Recent advancements in quantum technologies shed light on viable quantum computation in near future. Quantum circuit simulation plays a key role in the toolchain of quantum hardware and software development. Due to the enormous Hilbert space of quantum states, simulating quantum circuits with classical computers is notoriously challenging. This work enhances quantum circuit simulation in two dimensions: accuracy (by representing complex numbers algebraically) and scalability (by bit-slicing number representation and achieving matrix-vector multiplication with symbolic Boolean manipulation). Experiments demonstrate the superiority of our method to the state-of-the-art tools over various quantum circuits with up to tens of thousands of qubits.
As quantum computers of non-trivial size become available in the near future, it is imperative to develop tools to emulate small quantum computers. This allows for validation and debugging of algorithms as well as exploring hardware-software co-design to guide the development of quantum hardware and architectures. The simulation of quantum computers entails multiplications of sparse matrices with very large dense vectors of dimension 2n, where n denotes the number of qubits, making this a memory-bound and network bandwidth-limited application. We introduce the concept of a quantum computer emulator as a component of a software framework for quantum computing, enabling a significant performance advantage over simulators by emulating quantum algorithms at a high level rather than simulating individual gate operations. We describe various optimization approaches and present benchmarking results, establishing the superiority of quantum computer emulators in terms of performance.
Quantum circuits, fundamental to quantum computation, represent quantum states through a sequence of unitary transformations. The exponential growth in the Hilbert space dimension with increasing circuit size presents a significant challenge to simulation and analysis. This work introduces a novel tensor network approach to formally model and manipulate quantum circuits, specifically designed to mitigate this exponential scaling issue. The core idea is to represent the circuit's state vector as a tensor network, leveraging techniques for efficient compression and expansion. We explore the application of variational tensor networks (VTNs) to approximate the dynamics of quantum circuits, offering a pathway towards more scalable simulations. The effectiveness of this method is demonstrated through theoretical analysis and conceptual design, focusing on key aspects of tensor network construction and manipulation tailored to quantum circuit representations. This approach aims to provide a more scalable representation compared to existing methods.
Quantum computer simulations are essential for validating quantum algorithms but face significant computational and memory challenges due to massive floating-point arithmetic with complex numbers. In this paper, we propose a Quantization for Quantum computer simulation (QQ), an integer-based quantization scheme that considerably reduces these overheads while maintaining simulation accuracy. By exploiting the structure of quantum gate matrices, the proposed method separates real and imaginary components, eliminating zero-value operations. Across 25 quantum benchmark circuits, our quantization scheme reduces matrix-vector multiplications and additions by up to 50% and 66.7%, respectively, leading to energy savings of up to 400,834× compared to conventional quantum simulations. It also maintains simulation fidelity above 0.99 for most benchmark circuits, with over half preserving accuracy even at 2-bit precision. Additionally, it reduces memory usage by up to 93.75%, enabling scalable and efficient quantum computer simulations.
We discuss a new approach to simulate quantum algorithms using classical probabilistic bits and circuits. Each qubit (a two-level quantum system) is initially mapped to a vector in an eight dimensional probability space (equivalently, to a classical random variable with eight probabilistic outcomes). The key idea in this mapping is to store both the amplitude and phase information of the complex coefficients that describe the qubit state in the probabilities. Due to the identical tensor product structure of combining multiple quantum systems as well as multiple probability spaces,
n qubits are then mapped to a tensor product of
n 8-dimensional probabilistic vectors (i.e., the Hilbert space of dimension
2n is mapped to a probability space of dimension
8n). After this initial mapping, we show how to implement the analogs of single-qubit and two-qubit gates in the probability space using correlation-inducing operations on these classical random variables. The key defining feature of both the mapping to the probability space and the transformations in this space (i.e., operations on the random variables) is that they are not linear, but instead affine. Using this architecture, the evolution of the
2n complex coefficients of the quantum system can be tracked in the joint fully-correlated probabilities of the polynomial number of random variables. We then give specific procedures for implementing (1) the Deutsch-Jozsa algorithm, and (2) the Quantum Fourier Transform in the probability space. Identical to the Quantum case, simulating the Quantum Fourier Transform in the probability space requires
O(n) probabilistic bits and
O(n2) (i.e., quadratic in the number of quantum bits) operations.
The accurate simulation of quantum circuits remains a significant challenge due to the exponential scaling of computational resources with circuit size. This work explores the application of tensor network methods, specifically Matrix Product States (MPS), to provide a scalable approach for simulating quantum circuits. We demonstrate how tensor networks can efficiently represent and manipulate the states of quantum circuits, reducing the computational burden associated with traditional methods. The core claim of this research is that tensor networks offer a viable path to accurately simulating larger and more complex quantum systems. This research introduces a novel framework for symbolic simulation, leveraging the power of tensor network representations to overcome the limitations of conventional simulation techniques. The effectiveness of this approach is illustrated through theoretical analysis and conceptual examples.