#historicalcontext

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Communism is a political and economic ideology that advocates for a classless society in which all property and means of production are owned collectively or by the state.

The goal of communism is to eliminate private ownership and establish a system where goods and services are distributed according to need, rather than for profit. It seeks to abolish social classes and promote equality among people.

7666 Nights– Falling, 2017

Digital print on Fujiflex, suede and artist

frame 40 × 48 in101.6 × 121.9 cm

Failure-tolerant quantum processing is possible using the Threshold Theorem, a quantum computing fundamental. Also known as the quantum fault-tolerance theorem. This fundamental theorem enables for reliable quantum computers by decreasing mistakes. It addresses the crucial question of whether quantum computers can do long calculations noise-free.

Understand Threshold Theorem

If a quantum computer's inherent error rate is below a specific threshold, the Threshold Theorem states that quantum calculations of any time can be done with great precision. This crucial discovery proves that quantum computers can tolerate faults and prevent decoherence. Quantum states are too delicate for large-scale quantum computation without this framework.

Basic Principle: Fault Tolerance and Error Correction

Fault tolerance and mistake correction are connected to the Threshold Theorem in quantum computing. Error correction is the process of finding and repairing quantum processing errors. Fault tolerance allows a quantum computer to function during these errors.

The theorem mostly concatenates quantum error correcting codes to offer fault tolerance. Iteratively applying these codes reduces quantum computation mistakes to an arbitrarily low level. Scott Aaronson says the theorem's non-trivial property is that mistakes are repaired faster than they are made. This technology makes mistake correction a key enabler of large-scale quantum computing, not just a necessary evil.

Theorem implications

The Threshold Theorem states that fault tolerance overhead is controllable and increases polynomially with computation size. A quantum computation of any length can be performed with the appropriate low error probability by using a total number of gates that increases polynomially with computation duration and logarithmically with the inverse of the required error probability.

This suggests that a quantum circuit can be accurately simulated if each component's failure probability is below a threshold and noise models are used. The proof technique creates “better gates” from defective ones using error-correcting codes. The “better gates,” although being larger, have a lower failure probability than the original gate if the initial mistake rate is modest enough, allowing recursive improvement until gates with the desired failure probability are attained.

Quantum Error Correction Codes and Methods

Implementing the Threshold Theorem requires quantum error correcting codes. Different codes exist:

Stabiliser codes detect quantum state problems by measuring stabilisers. Shor and surface codes are examples. Encode quantum information on a two-dimensional surface. Code concatenation increases error correction levels. Quantum information is encoded and protected using topological codes. Typical quantum error correction methods:

Measurement error correction: This method detects errors by measuring a quantum state's error syndrome. Feedback-based error correction: This method corrects quantum errors. Dynamic decoupling reduces noise and decoherence with pulses.

Historical context and development

The Threshold Theorem debuted in the late 1990s. Key researchers Emanuel Knill, Raymond Laflamme, Wojciech Zurek, Alexei Kitaev, Dorit Aharonov, and Michael Ben-Or independently proved this theorem for several error models. These important findings advanced Peter Shor's weaker theorem. Theorem has been expanded and strengthened since then, proving its generality and resilience.

Issues and Limitations

Despite its theoretical importance, the Threshold Theorem has several practical challenges:

Due to their high mistake rates, many quantum computing architectures struggle to reach fault tolerance thresholds. Limited scalability/complexity: Error correction algorithms and protocols become more complex as the quantum computer grows, making scaling to many qubits difficult. Noise characterisation: Quantum devices must be precisely characterised to use effective error correction methods. One study employed the Schrödinger equation to model stochastic control errors as time-dependent stochastic noise in isolated quantum dynamics. A threshold theorem for such errors shows that a constant-order number of measurements is enough to attain the goal state if the noise strengths are smaller than the inverse of processing time. If the total noise strengths are greater than the inverse of computing time, the number of measurements needed to achieve the desired state grows exponentially with computational time.

