Preface

This manual describes how to use Digital Annealer service and operation management procedures.

Intended Audience

This manual is intended for users who develop programs and applications to solve combinatorial optimization problems on Digital Annealer and who execute those programs and applications.
To fully benefit from this manual, the following knowledge is required:

• Basic knowledge related to combinatorial optimization problems

• Basic knowledge related to algorithms for combinatorial optimization problems such as quantum annealing and simulated annealing

• Basic knowledge of Web APIs

Conventions

This manual uses abbreviations and symbols.

Product/Technology Name Abbreviations
Product/Technology Name Abbreviation

Symbol Meaning

" "

If the reference destination is another manual, the manual name is enclosed in " "

`In addition, the following markings are used.`
 CAUTION
 NOTE
Glossary

Explanation of terms used in this manual.

Term Description

Digital Annealer

The quantum-inspired digital technology architecture, capable of performing parallel, real-time optimization calculations at speed, with precision and on a scale classical computing cannot.

Problem scale

The number of variables that make up a combinatorial optimization problem.

FujitsuDA3Solver

The 3rd generation Digital Annealer solver which can handle large scale problem. The maximum problem scale can be solved is 100K (100,000) bits.

FujitsuDA2PTSolver

The 2nd generation Digital Annealer solver with the parallel tempering feature. The maximum problem scale can be solved is 8192 bits.

FujitsuDA2Solver

The 2nd generation Digital Annealer solver. The maximum problem scale can be solved is 8192 bits.

FujitsuDA2MixedModeSolver

The 2nd generation Digital Annealer solver. The maximum problem scale can be solved is 8192 bits.

Higher Order Binary Optimization (HOBO)

An expression of combinatorial optimization problems with high-order monomials or high-order polynomials.

An expression of combinatorial optimization problems with quadratic polynomials.

Web API

An interface used between applications and between systems for calling over a network using the HTTP protocol.

Storage API

The Web API service for uploading problem data (QUBO) to the storage for FujitsuDA3Solver. The problem data (QUBO) uploaded using the Storage API can be specified for calculation by FujitsuDA3Solver. The maximum size of the problem data (QUBO) is 20GB, and the maximum size of the problem data (QUBO) that can be uploaded with a single API call is 5GB. If you are uploading an problem data (QUBO) larger than 5GB, divide them into multiple files of 5GB and upload one by one.

Export Control Regulations

Exportation/release of this document may require necessary procedures in accordance with the regulations of your resident country and/or US export control laws.

High Risk Activity

The Customer acknowledges and agrees that the Service is designed, developed and manufactured as contemplated for general use, including without limitation, general office use, personal use, household use, and ordinary industrial use, but is not designed, developed and manufactured as contemplated for use accompanying fatal risks or dangers that, unless extremely high safety is secured, could lead directly to death, personal injury, severe physical damage or other loss (hereinafter "High Safety Required Use"), including without limitation, nuclear reaction control in nuclear facility, aircraft flight control, air traffic control, mass transport control, medical life support system, missile launch control in weapon system.
The Customer, shall not use the Service without securing the sufficient safety required for the High Safety Required Use. In addition, Fujitsu (or other affiliate’s name) shall not be liable against the Customer and/or any third party for any claims or damages arising in connection with the High Safety Required Use of the Service.

• Other company names and product names are trade names, registered trademarks, or trademarks of their respective companies.

• Trademark symbols are not always added to names such as company names, system names, and product names.

## 1. Overview

This chapter describes an overview of Digital Annealer.

### 1.1. What Is Digital Annealer?

Digital Annealer is a digital circuit designed with inspiration from a computation method that uses quantum phenomena. Using annealing methods enables it to solve large-scale combinatorial optimization problems rapidly. Unlike conventional computers, programming is not required, and computation is enabled only by setting parameters. In addition, adoption of a fully connected architecture enabling any element to freely exchange signals has enabled calculation of computationally intensive and complicated problems that have been difficult to solve with classical computers or quantum annealing machines.

Digital Annealer has Quadratic Unconstrained Binary Optimization (QUBO) as its input data and searches for combinations to minimize the following evaluation function (energy).

$\displaystyle{E(x) = \sum_{i} \sum_{j>i} J_{ij}x_{i}x_{j} + \sum_{i}h_{i}x_{i} + c}$

The condition of the combination is represented by a binary variable $x \; (x \in \{0, 1\})$.

#### 1.1.1. Digital Annealer Service

Digital Annealer service is a cloud service used to rapidly solve combinatorial optimization problems using software for quantum computers and the hardware equipped with the optimization circuit Digital Annealer.

Figure 1. Web API Service

## 2. Starting the Use of Services

This chapter describes how to start the use of Digital Annealer service.

