Number Partitioning on a Quantum Computer
H. De Raedt, K. Michielsen, K. De Raedt, S. Miyashita
我们提出了一个算法来计算（约束）数划分问题的解决方案的数量。给出了该算法在Ising型量子计算机上的具体实现。
We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.
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Optimal Partitioning of Quantum Circuits using Gate Cuts and Wire Cuts
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Dynamic Hypergraph Partitioning of Quantum Circuits with Hybrid Execution
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In this work we investigate the capabilities of a hybrid quantum-classical procedure to explore the solution space using the D-Wave $2000Q^{TM}$ Quantum Annealer device. Here we study the ability of the Quantum hardware to solve the Number Partitioning Problem, a well-known NP-Hard optimization model that poses some challenges typical of those encountered in real-world applications. This represents one of the most complex scenario in terms of qubits connectivity and, by increasing the input problem size, we analyse the scaling properties of the quantum-classical workflow. We find remarkable re…
Circuit Partitioning and Transmission Cost Optimization in Distributed Quantum Circuits
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Optimised Baranyai partitioning of the second quantised Hamiltonian
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We propose an efficient algorithm for partitioning Pauli strings into subgroups, which can be simultaneously measured in a single quantum circuit. Our partitioning algorithm drastically reduces the total number of measurements in a variational quantum eigensolver for a quantum chemistry, one of the most promising applications of quantum computing. The algorithm is based on the Ising model optimization problem, which can be quickly solved using an Ising machine. We develop an algorithm that is applicable to problems with sizes larger than the maximum number of variables that an Ising machine ca…
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Dynamics of quantum adiabatic evolution algorithm for Number Partitioning
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Quantum algorithms are usually described as monolithic circuits, becoming large at modest input size. Near-term quantum architectures can only manage a small number of qubits. We develop an automated method to distribute quantum circuits over multiple agents, minimising quantum communication between them. We reduce the problem to hypergraph partitioning and then solve it with state-of-the-art optimisers. This makes our approach useful in practice, unlike previous methods. Our implementation is evaluated on five quantum circuits of practical relevance.
Current quantum computer designs will not scale. To scale beyond small prototypes, quantum architectures will likely adopt a modular approach with clusters of tightly connected quantum bits and sparser connections between clusters. We exploit this clustering and the statically-known control flow of quantum programs to create tractable partitioning heuristics which map quantum circuits to modular physical machines one time slice at a time. Specifically, we create optimized mappings for each time slice, accounting for the cost to move data from the previous time slice and using a tunable lookahe…
To obtain estimates of electronic energies, the Variational Quantum Eigensolver (VQE) technique performs separate measurements for multiple parts of the system Hamiltonian. Current quantum hardware is restricted to projective single-qubit measurements, and thus, only parts of the Hamiltonian which form mutually qubit-wise commuting groups can be measured simultaneously. The number of such groups in the electronic structure Hamiltonians grows as $N^4$, where $N$ is the number of qubits, and thus puts serious restrictions on the size of the systems that can be studied. Using a partitioning of th…
The main objective of this paper is to improve the communication costs in distributed quantum circuits. To this end, we present a method for generating distributed quantum circuits from monolithic quantum circuits in such a way that communication between partitions of a distributed quantum circuit is minimized. Thus, the communication between distributed components is performed at a lower cost. Compared to existing works, our approach can effectively map a quantum circuit into an appropriate number of distributed components. Since teleportation is usually the protocol used to connect component…
