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Expand Up @@ -13,8 +13,6 @@
"\n",
"# Introduction\n",
"\n",
"Before beginning, please complete this short [pre-course survey](https://your.feedback.ibm.com/jfe/form/SV_1RB2olXRTPUUmLc), which is important to help improve our content offerings and user experience.\n",
"\n",
"In the following video, John Watrous steps you through the content in this lesson on single systems. Alternatively, you can open the [YouTube video](https://youtu.be/3-c4xJa7Flk?list=PLOFEBzvs-VvqKKMXX4vbi4EB1uaErFMSO) for this lesson in a separate window. [Download the slides](https://ibm.box.com/public/static/95va6f5vqru3mpsv9p5ivwcyxino4rk7.pdf) for this lesson.\n",
"\n",
"<IBMVideo id=\"134056207\" title=\"In this video, John Watrous describes classical and quantum state vectors. He introduces some critical notation for quantum states and operators, including unitary matrices for operations on qubit systems.\"/>\n",
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Expand Up @@ -16,8 +16,6 @@
"\n",
"# Introduction\n",
"\n",
"Before beginning, please complete this short [pre-course survey](https://your.feedback.ibm.com/jfe/form/SV_3dU0dtXlJsTnlSm), which is important to help improve our content offerings and user experience.\n",
"\n",
"Quantum computing has the potential to enable efficient solutions to computational tasks for which efficient classical algorithms are not known, and possibly don't exist.\n",
"There are, however, very significant challenges that must be overcome before we can reliably implement the sorts of large-scale quantum computations we hope will one day be possible.\n",
"\n",
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Expand Up @@ -16,8 +16,6 @@
"\n",
"# Introduction\n",
"\n",
"Before beginning, please complete this short [pre-course survey](https://your.feedback.ibm.com/jfe/form/SV_cZ20ssflsjutfcG), which is important to help improve our content offerings and user experience.\n",
"\n",
"In this first lesson of the course, we'll formulate a simple algorithmic framework — known as the *query model* — and explore the advantages that quantum computers offer within this framework.\n",
"\n",
"The query model of computation is like a petri dish for quantum algorithmic ideas.\n",
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Expand Up @@ -17,8 +17,6 @@
"\n",
"# Introduction\n",
"\n",
"Before beginning, please complete this short [pre-course survey](https://your.feedback.ibm.com/jfe/form/SV_a64TTfW8cUM9Mc6), which is important to help improve our content offerings and user experience.\n",
"\n",
"In the \"Basics of quantum information\" course, we discussed a framework for quantum information in which quantum states are represented by quantum state vectors, operations are represented by unitary matrices, and so on.\n",
"We then used this framework in the \"Fundamentals of quantum algorithms\" course to describe and analyze quantum algorithms.\n",
"\n",
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Expand Up @@ -66,18 +66,15 @@
"Some of the scaling concepts from this section will be applicable to the next section on quantum computing resources. Some other aspects of quantum resources will be quantified in new ways.\n",
"\n",
"#### Check your understanding\n",
"<details>\n",
"<summary>\n",
"\n",
"Use the descriptions above to infer some advantages and disadvantages of the different scaling approaches: vertical and horizontal?\n",
"\n",
"</summary>\n",
"<Accordion>\n",
"<AccordionItem title=\"Use the descriptions above to infer some advantages and disadvantages of the different scaling approaches: vertical and horizontal?\">\n",
"\n",
"__Answer:__\n",
"\n",
"There may be many correct answers. Vertical scaling is often simpler, especially if you have predictable workloads that will need a fixed amount of resources. But vertical scaling could be more expensive to upgrade, since the fundamental unit of computing cannot be broken down as easily as in horizontal scaling. Horizontal scaling is more complex to manage and sometimes there are difficulties or latencies related to connections between nodes. But it is much more adaptive to varying resource requirements and is modular when upgrades are required.\n",
"\n",
"</details>"
"</AccordionItem>\n",
"</Accordion>"
]
},
{
Expand Down Expand Up @@ -159,20 +156,17 @@
"![An image showing vertical scaling of quantum resources as more qubits on a chip, and horizontal scaling of quantum resources as connecting many chips together with couplers.](/learning/images/courses/integrating-quantum-and-high-performance-computing/compute-resources/quantum-scaling.svg)\n",
"\n",
"#### Check your understanding\n",
"<details>\n",
"<summary>\n",
"\n",
"What are the quantum analogs of classical (a) bits of information, and (b) processor speed?\n",
"\n",
"</summary>\n",
"<Accordion>\n",
