Physicist Richard Feynman is credited with proposing quantum computers through a "Physics of Computation" conference organized by MIT and IBM in 1981 along with the associated papers published afterwards by multiple participants of that conference. 
Quantum computers use quantum mechanics to manipulate data, such as superposition and entanglement. Superposition refers to a quantum variable that simultaneously exists in multiple states. Entanglement refers to multiple quantum variables having related states regardless of distance between each other.
Instead of using 1 and 0 to represent data, quantum computers use quantum bits (qubits). Electrons (up spin and down spin) and photons (vertical and horizontal polarization) are used. Qubits can be in both states at the same time (superposition).
This allows a combination of a very large number of states. The difference between a classical supercomputer and a quantum computer is that a quantum computer uses quantum mechanical effects to manipulate data in a way that defies intuition. 
Algorithms are quantum logic operations performed on qubits. The algorithm is repeated until a confidence interval is achieved.
Quantum dots are small semiconductor particles.
One of the biggest problems of developing quantum computers is disruption from the slightest of disturbance. Current quantum computers suffer one error for every 1,000 operations. A practical quantum computer requires error rates lower by a billionfold.
Some of the different types of qubits that have been used for quantum computers are:
- Superconducting qubits: Based on the Josephson junction, a device that allows the flow of supercurrent without resistance. These qubits include transmon, flux, and phase qubits.
- Trapped ion qubits: Based on electronic and nuclear spin states of individual ions trapped and manipulated by electromagnetic fields. This includes calcium, magnesium, and beryllium ions.
- Quantum dot qubits: Based on electronic spin states of electrons confined in semiconductor quantum dots. Electrical gates and magnetic fields manipulate the qubits.
- Topological qubits: Based on topological properties of materials, such as Majorna fermions.
- Diamond nitrogen-vacancy center qubits: Based on electronic spin states of nitrogen-vacancy centers in diamond. Microwave and optical fields manipulate the qubits.
- Nuclear magnetic resonance qubits: Based on nuclear spins of atoms or molecules manipulated using radiofrequency pulses in a magnetic field.
- Photonic qubits: Based on quantum properties of light manipulated using optical components.
Quantum-Resistant Cryptographic Algorithms
Quantum computing can break any cybersecurity protocol.
In 2022, the U.S. Department of Commerce's National Institute of Standards and Technology (NIST) selected the first group of encryption tools designed to withstand quantum computer cyberattacks. 
Encryption uses math to protect information using public-key encryption systems. Quantum computers are capable of solving these math problems quickly, compared to the most advanced computers that exist at the moment.
The quantum-resistant algorithms that were selected rely on math problems that both classical and quantum computers may find difficult to solve. These algorithms are designed for general encryption and digital signatures.
General Encryption: CRYSTALS-Kyber algorithm.
Digital Signatures: CRYSTALS-Dilithium, FALCON, and SPHINCS+. NIST recommends CRYSTALS-Dilithium as the primary algorithm. FALCON is for applications that need smaller signatures than Dilithium provides. SPHINCS+ is a backup because it is based on a different math approach than the other three algorithms.
SPHINCS+ uses hash functions while the other three use structural lattices.
NIST recommends that developers take inventory of software that uses public-key cryptography and alert the appropriate I.T. vendors and departments, but not to formally adopt these new algorithms until the final NIST review is complete. Public-key cryptography will need to be replaced before quantum computers become viable.
2023 Nobel Prize
The 2023 Nobel Prize in Physics was awarded to Pierre Agostini, Ferenc Krausz and Anne L'Huillier "for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter." 
The 2023 Nobel Prize in Chemistry was awarded to Moungi Bawendi, Louis Brus and Alexei Ekimov "for the discovery and synthesis of quantum dots." 
Both prizes are related to quantum computers.
IBM has the largest quantum computing fleet in the world. The Qiskit Runtime, an open-source python-based quantum SDK, is the IBM quantum computing service and programming model.
IBM offers 127-qubit systems based on the Eagle processor, 27-qubit systems based on the Falcon processor, and simulators.
IBM is working on quantum-safe algorithms. A realistic scenario is "harvest now, decrypt later" attacks where encrypted files are stored until better technology is available. A quantum attack requires a quantum-safe strategy to protect data. IBM created the "IBM Quantum Safe" roadmap.
Quantum computers offer the potential to perform the calculations needed to accurately simulate the building blocks of nature to understand the universe. The CERN Large Hadron Collider collects one petabyte of data per second. Analysis of this data requires one million classical CPU cores in 170 locations around the world. Another example is molecular simulation for the design of better electric car batteries.
IBM led the U.S. with the most patent applications for 29 years. At the company's peak, it filed 10,000 patents in a single year. IBM recently shifted it's patent focus. 2022 was the first year since 1993 that IBM wasn't number one on the list of companies with the most U.S. patents. One explanation is quantum computers. IBM's work with quantum computers has been proprietary and open innovation. In 2016, IBM made their quantum computers available on the cloud and open-sourced Qiskit. IBM adopted collaboration over exclusivity to advance the future of quantum computing, even though the company will still pursue patents.
