19 research outputs found
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