Noisy Intermediate-Scale Quantum (NISQ) devices face many critical challenges that limit their usefulness for practical applications. A primary challenge is classical-to-quantum (C2Q) data encoding, which requires specific circuits for quantum state initialization, particularly for I/O intensive applications. The required state initialization circuits are often complex, and violate decoherence constraints. Another critical challenge for quantum computers is quantum state readout or quantum-to-classical (Q2C) data decoding. The general approach for Q2C involves repeated sampling of the quantum circuit, which often incurs significant overhead in the overall execution time. In this paper, we propose time-efficient methods for C2Q data encoding and Q2C data decoding for quantum algorithms. Decoherence optimized circuits for C2Q data encoding are presented along with analysis of their circuit depths. For Q2C, a novel approach based on more efficient sampling of the output state using the Quantum Wavelet Transform is proposed. The proposed methods are experimentally evaluated on a state-of-the-art quantum computing device from IBM Quantum using realistic multi-spectral data. Experimental results are consistent with our theoretical expectations and confirm the efficiency of our proposed methods compared to existing techniques. More specifically, our proposed C2Q method demonstrates a theoretical 2x reduction in circuit depth which resulted in improving the experimental execution time compared to the state-of-the-art, while our Q2C method achieved a maximum of 89% reduction in circuit sampling time.
Noisy Intermediate-Scale Quantum (NISQ) devices face many critical challenges that limit their usefulness for practical applications. A primary challenge is classical-to-quantum (C2Q) data encoding, which requires specific circuits for quantum state initialization, particularly for I/O intensive applications. The required state initialization circuits are often complex, and violate decoherence constraints. Another critical challenge for quantum computers is quantum state readout or quantum-to-classical (Q2C) data decoding. The general approach for Q2C involves repeated sampling of the quantum circuit, which often incurs significant overhead in the overall execution time. In this paper, we propose time-efficient methods for C2Q data encoding and Q2C data decoding for quantum algorithms. Decoherence optimized circuits for C2Q data encoding are presented along with analysis of their circuit depths. For Q2C, a novel approach based on more efficient sampling of the output state using the Quantum Wavelet Transform is proposed. The proposed methods are experimentally evaluated on a state-of-the-art quantum computing device from IBM Quantum using realistic multi-spectral data. Experimental results are consistent with our theoretical expectations and confirm the efficiency of our proposed methods compared to existing techniques. More specifically, our proposed C2Q method demonstrates a theoretical 2x reduction in circuit depth which resulted in improving the experimental execution time compared to the state-of-the-art, while our Q2C method achieved a maximum of 89% reduction in circuit sampling time.
Abstract One of the challenges facing current Noisy-Intermediate-Scale-Quantum devices (NISQ) is achieving efficient quantum circuit measurement or readout. The process of extracting classical data from the quantum domain, termed in this work as quantum-to-classical (Q2C) data decoding, generally incurs significant overhead, since the quantum circuit needs to be sampled repeatedly to obtain useful data readout. In this paper, we propose and evaluate time-efficient and depth-optimized Q2C methods based on the multidimensional, multilevel-decomposable, quantum wavelet transform (QWT) whose packet and pyramidal forms are leveraged and optimized. We also propose a zero-depth technique that uses selective placement of measurement gates to perform the QWT operation. To demonstrate their efficiency, the proposed techniques are quantitatively evaluated in terms of execution time, circuit depth, and accuracy in comparison to existing Q2C techniques. Experimental evaluations of the proposed Q2C methods are performed using real high-resolution multispectral images on a 27-qubit state-of-the-art quantum computing device from IBM Quantum.
Algorithms such as quantum wavelet transform (QWT) can be utilized on quantum processors to gain significant speedup compared to their classical counterparts. Domains such as high-energy-physics and remote-sensing hyperspectral imagery require high compute capabilities and can benefit from applying QWT for dimension reduction of multidimensional data. However, quantum circuits for QWT include permutations that contribute to large overall circuit depth. Deep circuits pose a critical challenge for state-of-the-art quantum computers because of quantum decoherence. In this work, we propose QWT circuits, which are optimized in terms of circuit depth, to account for the effects of decoherence, and resulting in high fidelity and efficient implementation on quantum processors. We present the circuits in generalized forms and show that they can be used for multilevel decomposable, multidimensional wavelet operations. Experimental evaluation of the proposed circuits is performed through simulation using MATLAB and IBM-Q qasm, and implemented on a real 15-qubit quantum processor from IBM.
