Toshiba’s New Version of Quantum-Inspired SQBM+™ Optimization Solution
Supports 10 Million Variables

- Expanding combinatorial optimization for large-scale problems as typified by
investment portfolio management and computational drug discovery -

November 27, 2023
Toshiba Digital Solutions Corporation

Toshiba Digital Solutions Corporation (hereinafter “Toshiba Digital Solutions”), an industry leader in applying quantum-inspired solutions to complex real-world problems, today announced the launch of SQBM+ Version 2, the latest and most powerful version of its quantum-inspired optimization software1, now able to handle up to 10 million variables.

Optimization software quickly finds optimal solutions among an immense number of options. SQBM+ is derived from the Simulated Bifurcation Machine (SBM), a combinatorial optimization solver built on the quantum-inspired2 Simulated Bifurcation Algorithm (SB Algorithm)3 developed by Toshiba Corporation. 

SQBM+ Version 2 supports up to 10 million variables and finds approximate solutions faster and more accurately than its predecessor, advances that significantly expand the scale of the problems it can handle. It also supports high-order terms, which boosts its performance in solving real-world combinatorial optimization problems.

SQBM+ Version 2 is now available as "SQBM+ for AWS Version 2" on the AWS Marketplace4, provided by Amazon Web Services, Inc. Toshiba Digital Solutions intends to bring it to Microsoft’s Azure Marketplace in early 2024, as an Azure virtual machine. Additionally, upcoming developments include the extension to on-premises versions for highly confidential applications unsuitable for cloud environments, and for applications that require low latency.

Moving forward Toshiba Digital Solutions, has already initiated the beta evaluation of SQBM+ Version 2.1, in collaboration with selected partners. SQBM+ Version 2.1 is designed for specified purposes, and will deliver an easy and direct mechanism for finding solutions to specific problems. Its official release is scheduled for the first half of 2024.

Combinatorial optimization is an essential tool for addressing a wide range of social and industrial challenges that identifies optimal solutions from an enormous range of choices. Its diverse applications span domains that include financial decision-making, operating industrial robots, logistics, route planning, power grid optimization, and molecular level drug discovery. However, as the scale of any given problem expands, triggering an exponential increase in combination patterns, finding solutions on computers with a standard classical architecture becomes increasingly challenging. Companies around the world are addressing this problem by developing dedicated computers for combinatorial optimization.

In contrast, SQBM+ runs on standard computers and finds high-precision, approximate solutions (high-quality solutions) to complex, large-scale problems in a short time. The commercial launch of SQBM+ allowed Toshiba and its partners to verify the practicality of SQBM+ and the effectiveness of applying quasi-quantum computing to high-speed, high-frequency stock trading5, computational drug discovery6, energy management, and materials development. SQBM+ Version 2 can address larger scale problems related to investment portfolio management and drug development. Toshiba Digital Solutions aims to leverage SQBM+ across numerous fields, and to contribute to the resolution of complicated issues.

Key Features of “SQBM+ Version 2”
1. Can handle 10 million variables and solve large-scale problems
SQBM+ Version 2 supports a Quadratic Unconstrained Binary Optimization (QUBO) solver capable of handling QUBO problems with up to 10 million variables.
2. Improved speed and accuracy

An improved algorithm speeds up the search for an approximate solution and improves accuracy. For the 71 problems in the Gset7, a benchmark problems set with Maximum Cut Problem8, the number of problems where the Best Known Values9 are found has risen from 50 to 60 questions10.

3. Provides optimization solvers according to the intended application
In addition to the general-purpose QUBO solver, Toshiba Digital Solutions also offers solvers designed for specific purposes. This provides mechanisms/routes for securing easy and direct solutions to specific problems.

  • QUBO solver: A general-purpose solver, the basic solver of SQBM+, which uses the SB Algorithm to solve combinatorial optimization problems expressed in the format of quadratic unconstrained binary optimization (QUBO).
  • TSP solver: A solver that directly solves the traveling-salesman type problems without expressing the solution in QUBO.
  • SHIFT solver: A solver that directly solves shift scheduling problems, such as assigning jobs to employees while considering various constraints, without using QUBO.
  • QAP solver: A solver that directly solves quadratic assignment problems (QAP) without expressing them in QUBO. For example, the optimal placement of facilities to minimize the cost of transporting goods between them.

Special purpose solvers for SQBM+ Version 2 will be available in SQBM+ Version 2.1.

4. Expansion of application range
Toshiba Digital Solutions has enhanced SQBM+ capabilities by offering extended functions and solvers to improve usability and overall performance.

  • PUBO11 solver: A solver that supports cubic and quartic problems. Real-life combinatorial optimization problems may contain cubic or higher terms. Solving such problems with the QUBO solver requires conversion to quadratic expressions, which may degrade performance. SQBM+ Version 2 uses the capabilities of the SB Algorithm to support these higher-order terms, and to achieve higher-level solution performance for real-life combinatorial optimization problems.
  • QPLIB solver: For linearly constrained quadratic binary programming problems. It supports QPLIB12 as input data format.

