Quantum machine learning (QML) algorithms have obtained great relevance in the machine learning (ML) field due to the promise of quantum speedups when performing basic linear algebra subroutines (BLAS), a fundamental element in most ML algorithms. By making use of BLAS operations, we propose, implement and analyze a quantum k-means (qk-means) algorithm with a low time complexity of $\mathcal{O}(NK log(D)I/C)$ to apply it to the fundamental problem of discriminating quantum states at readout. Discriminating quantum states allows the identification of quantum states $\vert 0\rangle$ and $\vert 1\rangle$ from low-level in-phase and quadrature signal (IQ) data, and can be done using custom ML models. In order to reduce dependency on a classical computer, we use the qk-means to perform state discrimination on the IBMQ Bogota device and managed to find assignment fidelities of up to 98.7% that were only marginally lower than that of the k-means algorithm. We also performed a cross-talk benchmark on the quantum device by applying both algorithms to perform state discrimination on a combination of quantum states and using Pearson Correlation coefficients and assignment fidelities of discrimination results to conclude on the presence of cross-talk on qubits. Evidence shows cross-talk in the (1, 2) and (2, 3) neighboring qubit couples for the analyzed device.Quantum machine learning (QML) algorithms have obtained great relevance in the machine learning (ML) field due to the promise of quantum speedups when performing basic linear algebra subroutines (BLAS), a fundamental element in most ML algorithms. By making use of BLAS operations, we propose, implement and analyze a quantum k-means (qk-means) algorithm with a low time complexity of$\mathcal{O}(NK log(D)I/C)$to apply it to the fundamental problem of discriminating quantum states at readout. Discriminating quantum states allows the identification of quantum states$\vert 0\rangle$and$\vert 1\rangle$from low-level in-phase and quadrature signal (IQ) data, and can be done using custom ML models. In order to reduce dependency on a classical computer, we use the qk-means to perform state discrimination on the IBMQ Bogota device and managed to find assignment fidelities of up to 98.7% that were only marginally lower than that of the k-means algorithm. We also performed a cross-talk benchmark on the quantum device by applying both algorithms to perform state discrimination on a combination of quantum states and using Pearson Correlation coefficients and assignment fidelities of discrimination results to conclude on the presence of cross-talk on qubits. Evidence shows cross-talk in the (1, 2) and (2, 3) neighboring qubit couples for the analyzed device.

arXiv:2112.00313IEEE International Conference on Rebooting Computing (ICRC)Nov 1, 202113 citations

Quantum Algorithms from a Linear Algebra Perspective

Liam Michael Ogren, Lauren Michelle Baker

Apr 27, 20170 citations

Binary Tree Block Encoding of Classical Matrix

Zexian Li, Xiao‐Ming Zhang, Chunlin Yang +1 more

State preparation and block-encoding are essential subroutines in quantum computing. The former provides basic encoding of quantum states, while the latter transforms classical data into a matrix representation within a quantum circuit. Some quantum advantages are built on the assumption that the subroutine– block encoding has been compiled in the quantum circuit, and this derives a problem of how to efficiently compile a block encoding. The resource trade-offs of block encoding, such as circuit size, subnormalization factor, compilation complexity (both time and space), and robustness against errors are central to its efficiency. In this work, the Binary Tree Block-Encoding (BITBLE) protocol is introduced, which optimizes these trade-offs. For a classical matrix in C2n× 2n, our approach reduces the compilation time toO(n22n) using n ancilla qubits, achieving superior resource trade-offs compared to existing methods. Numerical experiments further reveal that the approach outlined in BITBLE enhances compilation efficiency, resource scalability, and robustness against single-qubit gate errors in various standard data encoding tasks. Moreover, all algorithms are available as open-source.State preparation and block-encoding are essential subroutines in quantum computing. The former provides basic encoding of quantum states, while the latter transforms classical data into a matrix representation within a quantum circuit. Some quantum advantages are built on the assumption that the subroutine– block encoding has been compiled in the quantum circuit, and this derives a problem of how to efficiently compile a block encoding. The resource trade-offs of block encoding, such as circuit size, subnormalization factor, compilation complexity (both time and space), and robustness against errors are central to its efficiency. In this work, the Binary Tree Block-Encoding (BITBLE) protocol is introduced, which optimizes these trade-offs. For a classical matrix in C2n× 2n, our approach reduces the compilation time toO(n22n) using n ancilla qubits, achieving superior resource trade-offs compared to existing methods. Numerical experiments further reveal that the approach outlined in BITBLE enhances compilation efficiency, resource scalability, and robustness against single-qubit gate errors in various standard data encoding tasks. Moreover, all algorithms are available as open-source.

arXiv:2504.05624IEEE Transactions on Quantum EngineeringOct 23, 20251 citation

Experimental demonstration of the Quantum Fourier Transform on up to 100 qubits using a convolutional compilation strategy

