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

Mapping Quantum Circuits to IBM QX Architectures Using the Minimal Number of SWAP and H Operations

The recent progress in the physical realization of quantum computers (the first publicly available ones--IBM's QX architectures--have been launched in 2017) has motivated research on automatic methods that aid users in running quantum circuits on them. Here, certain physical constraints given by the architectures which restrict the allowed interactions of the involved qubits have to be satisfied. Thus far, this has been addressed by inserting SWAP and H operations. However, it remains unknown whether existing methods add a minimum number of SWAP and H operations or, if not, how far they are away from that minimum--an NP-complete problem. In this work, we address this by formulating the mapping task as a symbolic optimization problem that is solved using reasoning engines like Boolean satisfiability solvers. By this, we do not only provide a method that maps quantum circuits to IBM's QX architectures with a minimal number of SWAP and H operations, but also show by experimental evaluation that the number of operations added by IBM's heuristic solution exceeds the lower bound by more than 100% on average. An implementation of the proposed methodology is publicly available at http://iic.jku.at/eda/research/ibm_qx_mapping

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