"<AccordionItem title=\"What are the quantum analogs of classical (a) bits of information, and (b) processor speed?\">\n",
"\n",
"__Answer:__\n",
"\n",
"(a) Quantum bits or qubits - units of information which unlike their classical counterparts (which can only adopt the state 0 or 1), can be in a superposition of 0 and 1 simultaneously.\n",
"\n",
"(b) Circuit layer operations per second or CLOPS - number of sequential operations the QPU can perform each second, including some interfacing with classical computing resources, as in loading parameters from the circuit.\n",
"\n",
"</details>"
"</AccordionItem>\n",
"</Accordion>"
]
},
{
Expand Down Expand Up @@ -262,15 +256,8 @@
"High-performance computing environments use special software to carry out these steps and manage resources. In the next section, we will learn about a widely-adopted resource management software systems: Slurm. It is important to note that Slurm does not have tools for all steps described above. Slurm does not provide support for planning jobs, nor detailed workload management such as communication between workload components. This is well-suited to the current state of quantum computing in HPC, since QPUs are typically accessed over the network.\n",
"\n",
"#### Check your understanding\n",
"<details>\n",
"<summary>\n",
"\n",
"Suppose you are trying to search an unsorted database to find an element which we will call the 'target'. For each of the following actions, state to which stage of resource management it corresponds:\n",
"(a) Estimating the size of the database and time required to check each element\n",
"(b) Ensuring that finding the target on one GPU stops the process on other GPUs to free them up for the next problem.\n",
"(c) Splitting the search space into regions for each of your (say 10) GPUs to search\n",
"\n",
"</summary>\n",
"<Accordion>\n",
"<AccordionItem title=\"Suppose you are trying to search an unsorted database to find an element which we will call the 'target'. For each of the following actions, state to which stage of resource management it corresponds: (a) Estimating the size of the database and time required to check each element (b) Ensuring that finding the target on one GPU stops the process on other GPUs to free them up for the next problem. (c) Splitting the search space into regions for each of your (say 10) GPUs to search\">\n",
"\n",
"__Answer:__\n",
"\n",
Expand All @@ -279,7 +266,8 @@
"(c) Allocating/scheduling,\n",
"\n",
"\n",
"</details>"
"</AccordionItem>\n",
"</Accordion>"
]
},
{
Expand Down Expand Up @@ -415,27 +403,19 @@
"```\n",
"\n",
"#### Check your understanding\n",
"<details>\n",
"<summary>\n",
"\n",
"Given the Slurm shell script below, what is (a) the name of the job, (b) the name of the Python file, and (c) the name of the output file? (d) Finally, could this use quantum resources or not?\n",
"\n",
"\n",
"```\n",
"<Accordion>\n",
"<AccordionItem title=\"Given the Slurm shell script below, what is (a) the name of the job, (b) the name of the Python file, and (c) the name of the output file? (d) Finally, could this use quantum resources or not? <br/><br/>\n",
"```shell\n",
"vim hello_learner.sh\n",
"\n",
"\n",
"#SBATCH --job-name=hello-learner\n",
"#SBATCH --output=hello-learner.out\n",
"#SBATCH --nodes=1\n",
"#SBATCH --ntasks-per-node=1\n",
"#SBATCH --cpus-per-task=1\n",
"#SBATCH --partition=quantum\n",
"\n",
"srun hello_learner_qm.py\n",
"```\n",
"\n",
"</summary>\n",
"\">\n",
"\n",
"__Answer:__\n",
"\n",
Expand All @@ -444,7 +424,8 @@
"(c) hello-learner.out\n",
"(d) Yes it could. It is using the quantum partition.\n",
"\n",
"</details>"
"</AccordionItem>\n",
"</Accordion>"
]
},
{
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Expand Up @@ -35,35 +35,27 @@
"![A diagram of transpilation showing how an abstract circuit is mapped into an instruction set architecture circuit. That is, the circuit is rewritten using the native gates and connectivity of the target hardware.](/learning/images/courses/integrating-quantum-and-high-performance-computing/programming-models/transpilation.svg)\n",
"\n",
"#### Check your understanding\n",
"<details>\n",
"<summary>\n",
"\n",
"How many qubits are in the circuit below?\n",
"![A circuit diagram with four horizontal lines and many gates.](/learning/images/courses/integrating-quantum-and-high-performance-computing/programming-models/checkin-circuit.svg)\n",
"\n",
"\n",
"</summary>\n",
"<Accordion>\n",
"<AccordionItem title=\"How many qubits are in the circuit below? ![A circuit diagram with four horizontal lines and many gates.](/learning/images/courses/integrating-quantum-and-high-performance-computing/programming-models/checkin-circuit.svg)\">\n",
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@0sophy1 a link (even to an image) will not render in the accordion - I suggest either putting the image directly below the accordion, or directly above (and change the language to "how many qubits are in the circuit above?")