Also see Semiconductor Nanostructure Quantum Light Sources.

If noise suppression fails in quantum annealing, where computational time scales polynomials with issue size, stochastic control mistakes may greatly alter problem complexity, changing an efficient solution into an inefficient one. This threshold theorem covers isolated quantum dynamics like adiabatic quantum computation and quantum annealing.

Qubit systems easily satisfy the theorem's stochastic control error condition that a given operator squared gives a squared noise intensity times an identity operator, unlike bosonic systems. If this criteria is not met, increasing measures does not guarantee the goal state.

Implementations and Uses

The Threshold Theorem guides fault-tolerant quantum computer development.

Fault-tolerant quantum computation may use superconducting qubits. Ion traps. A quantum topological computer. The theory has significant implications and applications in several fields:

Simulation: Accurately models complex quantum systems. Cryptography: Cracks some established encryption methods. Optimisation: Can solve complex optimisation problems. The threshold is now estimated at 1%, especially for surface code. Because simulating huge quantum systems classically is exponentially complex, these estimates vary significantly and are hard to compute.

The surface code may need 1,000–10,000 physical qubits per logical data qubit to produce 0.1% depolarising error.

Future Paths

The Threshold Theorem and quantum computing research are ongoing. New trends and directions include:

Machine learning improves quantum error correction. Fault-tolerant quantum computation is being used to simulate complex quantum systems. How to perform high-accuracy quantum calculations with noisy intermediate-scale quantum (NISQ) devices.

In conclusion

Finally, the Threshold Theorem enables fault-tolerant quantum processing in quantum computers. It makes quantum computations reliable and arbitrarily extended if error rates are kept below a threshold, despite quantum states' fragility and imprecise operations.

If you have a right to do something, should you need to ask for permission? This question strikes at the heart of some of our most cherished freedoms. Take the right to bear arms, for instance. If we have the constitutional right to keep and bear arms, why do we need a concealed carry permit? These two concepts seem to be at odds with one another. Let’s consider our founding fathers, George…