We demonstrate that a quantum annealer can be used to solve the NP-complete problem of graph partitioning into subgraphs containing Hamiltonian cycles of constrained length. We present a method to find a partition of a given directed graph into Hamiltonian subgraphs with three or more vertices, called vertex 3-cycle cover. We formulate the problem as a quadratic unconstrained binary optimisation and run it on a D-Wave Advantage quantum annealer. We test our method on synthetic graphs constructed by adding a number of random edges to a set of disjoint cycles. We show that the probability of sol…
Estimating Trotter Approximation Errors to Optimize Hamiltonian Partitioning for Lower Eigenvalue Errors
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Exploiting quantum properties to outperform classical ways of information-processing is an outstanding goal of modern physics. A promising route is quantum simulation, which aims at implementing relevant and computationally hard problems in controllable quantum systems. Here we demonstrate that in a trapped ion setup, with present day technology, it is possible to realize a spin model of the Mattis type that exhibits spin glass phases. Remarkably, our method produces the glassy behavior without the need for any disorder potential, just by controlling the detuning of the spin-phonon coupling. A…
Numerous conceptually important quantum algorithms rely on a black-box device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example is Grover's search algorithm. Here we propose a Grover search for solutions to a class of NP-complete decision problems known as subset sum problems, including the special case of number partitioning. Each problem instance is encoded in the couplings of a set of qubits to a central spin or boson, which enables a realization of the oracle without knowledge o…
Measuring the expectation value of Pauli operators on prepared quantum states is a fundamental task in a multitude of quantum algorithms. Simultaneously measuring sets of operators allows for fewer measurements and an overall speedup of the measurement process. We investigate the task of partitioning a random subset of Pauli operators into simultaneously-measurable parts. Using heuristics from coloring random graphs, we give an upper bound for the expected number of parts in our partition. We go on to conjecture that allowing arbitrary Clifford operators before measurement, rather than single-…
Efficient Time-Aware Partitioning of Quantum Circuits for Distributed Quantum Computing
本文提出基于束搜索的启发式算法，用于高效划分量子电路，以降低分布式量子计算中的通信开销，通过时间感知的方法优化qubit分配，降低通信成本。
Early but promising results in quantum computing have been enabled by the concurrent development of quantum algorithms, devices, and materials. Classical simulation of quantum programs has enabled the design and analysis of algorithms and implementation strategies targeting current and anticipated quantum device architectures. In this paper, we present a graph-based approach to achieve efficient quantum circuit simulation. Our approach involves partitioning the graph representation of a given quantum circuit into acyclic sub-graphs/circuits that exhibit better data locality. Simulation of each…
In this work, we explore graph partitioning (GP) using quantum annealing on the D-Wave 2X machine. Motivated by a recently proposed graph-based electronic structure theory applied to quantum molecular dynamics (QMD) simulations, graph partitioning is used for reducing the calculation of the density matrix into smaller subsystems rendering the calculation more computationally efficient. Unconstrained graph partitioning as community clustering based on the modularity metric can be naturally mapped into the Hamiltonian of the quantum annealer. On the other hand, when constraints are imposed for p…
Fast Partitioning of Pauli Strings into Commuting Families for Optimal Expectation Value Measurements of Dense Operators
本文提出一种将任意数量量子比特上的泡利串完全划分为最少对易族的线性时间算法，并集成到Qiskit中，在IBM硬件上对稠密哈密顿量实现接近理论极限(3/2)^m的测量加速。
GTQCP: Greedy Topology-Aware Quantum Circuit Partitioning
本文提出GTQCP，一种基于量子比特依赖图贪心启发式的量子电路划分方法，在保持与ScanPartitioner几乎相同划分质量的同时，运行时间比最快方法快18%，比最高质量方法快96%。
TITAN: A Distributed Large-Scale Trapped-Ion NISQ Computer
本文提出大规模分布式囚禁离子NISQ计算机TITAN，通过创新光子互连设计降低纠缠延迟，并采用先进分区与映射算法优化物质链路通信，使量子应用性能提升56.6%，保真度提升19.7%。
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本文综述了多参考密度矩阵嵌入和定域活性空间自洽场方法在经典和量子计算机上的最新进展，旨在解决强电子相关建模的计算标度问题，扩大多参考方法在复杂分子和材料中的应用范围。
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