For practical usage of quantum systems in solving real-world problems, large amounts of classical data are required to be transferred/encoded to the quantum domain. Arbitrary classical data is usually encoded onto quantum devices by synthesizing and initializing a corresponding quantum state. Current techniques of arbitrary state synthesis, however, produce deep and complex quantum circuits, leading to low state fidelity and possible violations of decoherence constraints. In this work, we propose an improved methodology and optimized circuits for synthesizing any arbitrary quantum state from given classical data. Compared to existing methods, the proposed methodology results in circuits with lower gate count, lower circuit depth, and high state fidelity. The proposed methods are evaluated by simulation in MATLAB and IBM qasm, and realistic implementation on an IBM quantum device. The experimental results show a reduction in gate count and circuit depth by a factor of two over existing methods.
Quantum computing is a rapidly expanding field with applications ranging from optimization all the way to complex machine learning tasks. Quantum memories, while lacking in practical quantum computers, have the potential to bring quantum advantage. In quantum machine learning applications for example, a quantum memory can simplify the data loading process and potentially accelerate the learning task. Quantum memory can also store intermediate quantum state of qubits that can be reused for computation. However, the depth, gate count and compilation time of quantum memories such as, Quantum Read Only Memory (QROM) scale exponentially with the number of address lines making them impractical in state-of-the-art Noisy Intermediate-Scale Quantum (NISQ) computers beyond 4-bit addresses. In this paper, we propose techniques such as, pre-decoding logic and qubit reset to reduce the depth and gate count of QROM circuits to target wider address ranges such as, 8-bits. The proposed approach reduces the number of gates and depth count by at least 2X compared to the naive implementation at only 36% qubit overhead. A reduction in circuit depth and gate count as high as 75X and compilation time by 85X at the cost of a maximum of 2.28X qubit overhead is observed. Experimentally, the fidelity with the proposed pre-decoding circuit compared to existing optimization approach is also higher (as much as 73% compared to 40.8%) under reduced error rates.
The rapid advancement of quantum computing has created new opportunities for solving computationally intensive problems across diverse fields such as optimization, physical system simulation, and machine learning. However, practical implementation on Noisy Intermediate-Scale Quantum (NISQ) devices remains challenging due to hardware limitations including noise, decoherence, and restricted qubit connectivity. A fundamental constraint further complicating this effort is that all quantum operations must be unitary, while many real-world problems are naturally expressed in non-unitary forms. This discrepancy necessitates novel techniques for transforming non-unitary mathematical structures into unitary or Hamiltonian representations compatible with quantum hardware.This thesis proposes a unified framework for converting structured, sparse, or otherwise non-unitary classical matrices into unitary forms that can be executed efficiently on NISQ devices. The methodology introduces general transformation strategies such as linear combinations of unitaries, structured embeddings, and resource-aware circuit construction, enabling the deployment of quantum algorithms without incurring prohibitive overhead. Each technique is developed with an emphasis on preserving problem structure, minimizing circuit depth, and ensuring compatibility with IBM’s NISQ hardware. The proposed frameworks are validated through theoretical analysis and quantum simulations, with performance benchmarks based on gate count, circuit fidelity, convergence behavior, and scalability. This work demonstrates how non-unitary formulations arising in various computational contexts can be systematically adapted for quantum execution, advancing the practical utility of NISQ-era devices.
Quantum computing (QC) is a new paradigm offering the potential of exponential speedups over classical computing for certain computational problems. Each additional qubit doubles the size of the computational state space available to a QC algorithm. This exponential scaling underlies QC’s power, but today’s Noisy Intermediate-Scale Quantum (NISQ) devices face significant engineering challenges in scalability. The set of quantum circuits that can be reliably run on NISQ devices is limited by their noisy operations and low qubit counts. This paper introduces CutQC, a scalable hybrid computing approach that combines classical computers and quantum computers to enable evaluation of quantum circuits that cannot be run on classical or quantum computers alone. CutQC cuts large quantum circuits into smaller subcircuits, allowing them to be executed on smaller quantum devices. Classical postprocessing can then reconstruct the output of the original circuit. This approach offers significant runtime speedup compared with the only viable current alternative—purely classical simulations—and demonstrates evaluation of quantum circuits that are larger than the limit of QC or classical simulation. Furthermore, in real-system runs, CutQC achieves much higher quantum circuit evaluation fidelity using small prototype quantum computers than the state-of-the-art large NISQ devices achieve. Overall, this hybrid approach allows users to leverage classical and quantum computing resources to evaluate quantum programs far beyond the reach of either one alone.