Paul Coote, Michael J. Biercuk, Yuval Baum

We present and experimentally validate the `Convolutional QFT': a constructive compilation strategy for the Quantum Fourier Transform (QFT) subroutine on a linear nearest neighbor (LNN) qubit topology. We first introduce a novel strategy that compiles the $n$ -qubit QFT onto an LNN topology using only $n^2 - n$ $CX$ gates, matching requirements of a direct compilation on an all-to-all architecture. We then derive the convolutional variant used in our experiments, which requires an additional two $CX$ gates in total, and is realized via a compact, translation-invariant kernel circuit gadget that traverses a quantum register. We demonstrate the power of the convolutional compilation strategy on the IBM Quantum Platform by executing QFT benchmarking circuits. We measure a process fidelity of 11.4% at 50 qubits, and 1.8% at 80 qubits. The correct output state remains clearly distinguishable above background noise up to 100 qubits. These results constitute the largest experimental QFT demonstrated on any quantum computing hardware to date.We present and experimentally validate the `Convolutional QFT': a constructive compilation strategy for the Quantum Fourier Transform (QFT) subroutine on a linear nearest neighbor (LNN) qubit topology. We first introduce a novel strategy that compiles the $n$-qubit QFT onto an LNN topology using only $n^2 - n$ $CX$ gates, matching requirements of a direct compilation on an all-to-all architecture. We then derive the convolutional variant used in our experiments, which requires an additional two $CX$ gates in total, and is realized via a compact, translation-invariant kernel circuit gadget that traverses a quantum register. We demonstrate the power of the convolutional compilation strategy on the IBM Quantum Platform by executing QFT benchmarking circuits. We measure a process fidelity of 11.4% at 50 qubits, and 1.8% at 80 qubits. The correct output state remains clearly distinguishable above background noise up to 100 qubits. These results constitute the largest experimental QFT demonstrated on any quantum computing hardware to date.

quant-pharXiv:2608.05435Aug 7, 20260 citations

Compiling quantum programs

Paolo Zuliani

Acta InformaticaMay 24, 200529 citations

QISKit, Awesome SDK for Quantum Programming in Python

Vladimir Silva

In this chapter you will get started with the QISKit, the best SDK out there for quantum programming. You will learn how easy it is to install the SDK in your local system. But before writing your first quantum program, it is always helpful to understand what quantum computation is and how it differs from classical computation. For this purpose, a very basic explanation of qubit states and quantum gates is presented using linear algebra. This section also shows how quantum computation can mirror its classical counterpart and furthermore find shortcuts to get results faster. Next, the chapter walks through the anatomy of a quantum program including system calls, circuit compilation formats, quantum assembly, and more.In this chapter you will get started with the QISKit, the best SDK out there for quantum programming. You will learn how easy it is to install the SDK in your local system. But before writing your first quantum program, it is always helpful to understand what quantum computation is and how it differs from classical computation. For this purpose, a very basic explanation of qubit states and quantum gates is presented using linear algebra. This section also shows how quantum computation can mirror its classical counterpart and furthermore find shortcuts to get results faster. Next, the chapter walks through the anatomy of a quantum program including system calls, circuit compilation formats, quantum assembly, and more.

Apress eBooksJan 1, 20183 citations

\mathcal{O}(NK log(D)I/C)

to apply it to the fundamental problem of discriminating quantum states at readout. Discriminating quantum states allows the identification of quantum states

\vert 0\rangle

and

\vert 1\rangle

from low-level in-phase and quadrature signal (IQ) data, and can be done using custom ML models. In order to reduce dependency on a classical computer, we use the qk-means to perform state discrimination on the IBMQ Bogota device and managed to find assignment fidelities of up to 98.7% that were only marginally lower than that of the k-means algorithm. We also performed a cross-talk benchmark on the quantum device by applying both algorithms to perform state discrimination on a combination of quantum states and using Pearson Correlation coefficients and assignment fidelities of discrimination results to conclude on the presence of cross-talk on qubits. Evidence shows cross-talk in the (1, 2) and (2, 3) neighboring qubit couples for the analyzed device.

n

-qubit QFT onto an LNN topology using only

n^2 - n

CX

gates, matching requirements of a direct compilation on an all-to-all architecture. We then derive the convolutional variant used in our experiments, which requires an additional two

CX

gates in total, and is realized via a compact, translation-invariant kernel circuit gadget that traverses a quantum register. We demonstrate the power of the convolutional compilation strategy on the IBM Quantum Platform by executing QFT benchmarking circuits. We measure a process fidelity of 11.4% at 50 qubits, and 1.8% at 80 qubits. The correct output state remains clearly distinguishable above background noise up to 100 qubits. These results constitute the largest experimental QFT demonstrated on any quantum computing hardware to date.