Add Bell State example

deps.edn

@@ -40,7 +40,10 @@
   org.lwjgl/lwjgl-stb$natives-windows         {:mvn/version "3.3.6"}
   org.lwjgl/lwjgl-stb$natives-macos           {:mvn/version "3.3.6"}
   generateme/fastmath                         {:mvn/version "3.0.0-alpha3"}
-  clj-http/clj-http                           {:mvn/version "3.13.1"}}
+  clj-http/clj-http                           {:mvn/version "3.13.1"}
+
+  org.soulspace/qclojure                      {:mvn/version "0.21.0"}
+  }
 
  :aliases
  {;; Build the site with `clojure -M:clay -A:markdown`

site/db.edn

@@ -130,6 +130,11 @@
    :affiliation [:cim]}
   {:id          :luke-zeitlin
    :name        "Luke Zeitlin"
+   :affiliation []}
+  {:id          :ludgersolbach
+   :name        "Ludger Solbach"
+   :url         "https://github.com/lsolbach"
+   :links       [{:icon "github" :href "https://github.com/lsolbach"}]
    :affiliation []}]
 
  :affiliation

src/qclojure/examples/bell_state_circuit.clj

@@ -0,0 +1,186 @@
+^{:kindly/hide-code true
+  :clay             {:title  "Bell State Circuit"
+                     :quarto {:author :ludgersolbach
+                              :draft true
+                              :type :post
+                              :date "2025-10-10"}}}
+(ns qclojure.examples.bell-state-circuit 
+  (:require
+   [scicloj.kindly.v4.kind :as kind]))
+
+;; # Bell State Circuit Example
+;; This example demonstrates how to create and visualize a Bell state circuit and how to simulate
+;; a quantum computer executing the circuit, using both an ideal simulator and a hardware simulator,
+;; on classical hardware using QClojure.
+;;
+;; ## What is QClojure?
+;; QClojure is a Clojure library for quantum computing that provides tools to create,
+;; execute, and visualize quantum circuits. It allows users to define quantum circuits using a
+;; high-level, functional programming approach.
+;; QClojure supports various quantum gates, measurements, and state manipulations, making it
+;; suitable for building quantum algorithms and exploring quantum computing concepts.
+;; It comes with a variety of quantum algorithms and provides simulators to run quantum circuits
+;; and algorithms on classical hardware.
+;;
+;; With extensions (e.g. for Amazon Braket), QClojure enables users to run their quantum
+;; circuits on real quantum hardware.
+;;
+;; To use QClojure, you have to include it as a dependency in your Clojure
+;; project. Please use the [latest version](https://clojars.org/org.soulspace/qclojure).
+;;
+;; ## What is a Quantum Computer?
+;; A quantum computer is a type of computing device that leverages the principles of quantum mechanics
+;; to perform computations. Unlike classical computers, which use bits as the basic unit of information
+;; (0s and 1s), quantum computers use quantum bits or qubits. Qubits can exist in multiple states simultaneously
+;; due to a property called superposition. This allows quantum computers to process a vast number of
+;; possibilities at once.
+;; Another key property of quantum computers is entanglement, where the state of one qubit can be
+;; directly related to the state of another, regardless of the distance between them. This phenomenon
+;; enables quantum computers to perform certain calculations much more efficiently than classical computers.
+;;
+;; ## What is a Quantum Circuit?
+;; A quantum circuit is a model for quantum computation in which a computation is represented as a
+;; sequence of quantum gates, which are the quantum analogs of classical logic gates. Quantum circuits
+;; manipulate qubits through these gates to perform operations and transformations on their quantum states.
+;; Quantum circuits are typically visualized using circuit diagrams, where qubits are represented as
+;; horizontal lines and quantum gates as symbols placed along these lines.
+;; Quantum circuits can be used to implement quantum algorithms, which are designed to solve specific
+;; problems more efficiently than classical algorithms. Examples of quantum algorithms include Shor's
+;; algorithm for factoring large numbers and Grover's algorithm for searching unsorted databases.
+;;
+;; ## What is a Quantum Gate?
+;; A quantum gate is a fundamental building block of quantum circuits, analogous to classical logic gates
+;; used in classical computing. Quantum gates manipulate the state of qubits, which are the basic
+;; units of quantum information. Unlike classical bits that can be either 0 or 1,
+;; qubits can exist in a superposition of states, allowing quantum gates to perform complex operations.
+;; Quantum gates are represented as unitary matrices, which ensure that the operations they perform
+;; are reversible.
+;;
+;; Common quantum gates include:
+;; - **Hadamard Gate (H)**: Creates superposition by transforming a qubit from a definite state (|0⟩ or |1⟩)
+;;   into an equal superposition of both states.
+;; - **Pauli-X Gate (X)**: Also known as the quantum NOT gate, it flips the state of a qubit (|0⟩ to |1⟩ and vice versa).
+;; - **Pauli-Y Gate (Y)**: Similar to the X gate but also introducess a phase shift.
+;; - **Pauli-Z Gate (Z)**: Introduces a phase flip to the |1⟩ state while leaving the |0⟩ state unchanged.
+;; - **CNOT Gate (Controlled NOT)**: A two-qubit gate that flips the state of the target qubit if the control
+;;   qubit is in the state |1⟩. It is essential for creating entanglement between qubits. 
+;;
+;; ## What is a Bell State?
+;; A Bell state is a specific quantum state of two qubits that represents the simplest and most
+;; well-known example of quantum entanglement. The Bell states are maximally entangled states
+;; and are used in various quantum information protocols, including quantum teleportation and
+;; superdense coding.
+;; Bell states are fundamental in the study of quantum mechanics and quantum computing,