5. Expansion of the types of GPUs supported
SQBM+ can solve large-scale combinatorial optimization problems on classical computers, and enhancing computer performance directly contributes to increasing the speed at which SQBM+ does this. An increase in the number of supported GPU types gives users the flexibility to select the most appropriate instance for their specific purpose from a variety of instance types optimized for various use cases.

SQBM+ for AWS Version 2 supports six Amazon EC2 accelerated computing instances.

  • Amazon EC2 P4 instance: p4d.24xlarge
  • Amazon EC2 P3 instance: p3.2xlarge、p3.8xlarge、p3.16xlarge、p3dn.24xlarge
  • Amazon EC2 G4dn instance: g4dn.xlarge


Pricing of SQBM+ for AWS Version 2
Two plans are available for “SQBM+ for AWS Version 2”: Learn & Development plan is designed for learning, evaluation, and development purposes, and the Business Standard plan is tailored for business operations. 

・ Pricing of SQBM+ for AWS Version 2

* Note: Customers are required to set up Amazon EC2.

 (As of November 2023)

The following feedback was received from collaborative partners on the release of SQBM+ Version 2. 

CogniFrame Inc.
“We have successfully used SQBM+ for a number of our customers projects in the health care, financial services and public sector verticals and look forward to further augmenting our partnership with Toshiba by offering direct access to SQBM+ solvers globally under a SaaS model via our patent pending plug and play FirstQ App Store and Infrastructure platform. SQBM+ Version 2 with its support for 10 million variables offers us the opportunity to address larger scale optimization challenges and would also continue to support a number of use cases offered via FirstQ”.
Vish Ramakrishnan, CEO, CogniFrame Inc. 

Fixstars Amplify Corporation
“We eagerly anticipate the advantages SQBM+’s new service offerings will provide our customers. We're excited about the synergy of our solutions and the potential they hold for addressing a broader spectrum of customer challenges in the evolving quantum computing industry.”
Takuji Hiraoka, President & CEO, Fixstars Amplify Corporation

Jij Inc.
“Jij Inc. specializes in research and development focused on quantum computing and mathematical optimization technologies, providing the optimization computing platform 'JijZept'. We have actively utilized Toshiba Digital Solutions Corporation's quantum-inspired optimization solution 'SQBM+' through JijZept. The recent update to SQBM+ Version 2 enables us to address a wider and more complex range of optimization problems, and we are looking forward to fully unleashing its potential. Moving forward, Jij is committed to deepening our partnership with Toshiba, leveraging SQBM+ for solving challenging problems and contributing to advancements in this field.”
Yu Yamashiro, CEO, Jij Inc.

Strangeworks Inc.
"We are thrilled to deepen our partnership with Toshiba, expanding our collaboration to bring their cutting-edge SQBM+ Version 2 system to our Strangeworks platform. Building on our successful utilization of the SQBM+ with several of our valued customers, we are excited to extend this technology to our existing partners and introduce it to a broader audience. This quantum technology extends our customers’ capabilities with more problem-specific solvers, accelerating the discovery and implementation of quantum solutions across industries.”
Steven Gibson, Chief Strategy Officer, Strangeworks, Inc.

1:    Toshiba Digital Solutions News Release(March 2022): Announcing the Launch of the Quantum-Inspired Optimization Solution SQBM+™:

2:    A new classical mechanics method derived from or directly inspired by a calculation method based on the principles of quantum mechanics. Also known as “pseudo-quantum.”

3:    Toshiba News Release (April 2019): Toshiba's Breakthrough Algorithm Realizes World's Fastest, Largest-scale Combinatorial Optimization:
H. Goto et al., Science Advances 5, eaav2372 (2019):

4:    Toshiba Digital Solutions News Release (February 2023): Toshiba Brings SQBM+™, its Quantum-Inspired Optimization Solution, to AWS Marketplace:

5:    Toshiba News Release (October 2019): Toshiba Develops Proof-of-concept Device for Ultra-high-speed Financial Transaction Machine with Simulated Bifurcation Algorithm:
(May 2021): Toshiba and Dharma Capital’s Joint Experiment in Financial Markets to Verify the Effectiveness of a Quasi-Quantum Computer When Applied to High Frequency Trading:

6:    Toshiba Digital Solutions News Release (June 2022): Toshiba and Revorf Advance Computational Drug Discovery Evaluation with Quantum-Inspired SQBM+™ Optimization Solution

8:    Maximum Cut Problem, a graph partitioning problem whose objective is to partition the nodes (vertices) of a graph into two subsets, such that the sum of the weights of the edges (lines) connecting the two subsets is maximum.

9:    The Best Known Value of Gset is the best objective function value known from previous studies for each problem included in Gset.

10:    Actual value measured by Toshiba Digital Solutions when the upper limit of calculation time is 3,000 seconds.

11:    PUBO: Polynomial Unconstrained Boolean Optimization.

12:    ©2017-2023 by Zuse Institute Berlin and GAMS.
For information about the author, refer to the link above.
QPLIB is licensed under CC-BY 4.0. (

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