Quantum circuit simulation is the basic tool for reasoning over quantum programs. Despite the tremendous advance in the simulator technology in the recent years, the performance of simulators is still unsatisfactory on non-trivial circuits, which slows down the development of new quantum systems. In this work, we develop a loop summarizing simulator based on multi-terminal binary decision diagrams (MTBDDs) with efficiently customized quantum gate operations. The simulator is capable of automatic loop summarization using symbolic execution, which saves repetitive computation for circuits with iterative structures. Experimental results show the simulator outperforms state-of-the-art simulators on some standard circuits, such as Grover's algorithm, by several orders of magnitude.
Quantum circuit simulation is the basic tool for reasoning over quantum programs. Despite the tremendous advance in the simulator technology in the recent years, the performance of simulators is still unsatisfactory on non-trivial circuits, which slows down the development of new quantum systems. In this work, we develop a loop summarizing simulator based on multi-terminal binary decision diagrams (MTBDDs) with efficiently customized quantum gate operations. The simulator is capable of automatic loop summarization using symbolic execution, which saves repetitive computation for circuits with iterative structures. Experimental results show the simulator outperforms state-of-the-art simulators on some standard circuits, such as Grover's algorithm, by several orders of magnitude.
With the rapid development of quantum computing, automatic verification of quantum circuits becomes more and more important. While several decision diagrams (DDs) have been introduced in quantum circuit simulation and verification, none of them supports symbolic computation. Algorithmic manipulations of symbolic objects, however, have been identified as crucial, if not indispensable, for several verification tasks. This paper proposes the first decision-diagram approach for operating symbolic objects and verifying quantum circuits with symbolic terms. As a notable example, our symbolic tensor decision diagrams (symbolic TDD) could verify the functionality of the 160-qubit quantum Fourier transform circuit within three minutes. Moreover, as demonstrated on Bernstein-Vazirani algorithm, Grover's algorithm, and the bit-flip error correction code, the symbolic TDD enables efficient verification of quantum circuits with user-supplied oracles and/or classical controls.
Quantum-mechanical phenomena are playing an increasing role in information processing as transistor sizes approach the nanometer level, while the securest forms of communication rely on quantum data encoding. When they involve a finite number of basis states, these phenomena can be modeled as quantum circuits, the quantum analogue of conventional or classical logic circuits. Simulation of quantum circuits can therefore be used as a tool to evaluate issues in the design of quantum information processors. Unfortunately, simulating such phenomena efficiently is exceedingly difficult. The matrices representing quantum operators (gates) and vectors modeling quantum states grow exponentially with the number of quantum bits. The information represented by quantum states and operators often exhibits structure that can be exploited when simulating certain classes of quantum circuits. We study the development of simulation methods that run on classical computers and take advantage of such repetitions and redundancies. In particular, we define a new data structure for simulating quantum circuits called the quantum information decision diagram (QuIDD). A QuIDD is a compressed graph representation of a vector or matrix and permits computations to be performed directly on the compressed data. We develop a comprehensive set of algorithms for operating on QuIDDs in both the state-vector and density-matrix formats, and evaluate their complexity. These algorithms have been implemented in a general-purpose simulator program for quantum-mechanical applications called QuIDDPro. Through extensive experiments conducted on representative quantum simulation applications, including Grover's search algorithm, error characterization, and reversible circuits, we demonstrate that QuIDDPro is faster than other existing quantum-mechanical simulators such as the National Institute of Standards and Technology's QCSim program, and is far more memory-efficient. Using QuIDDPro, we explore the advantages of quantum computation over classical computation, simulate quantum errors and error correction, and study the impact of numerical precision on the fidelity of simulations. We also develop several novel algorithms for testing quantum circuit equivalence and compare them empirically. The QuIDDPro software is equipped with a user-friendly interface and is distributed with numerous example scripts. It has been used as a laboratory supplement for quantum computing courses at several universities.