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Hi Abby, thanks for the heads‑up. I saw that the preview can render the image in the title, so I thought we could use it there.

"\n",
"__Answer:__\n",
"\n",
"Four.\n",
"\n",
"</details>\n",
"</AccordionItem>\n",
"</Accordion>\n",
"\n",
"#### Check your understanding\n",
"<details>\n",
"<summary>\n",
"\n",
"Suppose you are modeling the electrons in a molecule. You want to approximate (a) the ground state energy of the molecule, and (b) which computational basis states are most dominant in the ground state of the molecule. In each case, would you use the Estimator or Sampler primitive?\n",
"\n",
"</summary>\n",
"<Accordion>\n",
"<AccordionItem title=\"Suppose you are modeling the electrons in a molecule. You want to approximate (a) the ground state energy of the molecule, and (b) which computational basis states are most dominant in the ground state of the molecule. In each case, would you use the Estimator or Sampler primitive?\">\n",
"\n",
"__Answer:__\n",
"\n",
"(a) Estimator\n",
"(b) Sampler\n",
"\n",
"</details>"
"</AccordionItem>\n",
"</Accordion>"
]
},
{
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Expand Up @@ -109,34 +109,24 @@
"\n",
"\n",
"#### Check your understanding\n",
"<details>\n",
"<summary>\n",
"\n",
"True or False: SQD can be applied to chemical systems.\n",
"\n",
"</summary>\n",
"<Accordion>\n",
"<AccordionItem title=\"True or False: SQD can be applied to chemical systems.\">\n",
"\n",
"__Answer:__\n",
"\n",
"True\n",
"</details>\n",
"\n",
"#### Check your understanding\n",
"<details>\n",
"<summary>\n",
"\n",
"Call the set of all computational basis states that make up your ansatz $A$. Call the set of all computational basis states that make up the true ground state of your system $G$. Which of the following corresponds to a \"good\" ansatz? Select all that apply.\n",
"\n",
"(a) $A \\subset G \\\\$\n",
"(b) $A \\subseteq G\\\\$\n",
"(c) $G \\subset A\\\\$\n",
"(d) $G \\subseteq A\\\\$\n",
"</summary>\n",
"</AccordionItem>\n",
"<AccordionItem title=\"Call the set of all computational basis states that make up your ansatz A. Call the set of all computational basis states that make up the true ground state of your system G. Which of the following corresponds to a 'good' ansatz? Select all that apply:<br/>\n",
"(a) A ⊂ G <br/>\n",
"(b) A ⊆ G <br/>\n",
"(c) G ⊂ A <br/>\n",
"(d) G ⊆ A\">\n",
"\n",
"__Answer:__\n",
"\n",
"(c) and (d)\n",
"</details>"
"</AccordionItem>\n",
"</Accordion>"
]
},
{
Expand Down Expand Up @@ -180,18 +170,15 @@
"In experiments, SKQD has been used with up to 70 qubits and thousands of gates to study the ground state of complex 4-impurity Anderson models, achieving excellent agreement with state-of-the-art classical methods like DMRG.[[1]](#references)\n",
"\n",
"#### Check your understanding\n",
"<details>\n",
"<summary>\n",
"\n",
"What part of the SKQD algorithm makes it more amenable to physical problems like spin lattices than to chemical problems? Why?\n",
"\n",
"</summary>\n",
"<Accordion>\n",
"<AccordionItem title=\"What part of the SKQD algorithm makes it more amenable to physical problems like spin lattices than to chemical problems? Why?\">\n",
"\n",
"__Answer:__\n",
"\n",
"The time evolution requires Trotter circuits, which are very deep for Hamiltonians that are complicated and not sparse. Spin lattice interactions are governed by spin matrices, equivalent to Pauli matrices. Thus, the Hamiltonians for spin lattices tend to be more compactly expressible in Pauli matrices, especially those with nearest-neighbor interactions.\n",
"\n",
"</details>"
"</AccordionItem>\n",
"</Accordion>"
]
},
{
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Expand Up @@ -52,16 +52,13 @@ To get a better conversational understanding of the core concepts of quantum com

Read the question below, think about your answer, then click the triangle to reveal the solution.

