Mixed-Dimensional Quantum Circuit Simulation with Decision Diagrams

Quantum computers promise to solve several categories of problems faster than classical computers ever could. Current research mostly focuses on qubits, i.e., systems where the unit of information can assume only two levels. However, the underlying physics of most (if not all) of the technological platforms supports more than two levels, commonly referred to as qudits. Performing computations with qudits increases the overall complexity while, at the same time, reducing the number of operations and providing a lower error rate. Furthermore, qudits with different number of levels can be mixed in one system to ease the experimental control and keep representations as compact as possible. Exploiting these capabilities requires dedicated software support to tackle the increased complexity in an automated and efficient fashion. In this paper, we present a qudit simulator that handles mixed-dimensional systems based on Decision Diagrams (DDs). More precisely, we discuss the type of decision diagram introduced as underlying data structure as well as the resulting implementation. Experimental evaluations demonstrate that the proposed solution is capable of efficiently simulating mixed-dimensional quantum circuits, with specific use cases including more than 100 qudits in one circuit. The source code of the simulator is available via github.com/cda-tum/MiSiM under the MIT~license.Comment: 12 pages, 5 figures, 1 tabl

Exploiting Quantum Teleportation in Quantum Circuit Mapping

Quantum computers are constantly growing in their number of qubits, but continue to suffer from restrictions such as the limited pairs of qubits that may interact with each other. Thus far, this problem is addressed by mapping and moving qubits to suitable positions for the interaction (known as quantum circuit mapping). However, this movement requires additional gates to be incorporated into the circuit, whose number should be kept as small as possible since each gate increases the likelihood of errors and decoherence. State-of-the-art mapping methods utilize swapping and bridging to move the qubits along the static paths of the coupling map---solving this problem without exploiting all means the quantum domain has to offer. In this paper, we propose to additionally exploit quantum teleportation as a possible complementary method. Quantum teleportation conceptually allows to move the state of a qubit over arbitrary long distances with constant overhead---providing the potential of determining cheaper mappings. The potential is demonstrated by a case study on the IBM Q Tokyo architecture which already shows promising improvements. With the emergence of larger quantum computing architectures, quantum teleportation will become more effective in generating cheaper mappings.Comment: To appear in ASP-DAC 202

How to Efficiently Handle Complex Values? Implementing Decision Diagrams for Quantum Computing

Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum functionality. In the classical domain, decision diagrams have been successfully employed as a powerful alternative to straightforward means such as truth tables. This motivated extensive research on whether decision diagrams provide similar potential in the quantum domain -- resulting in new types of decision diagrams capable of substantially reducing the complexity of representing quantum states and functionality. From an implementation perspective, many concepts and techniques from the classical domain can be re-used in order to implement decision diagrams packages for the quantum realm. However, new problems -- namely how to efficiently handle complex numbers -- arise. In this work, we propose a solution to overcome these problems. Experimental evaluations confirm that this yields improvements of orders of magnitude in the runtime needed to create and to utilize these decision diagrams. The resulting implementation is publicly available as a quantum DD package at http://iic.jku.at/eda/research/quantum_dd

Just Like the Real Thing: Fast Weak Simulation of Quantum Computation

Quantum computers promise significant speedups in solving problems intractable for conventional computers but, despite recent progress, remain limited in scaling and availability. Therefore, quantum software and hardware development heavily rely on simulation that runs on conventional computers. Most such approaches perform strong simulation in that they explicitly compute amplitudes of quantum states. However, such information is not directly observable from a physical quantum computer because quantum measurements produce random samples from probability distributions defined by those amplitudes. In this work, we focus on weak simulation that aims to produce outputs which are statistically indistinguishable from those of error-free quantum computers. We develop algorithms for weak simulation based on quantum state representation in terms of decision diagrams. We compare them to using state-vector arrays and binary search on prefix sums to perform sampling. Empirical validation shows, for the first time, that this enables mimicking of physical quantum computers of significant scale.Comment: 6 pages, 4 figure

As Accurate as Needed, as Efficient as Possible: Approximations in DD-based Quantum Circuit Simulation

Quantum computers promise to solve important problems faster than conventional computers. However, unleashing this power has been challenging. In particular, design automation runs into (1) the probabilistic nature of quantum computation and (2) exponential requirements for computational resources on non-quantum hardware. In quantum circuit simulation, Decision Diagrams (DDs) have previously shown to reduce the required memory in many important cases by exploiting redundancies in the quantum state. In this paper, we show that this reduction can be amplified by exploiting the probabilistic nature of quantum computers to achieve even more compact representations. Specifically, we propose two new DD-based simulation strategies that approximate the quantum states to attain more compact representations, while, at the same time, allowing the user to control the resulting degradation in accuracy. We also analytically prove the effect of multiple approximations on the attained accuracy and empirically show that the resulting simulation scheme enables speed-ups up to several orders of magnitudes.Comment: 6 pages, 2 figures, to be published at Design, Automation, and Test in Europe 202

Approximation of Quantum States Using Decision Diagrams

The computational power of quantum computers poses major challenges to new design tools since representing pure quantum states typically requires exponentially large memory. As shown previously, decision diagrams can reduce these memory requirements by exploiting redundancies. In this work, we demonstrate further reductions by allowing for small inaccuracies in the quantum state representation. Such inaccuracies are legitimate since quantum computers themselves experience gate and measurement errors and since quantum algorithms are somewhat resistant to errors (even without error correction). We develop four dedicated schemes that exploit these observations and effectively approximate quantum states represented by decision diagrams. We empirically show that the proposed schemes reduce the size of decision diagrams by up to several orders of magnitude while controlling the fidelity of approximate quantum state representations