Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Sawaya, Nicolas PD; Schmitz, Albert T; Hadfield, Stuart

doi:10.48550/arxiv.2203.14432

Cited by 3 publications

(17 citation statements)

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“…The built-in encodings are unary (also called one-hot), standard binary (SB), Gray code, and block unary. The latter is in fact a class of encodings, for which one must specify the local encoding and the block size g [29,30,33]. For a d-level particle, unary requires d qubits, Gray and SB require ⌈log 2 d⌉ qubits, and block unary requires ⌈ d g ⌉⌈log 2 (g + 1)⌉, where ⌈•⌉ is the ceiling function.…”

Section: B Compiling Into Qubit Operatorsmentioning

confidence: 99%

“…To do so, the user must define functions for both the integer-to-bit mapping and the bitmask subset, which determines the set of qubits over which a particular matrix element operates. Previous work discusses this concept more thoroughly [29,30]. Once these functions are defined they may be introduced by directly modifying integer2bit.py.…”

Section: B Compiling Into Qubit Operatorsmentioning

confidence: 99%

“…Further, there are built-in operators that can effectively be used to implement the discrete quantum intermediate representation (DQIR) [30]. The DQIR is an intermediate representation that was previously introduced in order to facilitate compilation and analysis of classical optimization problems defined over discrete variables.…”

Section: Built-in and User-defined Local Operatorsmentioning

confidence: 99%

“…α are square matrix operators of arbitrary size, I is the identity, and {σ x , σ y , σ z } are the Pauli matrices. Each subsystem on the left-hand side maps to a disjoint set of qubits; the compilation procedure is described in detail in previous work [29,30]. The current version of mat2qubit allows only for trivial (equivalent to bosonic) commutation relations, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…One purpose of this code is to simplify and automate the implementation of a wide range of encodings. Several previous works have studied the resource tradeoffs (for example depth-space tradeoffs) between different encodings [8,16,29,30,[33][34][35][36]. mat2qubit was developed primarily for the specific task of preparing and compiling various problems into qubit representations; for other aspects of the compilation pipeline and for running the resulting qubit-based problems on quantum computers, we suggest the use of one of the many actively maintained quantum simulators [25,26,28,[37][38][39][40][41][42][43][44][45][46][47] and compilers [26,28,37,45,[47][48][49][50][51].…”

Section: Introductionmentioning

confidence: 99%

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mat2qubit: A lightweight pythonic package for qubit encodings of vibrational, bosonic, graph coloring, routing, scheduling, and general matrix problems

Sawaya¹

2022

Preprint

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Preparing problems for execution on quantum computers can require many compilation steps. Automated compilation software is useful not only for easier and faster problem execution, but also for facilitating the comparison between different algorithmic choices. Here we describe mat2qubit, a Python package for encoding several classes of classical and quantum problems into qubit representations. It is intended for use especially on Hamiltonians and functions defined over variables (e.g. particles) with cardinality larger than 2. More specifically, mat2qubit may be used to compile bosonic, phononic/vibrational, and spin-s problems, as well as classical problems such as graph coloring, routing, scheduling, and classical linear algebra more generally. In order to facilitate numerical analyses and ease of programmability, a built-in computer algebra system (CAS) allows for fully symbolic preparation and manipulation of problems (with symbolic operators, symbolic coefficients, and symbolic particle labels) before the final compilation into qubits is performed. We expect this code to be useful in the preparation and analysis of various classes of physics, chemistry, materials, and optimization problems for execution on digital quantum computers.

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Section: B Compiling Into Qubit Operatorsmentioning

confidence: 99%

Section: B Compiling Into Qubit Operatorsmentioning

confidence: 99%

Section: Built-in and User-defined Local Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

mat2qubit: A lightweight pythonic package for qubit encodings of vibrational, bosonic, graph coloring, routing, scheduling, and general matrix problems

Sawaya¹

2022

Preprint

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Improved Resource‐Tunable Near‐Term Quantum Algorithms for Transition Probabilities, with Applications in Physics and Variational Quantum Linear Algebra

Sawaya

Huh

2023

Adv Quantum Tech

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Transition amplitudes and transition probabilities are relevant to many areas of physics simulation, including the calculation of response properties and correlation functions. These quantities can also be related to solving linear systems of equations. This study presents three related algorithms for calculating transition probabilities. First, a previously published short‐depth algorithm is extended, allowing for the two input states to be non‐orthogonal. Building on this first procedure, a higher‐depth algorithm based on Trotterization and Richardson extrapolation is derived that requires fewer circuit evaluations. Third, a tunable algorithm that allows for trading off circuit depth and measurement complexity is introduced, yielding an algorithm that can be tailored to specific hardware characteristics. Finally, proof‐of‐principle numerics are presented for models in physics and chemistry and for a subroutine in variational quantum linear solving (VQLS). The primary benefits of these approaches are that a) arbitrary non‐orthogonal states may now be used with small increases in quantum resources, b) they (like another recently proposed method) entirely avoid subroutines such as the Hadamard test that may require three‐qubit gates to be decomposed, and c) in some cases fewer quantum circuit evaluations are required as compared to the previous state‐of‐the‐art in NISQ algorithms for transition probabilities.

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Encoding-independent optimization problem formulation for quantum computing

Dominguez,

Unger,

Traube

et al. 2023

Front. Quantum Sci. Technol.

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We review encoding and hardware-independent formulations of optimization problems for quantum computing. Using this generalized approach, an extensive library of optimization problems from the literature and their various derived spin encodings are discussed. Common building blocks that serve as a construction kit for formulating these spin Hamiltonians are provided. This previously introduced approach paves the way toward a fully automatic construction of Hamiltonians for arbitrary discrete optimization problems and this freedom in the problem formulation is a key step for tailoring optimal spin Hamiltonians for different hardware platforms.

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Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Cited by 3 publications

References 0 publications

mat2qubit: A lightweight pythonic package for qubit encodings of vibrational, bosonic, graph coloring, routing, scheduling, and general matrix problems

mat2qubit: A lightweight pythonic package for qubit encodings of vibrational, bosonic, graph coloring, routing, scheduling, and general matrix problems

Improved Resource‐Tunable Near‐Term Quantum Algorithms for Transition Probabilities, with Applications in Physics and Variational Quantum Linear Algebra

Encoding-independent optimization problem formulation for quantum computing

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