[Paper Review] QSystem: bitwise representation for quantum circuit simulations

Evandro C. R. Rosa, Bruno G. Taketani|arXiv (Cornell University)|Apr 7, 2020

Quantum Computing Algorithms and Architecture3 references4 citations

TL;DR

This paper introduces QSystem, an open-source quantum circuit simulator that uses a novel bitwise representation based on Hashmaps and bitwise operations to achieve exponential speedup in simulating quantum states with limited superposition. By efficiently storing and manipulating only the non-zero basis states via bit-level operations, QSystem outperforms Qiskit, Cirq, and Forest SDK, especially in scenarios with sparse quantum states, demonstrating significant performance gains without prior knowledge of the state structure.

ABSTRACT

We present QSystem, an open-source platform for the simulation of quantum circuits focused on bitwise operations on a Hashmap data structure storing quantum states and gates. QSystem is implemented in C++ and delivered as a Python module, taking advantage of the C++ performance and the Python dynamism. The simulators API is designed to be simple and intuitive, thus streamlining the simulation of a quantum circuit in Python. The current release has three distinct ways to represent the quantum state: vector, matrix, and the proposed bitwise. The latter constitutes our main results and is a new way to store and manipulate both states and operations which shows an exponential advantage with the amount of superposition in the systems state. We benchmark the bitwise representation against other simulators, namely Qiskit, Forest SDK QVM, and Cirq.

Motivation & Objective

• To develop a quantum circuit simulator that efficiently handles quantum states with limited superposition, reducing memory and time costs.
• To address the exponential resource scaling of traditional quantum simulators by introducing a novel data representation based on bitwise operations.
• To provide a high-performance, open-source simulation platform that integrates C++ speed with Python usability for quantum algorithm development.
• To benchmark the new bitwise representation against established simulators under various quantum circuit workloads.
• To demonstrate that exponential speedup is achievable without prior knowledge of the relevant basis states, relying only on the sparsity of the state.

Proposed method

• The bitwise representation stores quantum states as Hashmaps where keys are computational basis state indices (integers) and values are complex amplitudes, enabling sparse storage.
• Quantum gates are implemented using bitwise logical operations (e.g., XOR for CNOT) and bit shifts, allowing direct manipulation of state indices without full matrix operations.
• The simulator uses a C++ core for performance and exposes a Python API for ease of use, enabling intuitive circuit construction with quantum computing terminology.
• Three representations are supported: vector (dense state), matrix (density matrix for error modeling), and the proposed bitwise (sparse state with bit operations).
• The measurement process applies Algorithm 4 sequentially to each qubit, collapsing the state and extracting measurement outcomes via probabilistic sampling from the Hashmap.
• The framework supports arbitrary basis states, with the current implementation using the computational basis defined by the Pauli Z operator, but extensible to other bases like those used in Matrix Product States.

Experimental results

Research questions

• RQ1 Can a bitwise representation using Hashmaps and bit operations achieve exponential speedup in quantum circuit simulation for states with limited superposition?
• RQ2 How does the performance of the bitwise representation compare to established simulators like Qiskit, Cirq, and Forest SDK under varying circuit complexity and state sparsity?
• RQ3 Does the observed speedup depend on prior knowledge of the basis states, or is it effective even when the relevant states are unknown?
• RQ4 Can the bitwise approach maintain exponential scaling advantages in entangled state preparation, such as GHZ states, despite high entanglement?
• RQ5 To what extent can the method be generalized to other data structures or basis sets beyond the computational basis?

Key findings

• The bitwise representation achieves exponential speedup in simulation time for quantum states that require only a small, unknown set of basis states, as predicted by the theoretical model.
• Benchmarking on GHZ state preparation showed that QSystem's bitwise representation scaled significantly better than Qiskit, Cirq, and Forest SDK, with reduced time growth as qubit count increased.
• In measurement operations, the bitwise method reduced overhead by more than an order of magnitude compared to Cirq, despite no optimization for simultaneous measurements.
• The exponential scaling advantage was observed even in cases where no speedup was expected, such as in dense state simulations, indicating robustness across state types.
• The method achieved performance gains without requiring knowledge of the relevant basis states, relying solely on the sparsity of the state representation.
• The framework successfully simulated entangled states like GHZ states with high efficiency, demonstrating that entanglement alone does not limit the speedup, which is instead governed by state sparsity.