Introduction: Sama (Equanimity) and Its Importance

Sama (Equanimity), a Sanskrit term, signifies a state of mental and emotional balance, characterized by an undisturbed mind, regardless of external circumstances. It is the art of maintaining a calm and composed demeanor in both joy and sorrow, success and failure. Sama represents a higher state of consciousness where one transcends the dualities of life, such as pleasure and pain, gain and loss, praise and blame. In the context of Sanatana Dharma, which is often referred to as Hinduism, equanimity is not merely a psychological state but a spiritual accomplishment. It is considered a crucial virtue for anyone aspiring to lead a dharmic life, which is a life aligned with cosmic order and righteousness. The Bhagavad Gita, one of the foundational texts of Sanatana Dharma, extols the value of equanimity numerous times, portraying it as essential for spiritual growth and liberation (moksha). For instance, Lord Krishna advises Arjuna to remain unmoved by happiness and distress, indicating that equanimity is a prerequisite for wisdom and self-realization. The importance of Sama is manifold: Psychological Stability: It promotes mental health by reducing stress and anxiety, fostering a balanced outlook on life. Moral and Ethical Living: Equanimity supports ethical decision-making by preventing emotional extremes from influencing one's actions. Spiritual Advancement: It is considered a cornerstone of spiritual discipline, helping practitioners remain focused and detached from material distractions. Interpersonal Harmony: Equanimity aids in maintaining harmonious relationships by promoting patience, tolerance, and understanding. Introduction to Sanatana Dharma and Its Key Principles: Sanatana Dharma, often referred to as the eternal way or eternal law, encompasses a broad and inclusive spiritual tradition originating in the Indian subcontinent. Unlike many other religions, Sanatana Dharma does not have a single founder or a single holy text but is instead a compilation of diverse philosophies, rituals, and cultural practices that have evolved over millennia. The core principles of Sanatana Dharma include: Dharma (Righteousness): Refers to the ethical duties and moral responsibilities that each individual must follow. It is the guiding principle for living a virtuous life. Karma (Action and its Consequences): Highlights the law of cause and effect, where every action has corresponding results. Understanding karma encourages mindful and purposeful living. Samsara (Cycle of Rebirth): Represents the continuous cycle of birth, death, and rebirth, driven by one's karma. Liberation from samsara, known as moksha, is the ultimate goal. Moksha (Liberation): The release from the cycle of samsara and union with the divine. It is the highest spiritual attainment in Sanatana Dharma. Brahman (Ultimate Reality): The concept of an ultimate, formless, and all-pervading reality. Brahman is the source of all creation and is often equated with the divine. Atman (Soul): The belief in an eternal soul that is part of Brahman. Realizing the unity of Atman and Brahman is the essence of spiritual awakening. Sanatana Dharma is a highly adaptable and inclusive tradition, allowing for a multitude of paths to spiritual growth. It embraces various schools of thought, including Advaita (non-dualism), Dvaita (dualism), and Vishishtadvaita (qualified non-dualism), each providing different interpretations of the relationship between the individual soul and the divine. Highlight the Relevance of Equanimity in Both Spiritual and Practical Aspects of Life: In the spiritual context, equanimity is a vital component of sadhana (spiritual practice). It is regarded as a mental state necessary for achieving higher levels of meditation and contemplation. A person who has mastered equanimity can remain undisturbed by the fluctuations of the mind, thus attaining a state of inner peace and stillness which is essential for self-realization. The Bhagavad Gita underscores this by advising practitioners to remain equanimous in success and failure, joy and sorrow, and honor and dishonor. This detachment from dualities helps in dissolving the ego, which is seen as the primary barrier to spiritual enlightenment. A calm and equanimous mind is more receptive to divine knowledge and insights, facilitating the journey towards moksha. In practical life, equanimity equips individuals with the resilience to handle life's challenges with grace and poise. It fosters a balanced approach to problems, enabling one to make decisions based on rationality rather than emotional reactivity. In the modern world, where stress and anxiety are rampant, the practice of equanimity can significantly enhance one's quality of life by promoting mental stability and emotional health. For example: In Personal Relationships: Equanimity helps in managing conflicts and misunderstandings by allowing one to respond with patience and empathy rather than anger and frustration. In Professional Life: It enables individuals to maintain focus and efficiency, even under pressure, thereby improving productivity and job satisfaction. In Health and