### 2.1. Account Registration

To use the Digital Annealer service, access the Digital Annealer account creation page at the following URL in the Digital Annealer portal and register an account.

For users in Japan region:
For users in other regions:
 To access the Digital Annealer portal, use Google Chrome. It is recommended that the screen resolution is 1366 $\times$ 768 pixels or higher.

## 3. Using Services

This chapter describes how to use Digital Annealer service and other points to be noted.

### 3.1. Provided APIs

The APIs provided in the Web API service are as follows:

#### 3.1.1. QUBO APIs

ContractType API Type Description

Standard
Trial

qubo/hobo2qubo

Synchronous (sync)

Converts Higher Order Binary Optimization (HOBO) to Quadratic Unconstrained Binary Optimization (QUBO)

qubo/solve

Finds optimal solution for QUBO using FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver. The problem scale that can be calculated is 1024 bits or less.

Standard-2
Trial-2

qubo/hobo2qubo

Synchronous (sync)

Converts Higher Order Binary Optimization (HOBO) to Quadratic Unconstrained Binary Optimization (QUBO)

qubo/solve

Finds optimal solution for QUBO using FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver. The problem scale that can be calculated is 2048 bits or less.

async/qubo/solve

Asynchronous (async)

Registers a job to find optimal solution for QUBO using FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver. The problem scale that can be calculated is 8192 bits or less.

async/jobs

Retrieves a list of jobs

async/jobs/result

Retrieves or deletes the result of a job

async/jobs/cancel

Cancels a job

Standard-3
Trial-3

qubo/hobo2qubo

Synchronous (sync)

Converts Higher Order Binary Optimization (HOBO) to Quadratic Unconstrained Binary Optimization (QUBO)

async/qubo/solve

Asynchronous (async)

Registers a job to find optimal solution for QUBO using FujitsuDA3Solver. The problem scale that can be calculated is 100K (100,000) bits or less.

async/jobs

Retrieves a list of jobs

async/jobs/result

Retrieves or deletes the result of a job

async/jobs/cancel

Cancels a job

#### 3.1.2. Optimization Solutions APIs

Contract Type API Description

Warehouse Pickup Optimization API

picking/mapfile

Uploads (POST) or downloads (GET) a map file (a list of the shelves and aisles in the warehouse)

picking/showroute

Finds the shortest pickup route with its total distance

 The Optimization Solutions APIs can only be used in Japan region.
 The number of shelves that can be specified for picking/showroute is within the following range.   $\sum x^2 \leq 1024$   $x$: The number of shelves with the same priority. Except the selves that have no other shelves with the same priority. Example 1: In the case of that 1 shelf is level of priority 0, 30 shelves are level of priority 1, 5 shelves are   level of priority 2, and 2 shelves are level of priority 3   $30^2 + 5^2 + 2^2 = 900 + 25 + 4 = 929$   (Level of priority 0 is only 1 shelf, therefore this value is omitted)   ⇒ The number (929) is less than 1024, therefore the route can be optimized. Example 2: In the case of that 30 shelves are level of priority 1, 10 shelves are level of priority 2, 1 shelf is   level of priority 3, and 5 shelves are level of priority 4   $30^2 + 10^2 + 5^2 = 900 + 100 + 25 = 1025$   (Level of priority 3 is only 1 shelf, therefore this value is omitted)   ⇒ The number (1025) is more than 1024, therefore the route cannot be optimized. Even though the above conditions are met, if the number of shelves (nodes) specified in the request body is more than 200, the processing time becomes long and a timeout error (HTTP 504 Gateway Time-out) may occur. Only one map file can be registered to Digital Annealer server with picking/mapfile. The most recently uploaded file is registered to Digital Annealer server. A previously registered map file will be overwritten, therefore please back up the map files if necessary.

## 4. How to Use the QUBO APIs

This chapter describes the procedure to solve combinatorial optimization problems using mathematical models.

### 4.1. Calculation Precision of Digital Annealer

Digital Annealer encodes the coefficient of a binary quadratic polynomial as an integer.
Calculation precision of Digital Annealer is as follows. To find the optimal solution, it is recommended to specify coefficients in a QUBO expression within the range of calculation precision of Digital Annealer.

Solver Scale of the Problem Quadratic Term Linear Term

FujitsuDA3Solver

Up to 100,000 bits

64 bits signed integer (*1)

76 bits signed integer

FujitsuDA2PTSolver
FujitsuDA2Solver
FujitsuDA2MixedModeSolver

Up to 4096 bits

64 bits signed integer (*1)

76 bits signed integer

From over 4096 bits to 8192 bits

16 bits signed integer

76 bits signed integer

*1: The available range is $-2^{63} + 1$ to $2^{63} - 1$

#### 4.1.1. Scaling and Rounding

This is a feature that automatically converts a QUBO that has one or more terms whose coefficient is out of the calculation precision range of Digital Annealer or not an integer into a QUBO that has only terms whose coefficient is integers in the calculation precision range of Digital Annealer.
If one of the following solvers is used, this function is enabled for annealing.

