25,598 research outputs found
Gate-Level Simulation of Quantum Circuits
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
Improving Gate-Level Simulation of Quantum Circuits
Simulating quantum computation on a classical computer is a difficult problem. The matrices representing quantum gates, and the vectors modeling qubit states grow exponentially with an increase in the number of qubits. However, by using a novel data structure called the Quantum Information Decision Diagram (QuIDD) that exploits the structure of quantum operators, a useful subset of operator matrices and state vectors can be represented in a form that grows polynomially with the number of qubits. This subset contains, but is not limited to, any equal superposition of n qubits, any computational basis state, n-qubit Pauli matrices, and n-qubit Hadamard matrices. It does not, however, contain the discrete Fourier transform (employed in Shor's algorithm) and some oracles used in Grover's algorithm. We first introduce and motivate decision diagrams and QuIDDs. We then analyze the runtime and memory complexity of QuIDD operations. Finally, we empirically validate QuIDD-based simulation by means of a general-purpose quantum computing simulator QuIDDPro implemented in C++. We simulate various instances of Grover's algorithm with QuIDDPro, and the results demonstrate that QuIDDs asymptotically outperform all other known simulation techniques. Our simulations also show that well-known worst-case instances of classical searching can be circumvented in many specific cases by data compression techniques.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45525/1/11128_2004_Article_482625.pd
2QAN: A quantum compiler for 2-local qubit Hamiltonian simulation algorithms
Simulating quantum systems is one of the most important potential applications of quantum computers. The high-level circuit defning the simulation needs to be compiled into one that complies with hardware limitations such as qubit architecture (connectivity) and instruction (gate) set. General-purpose quantum compilers work at the gate level and have little knowledge of the mathematical properties of quantum applications, missing further optimization opportunities. Existing application-specifc compilers only apply advanced optimizations in the scheduling procedure and are restricted to the CNOT or CZ gate set. In this work, we develop a compiler, named 2QAN, to optimize quantum circuits for 2-local qubit Hamiltonian simulation problems, a framework which includes the important quantum approximate optimization algorithm (QAOA). In particular, we exploit the flexibility of permuting different operators in the Hamiltonian (no matter whether they commute) and propose permutation-aware techniques for qubit routing, gate optimization and scheduling to minimize compilation overhead. 2QAN can target different architectures and different instruction sets. Compilation results on four applications (up to 50 qubits) and three quantum computers (namely, Google Sycamore, IBMQ Montreal and Rigetti Aspen) show that 2QAN outperforms state-of-theart general-purpose compilers and application-specifc compilers. Specifcally, 2QAN can reduce the number of inserted SWAP gates by 11.5X, reduce overhead in hardware gate count by 68.5X, and reduce overhead in circuit depth by 21X. Experimental results on the Montreal device demonstrate that benchmarks compiled by 2QAN achieve the highest fdelity
Faster-than-Clifford Simulations of Entanglement Purification Circuits and Their Full-stack Optimization
Quantum Entanglement is a fundamentally important resource in Quantum
Information Science; however, generating it in practice is plagued by noise and
decoherence, limiting its utility. Entanglement distillation and forward error
correction are the tools we employ to combat this noise, but designing the best
distillation and error correction circuits that function well, especially on
today's imperfect hardware, is still challenging. Here, we develop a simulation
algorithm for distillation circuits with gate-simulation complexity of
steps, providing for drastically faster modeling compared to
Clifford simulators or wavefunction
simulators over qubits.
This new simulator made it possible to not only model but also optimize
practically interesting purification circuits. It enabled us to use a simple
discrete optimization algorithm to design purification circuits from raw
Bell pairs to purified pairs and study the use of these circuits in the
teleportation of logical qubits in second-generation quantum repeaters. The
resulting purification circuits are the best-known purification circuits for
finite-size noisy hardware and can be fine-tuned for specific hardware error
models. Furthermore, we design purification circuits that shape the
correlations of errors in the purified pairs such that the performance of the
error-correcting code used in teleportation or other higher-level protocols is
greatly improved. Our approach of optimizing multiple layers of the networking
stack, both the low-level entanglement purification, and the forward error
correction on top of it, are shown to be indispensable for the design of
high-performance second-generation quantum repeaters
Cross-level Validation of Topological Quantum Circuits
Quantum computing promises a new approach to solving difficult computational
problems, and the quest of building a quantum computer has started. While the
first attempts on construction were succesful, scalability has never been
achieved, due to the inherent fragile nature of the quantum bits (qubits). From
the multitude of approaches to achieve scalability topological quantum
computing (TQC) is the most promising one, by being based on an flexible
approach to error-correction and making use of the straightforward
measurement-based computing technique. TQC circuits are defined within a large,
uniform, 3-dimensional lattice of physical qubits produced by the hardware and
the physical volume of this lattice directly relates to the resources required
for computation. Circuit optimization may result in non-intuitive mismatches
between circuit specification and implementation. In this paper we introduce
the first method for cross-level validation of TQC circuits. The specification
of the circuit is expressed based on the stabilizer formalism, and the
stabilizer table is checked by mapping the topology on the physical qubit
level, followed by quantum circuit simulation. Simulation results show that
cross-level validation of error-corrected circuits is feasible.Comment: 12 Pages, 5 Figures. Comments Welcome. RC2014, Springer Lecture Notes
on Computer Science (LNCS) 8507, pp. 189-200. Springer International
Publishing, Switzerland (2014), Y. Shigeru and M.Shin-ichi (Eds.
0.5 Petabyte Simulation of a 45-Qubit Quantum Circuit
Near-term quantum computers will soon reach sizes that are challenging to
directly simulate, even when employing the most powerful supercomputers. Yet,
the ability to simulate these early devices using classical computers is
crucial for calibration, validation, and benchmarking. In order to make use of
the full potential of systems featuring multi- and many-core processors, we use
automatic code generation and optimization of compute kernels, which also
enables performance portability. We apply a scheduling algorithm to quantum
supremacy circuits in order to reduce the required communication and simulate a
45-qubit circuit on the Cori II supercomputer using 8,192 nodes and 0.5
petabytes of memory. To our knowledge, this constitutes the largest quantum
circuit simulation to this date. Our highly-tuned kernels in combination with
the reduced communication requirements allow an improvement in time-to-solution
over state-of-the-art simulations by more than an order of magnitude at every
scale
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