<details>
<summary>

True or false: Only people with advanced degrees in mathematics and physics can understand quantum computing concepts.

</summary>
<Accordion>
<AccordionItem title="True or false: Only people with advanced degrees in mathematics and physics can understand quantum computing concepts.">

False. Being only a little more complex than high school algebra, quantum concepts are more accessible that one might think. Their difficulty lies in their counterintuitive nature.

</details>
</AccordionItem>
</Accordion>



Expand Down Expand Up @@ -119,20 +116,19 @@ For more intuition of how interference works, watch this [video](https://youtu.b

Read the question below, think about your answer, then click the triangle to reveal the solution.

<details>
<summary>

Quantum physics contains some counterintuitive ideas, such as:
(a) A physical system in a definite state can still behave randomly.
(b) Two systems that are too far apart to influence each other are somehow strongly correlated.
(c) It is possible to have a state in a quantum system that cannot be described as the product of the independent components of the qubits that make up the state.
(d) All of the above
<Accordion>
<AccordionItem title="Quantum physics contains some counterintuitive ideas, such as:<br/>
(a) A physical system in a definite state can still behave randomly.<br/>
(b) Two systems that are too far apart to influence each other are somehow strongly correlated.<br/>
(c) It is possible to have a state in a quantum system that cannot be described as the product of the independent components of the qubits that make up the state.<br/>
(d) All of the above">

</summary>
__Answer:__

The correct answer is "All of the above." The first idea relates to the probabilistic nature of qubits. The second two ideas arise in entangled systems.

</details>
</AccordionItem>
</Accordion>


## Quantum circuits
Expand All @@ -147,16 +143,13 @@ Quantum circuits represent a set of instructions that allow us to manipulate qub

Read the question below, think about your answer, then click the triangle to reveal the solution.

<details>
<summary>

True or false: Quantum circuits are not physical devices.

</summary>
<Accordion>
<AccordionItem title="True or false: Quantum circuits are not physical devices.">

True. A quantum circuit is an abstract representation of a set of instructions that make up a quantum algorithm. We can use a visual tool like the IBM [Composer](https://quantum.cloud.ibm.com/composer) or a programming language like [Qiskit](/docs/guides) to construct quantum circuits.

</details>
</AccordionItem>
</Accordion>


### Programming a quantum circuit
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Expand Up @@ -93,7 +93,7 @@ Read the question below, think about your answer, then click the triangle to rev
<Accordion>
<AccordionItem title="True or false: Quantum Volume refers to the size of the cryogenic refrigerators that house IBM quantum computers.">

False. Quantum Volume is a single number meant to encapsulate the performance of todays quantum computers.
False. Quantum Volume is a single number meant to encapsulate the performance of today's quantum computers.

</AccordionItem>
</Accordion>
Expand All @@ -117,11 +117,11 @@ The feedback loop between quantum and classical is key to advancing quantum tech

* In this experiment, we used all 127 qubits of our IBM Quantum Eagle processor to simulate the changing behavior of a system that naturally maps to a quantum computer, called the quantum Ising model. Ising models are simplifications of nature that represent interacting atoms as a lattice of interacting quantum two-choice systems in an energy field. These systems look a lot like the two-state qubits that make up our quantum computers, making them a good fit for testing the abilities of our methods. We used ZNE to try and accurately calculate a property of the system called its expectation value — essentially a weighted average of the possible outcomes of the circuit.

* Simultaneously, the Berkeley team attempted to simulate the same system using tensor network methods with the help of advanced supercomputers located at Lawrence Berkeley National Labs National Energy Research Scientific Computing Center (NERSC) and at Purdue University.
* Simultaneously, the Berkeley team attempted to simulate the same system using tensor network methods with the help of advanced supercomputers located at Lawrence Berkeley National Lab's National Energy Research Scientific Computing Center (NERSC) and at Purdue University.

* The quantum methods continued to agree with the exact methods. But eventually, the classical approximation methods started to falter as the difficulty was turned up.

* Finally, we asked both computers to run calculations beyond what could be calculated exactly — and the quantum computer returned an answer we were more confident to be correct. And while we cant prove whether that answer was actually correct, Eagles success on the previous runs of the experiment gave us confidence that they were.
* Finally, we asked both computers to run calculations beyond what could be calculated exactly — and the quantum computer returned an answer we were more confident to be correct. And while we can't prove whether that answer was actually correct, Eagle's success on the previous runs of the experiment gave us confidence that they were.

</AccordionItem>
</Accordion>
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