6 research outputs found
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