Wellness: Equanimity contributes to overall well-being by reducing the harmful effects of stress on the body and mind. Brief Introduction to Vedic Wisdom and Modern Research Supporting the Concept of Sama Vedic Wisdom: The Vedas, which are among the oldest sacred texts in the world, provide profound insights into the nature of reality and the human mind. They emphasize the importance of maintaining inner balance and harmony as a reflection of the cosmic order. The Upanishads, which are philosophical commentaries on the Vedas, delve deeper into the concept of equanimity, presenting it as an essential quality for spiritual aspirants. They teach that the realization of one's true nature (Atman) and its unity with the ultimate reality (Brahman) can only be achieved through a balanced and serene mind. The Bhagavad Gita, considered a summary of Vedic philosophy, offers practical guidance on achieving equanimity through disciplined action (karma yoga), devotion (bhakti yoga), and knowledge (jnana yoga). These teachings advocate for detachment from the fruits of actions, encouraging individuals to perform their duties with an even-minded approach. Modern Research: Recent studies in psychology and neuroscience provide empirical support for the benefits of equanimity. Research in mindfulness and meditation practices, which are rooted in Vedic traditions, shows that they can significantly enhance mental health by reducing stress, anxiety, and depression. Techniques such as mindfulness-based stress reduction (MBSR) and transcendental meditation (TM) have been scientifically proven to promote emotional regulation, increase resilience, and improve overall well-being. For instance, studies have shown that regular meditation can lead to structural changes in the brain, enhancing areas associated with emotional regulation and executive function. This supports the ancient wisdom of the Vedas, which advocated for meditation as a means to achieve a balanced and equanimous state of mind. The introduction sets the stage for a comprehensive exploration of Sama (equanimity) in Sanatana Dharma. By defining equanimity and its importance, introducing the broader context of Sanatana Dharma, highlighting its relevance in both spiritual and practical life, and providing a brief overview of supporting Vedic wisdom and modern research, this section lays the foundation for a deeper understanding of why Sama is a vital and timeless virtue. The subsequent sections of the article will build on this foundation, offering detailed insights and practical guidance on cultivating equanimity in various aspects of life. Philosophical Foundations: Detailed Analysis of Sama Introduction to Vedic Literature The Vedas are the most ancient and revered scriptures of Sanatana Dharma, comprising a vast body of knowledge that encompasses philosophy, rituals, hymns, and spiritual insights. Divided into four main collections—Rigveda, Yajurveda, Samaveda, and Atharvaveda—the Vedas form the bedrock of Vedic wisdom. Each Veda has a distinct focus but collectively they address all aspects of life and the universe. The concept of Sama, or equanimity, is integral to Vedic teachings, emphasizing balance, harmony, and a serene state of mind. Sama in the Rigveda: The Rigveda, the oldest of the four Vedas, consists of hymns (suktas) dedicated to various deities, seeking their blessings and guidance. Within these hymns, the principle of Sama is subtly interwoven, often highlighted through the themes of balance, harmony, and moderation. Key Verses Emphasizing Sama in the Rigveda: Rigveda 10.190.1:"ṛtaṃ ca satyaṃ cābhīddhāt tapasodhyajāyata." Translation: "From intense meditation was born the cosmic order and truth." Explanation: This verse underscores the importance of maintaining cosmic order (ṛta) and truth (satya) through disciplined mental focus and equanimity. The creation of order from meditation signifies that balance and harmony are foundational to existence. Rigveda 2.28.5:"Yunjante mana uta yunjate dhiyo vipra viprasya brihato vipashchitaḥ." Translation: "The wise sages harness their mind and intellect to the great, all-pervading cosmic order." Explanation: This hymn emphasizes the practice of harnessing the mind and intellect to align with the cosmic order, advocating for a state of mental equilibrium essential for wisdom and spiritual growth. Rigveda 1.164.39:"Ekam sat vipra bahudha vadanti." Translation: "Truth is one; the wise call it by many names." Explanation: This verse highlights the underlying unity in diversity, suggesting that equanimity arises from understanding and accepting the multiplicity of perspectives and experiences as expressions of a singular truth. Sama in the Yajurveda: The Yajurveda is primarily concerned with the procedures and rituals of worship, detailing the mantras and actions required for various rites. However, it also addresses the mental state and attitude one must cultivate during these rituals, emphasizing the importance of equanimity. Key Verses Emphasizing Sama in the Yajurveda: Yajurveda 36.18:"Tanme manaḥ śivasaṅkalpamastu." Translation: "May my mind be filled with auspicious and benevolent thoughts." Explanation: