrate the effectiveness of our protocol by devising an efficient quantum implementation of the Goemans-Williamson algorithm for various NP-hard problems.
  arXiv  Detail & Related papers  (2022-06-30T03:15:23Z)
• Binary Optimal Control Of Single-Flux-Quantum Pulse Sequences [0.0]
  We introduce a binary, relaxed gradient, trust-region method for optimizing pulse sequences for single flux quanta (SFQ) control of a quantum computer. We present numerical results for the H and X gates, where the optimized pulse sequences give gate fidelity's better than $99.9%$, in $approx 25$ trust-region.
  arXiv  Detail & Related papers  (2021-06-18T19:40:10Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

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.