+;; illustrating the non-classical correlations that can exist between quantum systems.
+;;
+;; There are four different Bell states, but the most commonly referenced one is:
+;; |Φ+⟩ = (|00⟩ + |11⟩) / √2
+;;
+;; This state indicates that if one qubit is measured to be in the state |0⟩, the other qubit will
+;; also be in the state |0⟩, and similarly for the state |1⟩, demonstrating perfect correlation between
+;; the two qubits.
+;; The probability of measuring either |00⟩ or |11⟩ is equal, each with a probability of 0.5,
+;; which means that other combinations like |01⟩ or |10⟩ will never be observed in this state.
+;;
+;; ## Creating the Bell State Circuit
+;; The following code creates a simple quantum circuit that generates a Bell state.
+;; First, we need to require the necessary namespaces from QClojure.
+(require '[org.soulspace.qclojure.domain.state :as state]
+         '[org.soulspace.qclojure.domain.circuit :as circuit]
+         '[org.soulspace.qclojure.application.visualization :as viz]
+         '[org.soulspace.qclojure.adapter.visualization.ascii :as ascii]
+         '[org.soulspace.qclojure.adapter.visualization.svg :as svg])
+
+;; Next, we create a quantum circuit with two qubits and apply the necessary quantum gates
+;; to generate the Bell state. We use the Hadamard gate (H) on the first qubit to create
+;; superposition, followed by a CNOT gate to entangle the two qubits.
+
+(def bell-state-circuit
+  (-> (circuit/create-circuit 2 "Bell State Circuit" "Creates a Bell state.")
+      (circuit/h-gate 0)
+      (circuit/cnot-gate 0 1)))
+
+;; We can visualize the circuit as ASCII art for the REPL.
+^kind/code
+(viz/visualize-circuit :ascii bell-state-circuit)
+
+;; For notebooks and documents, we can also visualize the circuit as SVG.
+^kind/hiccup
+(viz/visualize-circuit :svg bell-state-circuit)
+
+;; ## Executing the Bell State Circuit
+;; To quickly test the circuit in the REPL, we can use the execute-circuit function
+;; from the circuit namespace.
+(def result (circuit/execute-circuit bell-state-circuit))
+
+;; The result is a map that contains the final state of the qubits after executing the circuit.
+result
+
+;; ## Using Simulators to Execute the Circuit
+;; We can also use a quantum backend to execute the circuit with more options.
+;; QClojure provides two different simulator backends: an ideal simulator backend
+;; and a hardware simulator backend.
+;; The ideal simulator simulates the quantum circuit without any noise or errors,
+;; while the hardware simulator simulates the quantum circuit with noise and errors
+;; that are present in real quantum hardware.
+;;
+;; First, we need to require the necessary namespaces for the simulators.
+(require 
+ '[org.soulspace.qclojure.application.backend :as backend]
+ '[org.soulspace.qclojure.adapter.backend.ideal-simulator :as ideal-sim]
+ '[org.soulspace.qclojure.adapter.backend.hardware-simulator :as hw-sim])
+
+;; Let's first use the ideal simulator to execute the Bell state circuit.
+(def ideal-simulator (ideal-sim/create-simulator))
+
+;; We define some options for the execution, such as the results we want to obtain.
+;; In this case, we want to measure the qubits 100 times (shots).
+(def options {:result-specs {:measurements {:shots 100}}})
+
+;; Now we can execute the circuit using the ideal simulator and the defined options.
+(def ideal-result
+  (backend/execute-circuit ideal-simulator bell-state-circuit options))
+
+;; The result is a map that contains the measurement results and other information
+;; about the execution.
+ideal-result
+
+;; We can visualize the frequencies of the measurements obtained from the
+;; ideal simulator as a histogram.
+^kind/hiccup
+(viz/visualize-measurement-histogram :svg (get-in ideal-result [:results :measurement-results :frequencies]))
+
+;; Now we you the hardware simulator to execute the Bell state circuit.
+;; The hardware simulator simulates the quantum circuit with noise and errors
+;; that are present in real quantum hardware.
+(def hardware-simulator (hw-sim/create-hardware-simulator))
+
+;; We can also select a specific quantum device to simulate. We choose the
+;; IBM Lagos quantum device for this example. The IBM Lagos is a 7-qubit quantum
+;; computer that is available on the IBM Quantum Experience platform.
+(backend/select-device hardware-simulator :ibm-lagos)
+
+;; We execute the circuit using the hardware simulator and the defined options.
+(def hardware-result
+  (backend/execute-circuit hardware-simulator bell-state-circuit options))
+
+;; Here is the result of the hardware simulation.
+hardware-result
+
+;; We can visualize the result of the hardware simulation as a histogram of the
+;; measurement frequencies to compare it with the ideal simulation result.
+^kind/hiccup
+(viz/visualize-measurement-histogram :svg (get-in hardware-result [:results :measurement-results :frequencies]))
+
+;; We results are probabilistic, so we may not get exactly the same results every time we
+;; execute the circuit. However, we should see that the results from the ideal simulator
+;; are closer to the expected Bell state results (|00⟩ and |11⟩ with similar counts) compared to the
+;; hardware simulator, which may show some deviations due to noise and errors.
+;; This demonstrates the impact of quantum noise and errors on the execution of quantum circuits
+;; on real quantum hardware.
+;;
+;; ## Conclusion
+;; In this example, we created a simple quantum circuit that generates a Bell state,
+;; visualized the circuit, and executed it using both an ideal simulator and a hardware
+;; simulator provided by QClojure. We observed the differences in the measurement results
+;; between the two simulators, highlighting the effects of noise and errors in quantum computing.