We present a tool QSeqSim, a Qiskit-integrated symbolic backend that fills the current gap of having no Qiskit-native support for simulating while-loop quantum programs and their induced sequential quantum circuits. QSeqSim takes Qiskit QuantumCircuit objects, translates them into OpenQASM 3 code, and organises the resulting program into a combination of combinational, dynamic, and sequential circuits, thereby assigning while-loops a precise sequential circuit semantics with explicit internal and external qubits. Building on this semantics, QSeqSim adopts a Binary Decision Diagram (BDD)-based symbolic representation and integrates weighted model counting to compute measurement probabilities efficiently by exploiting sharing in structured and sparse BDDs. On top of this Boolean backbone, it introduces dedicated symbolic operators for state composition and state retention, thereby enabling efficient symbolic execution of sequential quantum circuits. Our experiments demonstrate that QSeqSim scales to substantial while-induced sequential circuits; in particular, in the quantum random walk benchmark we successfully simulate circuits with over 1000 qubits for more than 10 loop iterations.
QSeqSim is available at https://github.com/Veri-Q/QSeqSim.
Since quantum computers can solve important problems faster than classical computers, many resources have gone into the development of this technology in recent decades. Despite the tremendous progress that has already been made toward the development of quantum computers, they are still an emerging technology, which restricts access and reliability. Thus, research on quantum algorithms still heavily relies on quantum circuit simulators that run on classical hardware. However, simulating the execution of a quantum computer on conventional hardware is exponentially difficult, which is also the reason why quantum computing is an interesting technology in the first place. Particularly complex is noise-aware simulation of quantum computers, i.e., the consideration of noise effects that are common in today’s quantum hardware during quantum circuit simulation. In this work, we investigate the use of decision diagrams for this task. To this end, we present two distinct approaches for noise-aware quantum circuit simulation, investigate how they can be realized using decision diagrams, and implement decision diagram-based solutions for each of the presented noise-aware simulation schemes. In an extensive evaluation, we unveil potential for further improvements and also demonstrate substantial speed-ups compared to the current state of the art.
The simulation of quantum programs by classical computers is a critical endeavor for several reasons: it provides proof-of-concept validation of quantum algorithms; it provides opportunities to experiment with new programming abstractions suitable for the quantum domain; and most significantly it is a way to explore the elusive boundary at which a quantum advantage may materialize. Here, we show that traditional techniques of symbolic evaluation and partial evaluation yield surprisingly efficient classical simulations for some instances of textbook quantum algorithms that include the Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, Grover, and Shor's algorithms. The success of traditional partial evaluation techniques in this domain is due to one simple insight: the quantum bits used in these algorithms can be modeled by a symbolic boolean variable while still keeping track of the correlations due to superposition and entanglement. More precisely, the system of constraints generated over the symbolic variables contains all the necessary quantum correlations and hence the answer to the quantum algorithms. With a few programming tricks explained in the paper, quantum circuits with millions of gates can be symbolically executed in seconds. Paradoxically, other circuits with as few as a dozen gates take exponential time. We reflect on the significance of these results in the conclusion.
While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design. However, since the work of Richard Feynman in the early 1980s little progress was made in practical quantum simulation. Most researchers focused on polynomial-time simulation of restricted types of quantum circuits that fall short of the full power of quantum computation. Simulating quantum computing devices and useful quantum algorithms on classical hardware now requires excessive computational resources, making many important simulation tasks infeasible. In this work we propose a new technique for gate-level simulation of quantum circuits which greatly reduces the difficulty and cost of such simulations. The proposed technique is implemented in a simulation tool called the Quantum Information Decision Diagram (QuIDD) and evaluated by simulating Grover's quantum search algorithm. The back-end of our package, QuIDD Pro, is based on Binary Decision Diagrams, well-known for their ability to efficiently represent many seemingly intractable combinatorial structures. This reliance on a well-established area of research allows us to take advantage of existing software for BDD manipulation and achieve unparalleled empirical results for quantum simulation.