Intel has the Tunnel Falls silicon spin qubit chip with the goal of building a full-stack commercial quantum computing system.
Quantum practicality requires quantum systems with millions of qubits and solutions to challenges like qubit fragility and software programmability.
The Intel Quantum Software Development Kit (SDK) is a full quantum computing stack in simulation that can also interface with Intel's quantum hardware. The SDK is used to program quantum algorithms in simulation with a C++ interface and low-level virtual machine (LLVM) compiler toolchain. It also allows interfacing with C/C++ and Python applications.
One option is a high-performance open-source generic qubit simulator with 32 qubits on a single node and more than 40 qubits on multiple nodes.
Amazon Braket lets users work with different types of quantum computers and circuit simulators. The quantum computing service involves building a quantum algorithm on managed Jupyter notebooks, testing the algorithm with a simulator, running the algorithm on a quantum computer or hybrid resources, and analyzing the results of the algorithm.
The goal of Amazon Braket is for researchers to perform experiments with different quantum hardware technologies, explore hybrid quantum-classical, quantum machine learning and variational algorithms, and develop error correct strategies for Noisy Intermediate-Scale Quantum hardware.
AWS offers the Amazon Braket Software Development Kit (SDK).
The AWS quantum hardware technology includes: (1) gate-based superconducting qubits processors built with electric circuits operating at cryogenic temperature; (2) gate-based ion-trap processors with ions confined and suspended in free space using electromagnetic fields; (3) neural atom-based quantum processors based on interactions between neural atoms arranged in 1, 2, or 3D arrays.
PennyLane is an open source software library for variational quantum computing, based on quantum differentiable programming. It is used to train quantum circuits the same as neural networks.
OpenQASM an an open source intermediate representation for quantum computing programs.
QuEra Computing -
- Aquila processor operates up to 256 qubits in analog mode with tens of qubit flips before decoherence
- Lasers to arrange and excite individual neutral atoms into highly energetic states
- Excited-atom qubits naturally interact at a distance, enabling entanglement and multi-qubit connectivity
- Strong quantum coherence properties of neutral atoms
- Aquila is programmed in two steps (1) define atom positions to fix qubit layout and connectivity and (2) determine time series of the atomic parameters.
- Individual ions are trapped in space and controlled with precise laser pulses to perform quantum gate operations and measurements.
- Laser-based architecture offers a high level of configurability to perform gate operations on any pair of qubits, referred to as "all-to-all connectivity".
- Long coherence times to determine qubit state.
Oxford Quantum Circuits:
- 8-qubit quantum computer
- designed for long coherence times, low cross-talk, and high-fidelity gate operation times.
- goal is commercial scalability
- compiler optimizes number of gates required to execute the circuit with the fewest used possible for the best result.
- sequences of optimized microwave pulses drive the most appropriate chains of qubits.
- universal, gate-model machines based on superconducting qubits.
- tileable lattices of alternating, fixed-frequency and tunable qubits with parametric entangling logic gates.
- user programs are optimized into machine-native instructions through a compiler tool chain.
- low latency hardware controller sequences the instructions into calibrated electrical signals.
- qubits transduce these electrical signals logically as digital quantum gates and measurement instructions.
AWS simulators include:
Local Simulator: Intended for quick validation of circuit designs up to 25 qubits without noise or 12 with noise.
SV1 simulator: state vector simulator for quantum circuits up to 34 qubits. Works by taking full wave function of the quantum state and applies the operations of the circuit to calculate the result. Supports up to 35 simulations in parallel.
DM1 simulator: density matrix simulator to investigate effects of noise on quantum algorithms. Supports circuits up to 17 qubits and 35 simulations in parallel.
TN1 simulator: tensor network simulator for circuits up to 50 qubits. Works by encoding quantum circuits into a structured graph for computing the outcome of the circuit.
Microsoft Azure Quantum 
Azure Quantum is cloud-based hardware, software, and solutions.
Copilot is used with Q# programming
Microsoft's goal is to engineer the world's first hardware protected qubit with the capabilities of one million quantum operations per second. This new type of qubit is based on Majorna Zero Modes. Microsoft's approach is to change qubit technology from analog to digital control. Digitally controlled hardware-protected qubits can be entangled and braided. Quantum supercomputing can be achieved with a Quantum Machine operating on true logical qubits with higher quality operations than underlying physical qubits. The Quantum supercomputer can run one million reliable quantum operations per second with an error rate of less than one every trillion steps.The goal is to pass 100 millions reliable per second and beyond.
There are both digital and analog quantum computers.
Analog hardware represents quantum information with continuous variables that include amplitude and phase of a quantum wave function. Quantum information is represented by a continuous range of values. Analog circuits and signal processing techniques manipulate these values.
Digital quantum computing is also known as gate-based quantum computing. Information is represented with quantum mechanics, such as a spin of an electron or polarization of a photon. A finite set of values (0 and 1) are used.