• FujitsuDA3Solver

• FujitsuDA2PTSolver

• FujitsuDA2Solver (with "false" specified for the expert_mode parameter)

• FujitsuDA2MixedModeSolver

 For the range of coefficients in a QUBO expression that can be specified for qubo/solve and async/qubo/solve, refer to "Digital Annealer API Reference (QUBO API V2)" or "Digital Annealer API Reference (QUBO API V3)."

### 4.2. API Usage

For details about the specification and usage of the provided APIs, refer to "Digital Annealer API Reference (QUBO API V2)" or "Digital Annealer API Reference (QUBO API V3).

• If you use FujitsuDA3Solver, please refer to "Digital Annealer API Reference (QUBO API V3)."

• If you use FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver, please refer to "Digital Annealer API Reference (QUBO API V2)."

### 4.3. Notes

This section describes the points to be noted to use the QUBO APIs.

• When a request is issued, even though the wrong parameter name (key) is specified (including spelling errors), the specified parameter is ignored and the process may continue. For this reason, an unexpected processing result may be obtained. Be careful to specify parameters.

• A running job cannot be stopped after a synchronous qubo/solve request is issued.
Even though a request is issued by mistake or a process takes a long time, please wait until the process ends.
However, if you use an asynchronous async/qubo/solve request, then you can cancel the job before it is executed (by using async/jobs/cancel).

• When a new qubo/solve request is issued during the annealing process performed by Digital Annealer, it waits for the completion of any running annealing processes.
The new request process starts after the completion of the running annealing processes.

• When using FujitsuDA3Solver, the calculation time (solve_time) is determined by the value (in seconds) specified in the following parameter that specifies the upper limit of execution time.

• time_limit_sec parameter

• When using FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver, the time required for annealing (anneal_time) is determined by the values specified for the following parameters.

• number_iterations parameter

• number_replicas parameter (for FujitsuDA2PTSolver)