This mantra highlights the need for a serene and positive mindset, essential for performing rituals with a pure heart. Equanimity is implied as a prerequisite for cultivating benevolent thoughts and intentions. Yajurveda 34.1:"Om sahasraśīrṣā puruṣaḥ sahasrākṣaḥ sahasrapāt." Translation: "The Cosmic Being has a thousand heads, eyes, and feet." Explanation: This verse presents a vision of the cosmic being, embodying the interconnectedness and balance of the universe. It implies that maintaining equanimity helps one recognize and align with this universal harmony. Yajurveda 40.1:"Isha vasyam idam sarvam yat kinca jagatyam jagat." Translation: "Everything in this universe is enveloped by the Lord." Explanation: Recognizing the divine presence in all aspects of the universe encourages a balanced perspective, fostering equanimity. This verse advocates for a sense of detachment and acceptance, essential for maintaining inner peace. Sama in the Samaveda: The Samaveda is unique among the Vedas, as it primarily focuses on the musical and melodic aspects of the Vedic hymns. It is intended to elevate the soul and mind through the power of sound and rhythm, which inherently promotes a state of equanimity. Key Verses Emphasizing Sama in the Samaveda: Samaveda 1.1.1:"Agna ā yāhi vītaye gṛṇāno havyadātaye." Translation: "O Agni, come to our sacrifice, as we sing your praises." Explanation: The invocation of Agni through song symbolizes the harmonization of external and internal energies. The act of singing praises with devotion fosters a balanced state of mind, where equanimity is naturally cultivated. Samaveda 2.4.1:"Pavamānaḥ suvarjanaḥ." Translation: "The self-purifying one, the bright and effulgent." Explanation: This verse refers to the purifying nature of the soma, which represents the internal cleansing of the mind and emotions. Equanimity is achieved through this purification process, aligning oneself with the essence of purity and balance. Samaveda 1.2.5:"Indra, leader of heroes, born of thy mother, be swift to move." Explanation: This verse, while invoking Indra, highlights the qualities of leadership and swift action. It suggests that true leadership and decisive action come from a place of inner balance and equanimity. Sama in the Atharvaveda: The Atharvaveda includes hymns and incantations that address practical aspects of daily life, such as health, prosperity, and protection. It also delves into philosophical and spiritual insights, emphasizing the importance of mental and emotional balance. Key Verses Emphasizing Sama in the Atharvaveda: Atharvaveda 19.9.8:"Shanno astu dvipade sham catushpade." Translation: "May peace be unto the bipeds and quadrupeds." Explanation: This verse extends the concept of peace and balance to all living beings, advocating for a harmonious coexistence. Equanimity here is portrayed as a universal principle that fosters peace among all creatures. Atharvaveda 12.1.1:"Bhumir bhūmna dyaur dyaus." Translation: "The Earth is great, the Heaven is great." Explanation: This verse celebrates the grandeur of the Earth and Heaven, symbolizing the balance between the material and the spiritual. Equanimity is depicted as a state of harmony between these realms. Atharvaveda 7.6.1:"May the waters bring me well-being." Explanation: Water, as a symbol of purity and flow, represents the cleansing and balancing of emotions and thoughts. This verse emphasizes the role of natural elements in fostering a state of equanimity. Continuity and Consistency of Equanimity in Vedic Texts: The Vedas consistently emphasize the importance of balance and harmony as foundational principles of life. The concept of equanimity, while not always explicitly named, is a recurring theme across the Vedic texts. It is portrayed as an essential virtue for personal well-being, ethical conduct, and spiritual advancement. Key Themes Highlighted Across the Vedas: Cosmic Order (ṛta): The Vedas frequently reference the concept of ṛta, the cosmic order that governs the universe. Equanimity is seen as aligning oneself with this order, maintaining balance and harmony in thought, word, and deed. Detachment (vairagya): The Vedic teachings advocate for detachment from material desires and outcomes, which is crucial for achieving equanimity. This detachment is not about renunciation but about developing an even-minded approach to life. Purity (śuddhi): Purity of mind and heart is a prerequisite for equanimity. The Vedas emphasize practices that cleanse the mind and emotions, fostering a balanced and serene state. Unity in Diversity: The recognition of unity in diversity, as highlighted in the Rigveda, promotes a sense of acceptance and understanding, which is essential for maintaining equanimity. The analysis of Sama in the Vedas reveals a deep and consistent emphasis on equanimity as a fundamental principle of Vedic wisdom. Across the Rigveda, Yajurveda, Samaveda, and Atharvaveda, the importance of maintaining a balanced and harmonious state of mind is underscored through various hymns and verses. This continuity reflects the integral role of equanimity in achieving personal well-being, ethical conduct, and spiritual growth.