Microsoft is pursuing topological qubits for scaled quantum computing.
Quantum computing stack layers:
1. Hardware: physical devices and systems that implement quantum computing, such a qubits.
2. Physical qubits: the individual quantum bits.
3. Quantum Error Correction: techniques and protocols to detect and correct errors in quantum information.
4. Logical qubits: abstraction of physical qubits
5. Quantum Intermediate Representation: describe quantum algorithms and circuits in a form that can be implemented on physical quantum hardware.
6. Quantum algorithm: set of instructions or operations to take advantage of quantum mechanics.
Google Quantum AI 
Google Quantum AI is a suite of software and hardware for quantum algorithms.
The Cirq framework is a Python library for quantum circuits. It includes simulators for wave functions and density matrices. The Quantum Virtual Machine (QVM) simulates quantum hardware. Cirq works with the "qsim" wave function simulator.
QVM is used to run circuits on simulated hardware to mock circuit constraints and noise behavior.
The Cirq simulator is used to calculate the results of an application of a quantum circuit.
The OpenFermion library is for quantum algorithms to simulate fermionic systems.
The TensorFlow Quantum Library is for hybrid quantum-classical machine learning.
Hardware is based on the Sycamore processor with up to 54 superconducting qubits in a square grid lattice.
Steps to build a quantum circuit (model for quantum computation):
- Define set of qubits (aka quantum register) to act on. "Devices" are pre-packaged qubits with rules for how to be used.
- A qubit is the software representation of quantum bits.
- A "Gate" is an effect that can be applied to a set of qubits.
- An "Operation" is a gate applied to a set of qubits.
- A "Circuit" is a collection of "Moments".
- A "Moment" is a collection of "Operations" that all act during the same abstract time slice.
- Each "Operation" must be applied to a disjoint set of qubits compared to each of the other "Operations" in the "Moment".
- A "Device" object is used to specify constraints to validate a circuit.
The MIT Lincoln Laboratory is working on (1) ion traps for capturing single atoms and (2) the Josephson junction, which are based on superconducting circuits. The goal is to scale up systems of qubits to address real computational problems.
The trapped-ion quantum computing facility uses cryogenically cooled ultrahigh vacuum systems. The trapped ions are manipulated using lasers and electromagnetic fields to perform quantum-processing operations. Strontium and calcium ions are involved with these systems.
The superconducting facility uses cryogenic dilution refrigerators with microwave test and measurement equipment.
To address error correction limitations, MIT created the fluxonium superconducting qubit with a longer lifespan that other qubits.
A superconducting quantum computer uses the flow of paired electrons ("Cooper pairs") through a resistance-free circuit as the qubit. MIT is involved with superconducting aluminum circuits chilled close to absolute zero.
A trapped ion quantum computer uses individual atoms as qubits. Lasers are used to control the ion's quantum behavior. This involves promoting one of the electrons in the atom to a higher or lower energy level. An electromagnetic field can hold a trapped ion just above the chip surface. Voltage applied to electrodes on a chip can move ions across the surface.
MIT found that background radiation emitted by trace elements in concrete walls and incoming cosmic rays are enough to cause qubit decoherence. Research is underway to shield qubits, such as building computers underground or designing radiation tolerant qubits.
Berkeley Lab (University of California and U.S. Department of Energy's Office of Science) is working on a Quantum Internet that connects quantum computers with highly secure data transmission. A conventional fiber optic network involves light sources to transport information. However, a quantum internet would involve working with individual photons. Quantum light emitters (color centers) are used to produce and manipulate photons.
Sources (Accessed 10/6/2023)
 Nature Reviews Physics - 40 years of quantum computing (https://www.nature.com/articles/s42254-021-00410-6)
 Here's a Blueprint for a Practical Quantum Computer - IEEE Spectrum (https://spectrum.ieee.org/heres-a-blueprint-for-a-practical-quantum-computer)
 U.S. Department of Commerce's National Institute of Standards and Technology (NIST) - NIST Announces First Four Quantum-Resistant Cryptographic Algorithms (https://www.nist.gov/news-events/news/2022/07/nist-announces-first-four-quantum-resistant-cryptographic-algorithms)
 The Nobel Prize in Physics (https://www.nobelprize.org/prizes/physics/)
 The Nobel Prize in Chemistry (https://www.nobelprize.org/prizes/chemistry/)
 IBM Quantum Computing (https://www.ibm.com/quantum)
 Quantum Computing and Systems with Intel Labs (https://www.intel.com/content/www/us/en/research/quantum-computing.html)
 Quantum Cloud Computing Service - Amazon Braket - AWS (https://aws.amazon.com/braket/)
 Microsoft Azure Quantum (https://quantum.microsoft.com/)
 Google Quantum AI (https://quantumai.google/)
 Quantum Computing Laboratory - MIT Lincoln Laboratory (https://www.ll.mit.edu/about/facilities/quantum-computing-laboratory)
 Quantum - Lawrence Berkeley National Laboratory (https://www.lbl.gov/research/quantum/)
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