• number_runs parameter (for FujitsuDA2Solver or FujitsuDA2MixedModeSolver)

```Example: In the case of number_iterations = 10000000 and number_runs = 100
Using FujitsuDA2Solver or FujitsuDA2MixedModeSolver: Approximately 5 seconds```

If a value is multiplied by 10, 100, …​, anneal_time is also multiplied by 10, 100, …​ in direct proportion, therefore be careful to specify these values.

• If the problem scale (the number of bits) is large, the scaling process, recalculation of energy, and other calculations that use CPU may take some time. The amount of time depends on the setting values that you specified for the solver and parameter.

• The following parameters have lower and upper limit values.

 Solver Parameter Lower Limit Upper Limit Synchronous Asynchronous FujitsuDA3Solver time_limit_sec 1 - 1800 FujitsuDA2PTSolver number_replicas 26 128 128 number_iterations 1 2000000000 2000000000 number_replicas $\times$number_iterations 100000 25600000000 256000000000 FujitsuDA2Solver FujitsuDA2MixedModeSolver number_runs 16 128 128 number_iterations 1 2000000000 2000000000 number_runs $\times$number_iterations 100000 25600000000 256000000000
• The annealing temperature schedule for the FujitsuDA2Solver or FujitsuDA2MixedModeSolver is defined by the following parameters: temperature_decay, temperature_interval, temperature_mode, and temperature_start.
For example, with "number_iterations = 100000" and "temperature_interval = 100" as shown below, the temperature is changed to the temperature calculated in the mode specified with the temperature_mode parameter every 100 searches.
If the number of searches per anneal (number_iterations) is 100000, the temperature is changed 1000 times (the result of $100000 \div 100$).

• In a cycle of annealing with FujitsuDA2Solver or FujitsuDA2MixedModeSolver, searches are performed the number of times specified with the number_iterations parameter at each temperature specified with the annealing temperature schedule as mentioned above, and the annealing is repeated the number of times specified with the number_runs parameter.
For both parameters, specifying a larger value takes a longer time.

• The offset_increase_rate parameter for FujitsuDA2PTSolver, FujitsuDA2Solver or FujitsuDA2MixedModeSolver is used to accelerate searches. If a state transition does not occur due to being trapped by a local solution, this parameter enables the process to increase the energy using the rate specified in offset_increase_rate for each search to improve the probability of a state transition. The energy that is accumulated according to offset_increase_rate is reset if a state transition occurs. To disable the offset_increase_rate parameter, specify 0 (zero).

• With the FujitsuDA2Solver or FujitsuDA2MixedModeSolver, to specify at least one of the following parameters, be sure to specify all of the following five parameters and the number_iterations parameter:

• offset_increase_rate

• temperature_decay

• temperature_interval

• temperature_mode

• temperature_start

• With the FujitsuDA2Solver or FujitsuDA2MixedModeSolver, the temperature_decay, temperature_interval, and temperature_start parameters are related to the temperature schedule, and optimal solutions can be obtained only if appropriate values are specified, especially for those parameters.
There are countless combinations of parameter values, requiring a tuning operation to search for an appropriate value to obtain an optimal solution.
With the FujitsuDA2PTSolver (using the parallel tempering function), specifying the following parameters is not required, which considerably reduces the time required for tuning.

• noise_model

• temperature_decay

• temperature_interval

• temperature_mode

• temperature_start

## 5. How to Use the Optimization Solutions APIs

This chapter describes the procedure used to solve combinatorial optimization problems specialized for business.

 The Optimization Solutions APIs can only be used in Japan region.

### 5.1. Warehouse Pickup Optimization API

Warehouse Pickup Optimization API is a Web API service for finding "the shortest route (pickup route: closed circuit)" to retrieve (pick up) specified products from multiple shelves or other areas in a warehouse.

#### 5.1.1. Procedure for Using the API

The following section describes the procedure for finding the pickup route with the shortest distance.

1. Create a map file

3. Optimize the pickup route

##### 1. Create a map file

To use the Warehouse Pickup Optimization API, you must create a map file on a client that includes information about the position of shelves and aisles in the warehouse where the pickup is performed (the pickup area).

• Things to prepare before creating a map file

• Ground plan of the pickup area (scaled map)

• Position of the shelves on which the products targeted for pickup are located

• How to create a map file

Step(1)

In the ground plan (scaled map) of the pickup area, record shelves on which the products targeted for pickup are located, and aisles it is possible to pass through for performing a pickup. (refer to "Example of ground plan of pickup area" in "Figure 2: Map File Creation Examples")

Step(2)

Place a plot point (a unique identification name in each area) on each shelf and point passed through along the aisles recorded in Step(1), and find the coordinates (absolute coordinates) of each plot point.
Plot points are also placed at the intersections of aisles, corners, and other places where the shelves and aisles connect.

Step(3)

Create a map file (.json) based on the coordinates found in Step(2).
The sets of coordinates for each plot point in the area defined as nodes, and the routes between the plot points defined as nodes that it is possible to pass through for performing a pickup are defined as edges. (refer to "Map file creation example 1" in "Figure 2: Map File Creation Examples")
If there are multiple areas, the nodes and edges are defined for each area, and the distances and routes between the areas are defined as cedges. (refer to "Map file creation example 2" in "Figure 2: Map File Creation Examples")
The direction of traffic for the routes defined as edges and cedges (two-way traffic (false) or one-way traffic (true)) is defined with directed.
For details about the data format of the map file, refer to "Digital Annealer API Reference (Warehouse Picup Optimization API)."

 Do not use the same name or coordinate more than once for the plot points of shelves and aisles to define the "nodes" and "edges" within each area. The values of the coordinates defined in the map file is not required to represent the actual distance. It is also possible to use the values of coordinates from a scaled ground plan.
 Map file creation is also available for order through Digital Annealer technical service (paid service).

Upload a map file created using "POST picking/mapfile." Then download (display) the uploaded map file using "GET picking/mapfile" and check that the map file is registered correctly.
For details about the specification of the API, refer to "Digital Annealer API Reference (Warehouse Picup Optimization API)."

##### 3. Optimize the pickup route

Find the shortest pickup route using "POST picking/showroute."
For details about the specification of the API, refer to "Digital Annealer API Reference (Warehouse Picup Optimization API)."

 If shelves (node) that does not exist in the map file are specified int the request, these shelves are excluded from being a target of optimization. Specifying of the priority ("priority") cannot be omitted. If the prioritize is not required, specify 0 for the priority ("priority").
 The total distance ("distance") is expressed in the unit defined for the coordinates of the plot points of the shelves and aisles recorded in the map file. For example, if the unit of the coordinates is defined as 50 cm, the actual total distance in the response example shown above is $1672 \times 0.5m = 836m$. ```Response example： { "distance": 1672.0, "route": [ {"area": "A1F", "node": "DEPOT"}, {"area": "A1F", "node": "F52"}, {"area": "A1F", "node": "F32"}, {"area": "A1F", "node": "R-4"}, {"area": "A2F", "node": "R-1"}, {"area": "A2F", "node": "B46"}, {"area": "A2F", "node": "A10"}, {"area": "A2F", "node": "B45" ] }```
Figure 2. Map File Creation Examples
Document History
Edition Date Modified location Description

First

January 2020

Whole document

Newly created

Second

January 2021

Whole document