The DiVincenzo Criteria

WOMANIUM Global Quantum Media Project Initiative — Winner of Global Quantum Media Project

Introduction

The DiVincenzo criteria, first proposed by David P. DiVincenzo in his paper "The Physical Implementation of Quantum Computation" in 2000, play a pivotal role in the field of quantum information processing. These criteria serve as essential principles, offering a comprehensive framework for efficiently harnessing quantum systems’ computational capabilities through their physical realization. By adhering to these criteria, researchers and engineers are empowered to address the challenges involved, propelling the progress of quantum computing hardware and facilitating the actualization of quantum systems’ superior computational power compared to classical systems. In this article, we will delve into the intricate nuances of the DiVincenzo criteria, shedding light on their paramount significance in the practical implementation of quantum systems.

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The first five conditions are:

1. A scalable physical system with well characterized qubits

The development of practical and powerful quantum computers hinges on a critical criterion: a “scalable” physical system comprising well “characterized” qubits. This criterion encompasses two crucial aspects: scalability and characterization.

Scalability is essential because quantum computers aim to solve complex problems that require a large number of qubits. A scalable physical system can accommodate the addition of more qubits without compromising the system’s functionality and reliability. This ability to scale allows quantum computers to handle increasingly complex computations and take advantage of the exponential growth in computational power that arises from adding qubits.

Characterization focuses on understanding and accurately measuring the physical properties and parameters of individual qubits. A well-characterized qubit has its internal Hamiltonian, energy eigenstates, and interactions with other qubits and external fields precisely known. This knowledge enables precise control and manipulation of qubits during quantum computations. Additionally, a well-characterized qubit has well-separated energy levels, minimizing the likelihood of unintended state transitions during computation.

The criteria ensure that quantum computers can perform reliable and accurate quantum operations. By having a scalable physical system, quantum computers can increase their computational power exponentially with the addition of qubits. Simultaneously, well-characterized qubits allow for precise control, manipulation, and measurement of qubit states. This understanding of qubit properties is essential for developing error correction techniques and minimizing errors in quantum computations.

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2. The ability to initialize the state of the qubits to a simple fiducial state, such as |000⟩

Quantum computers require that registers be initialized to a known value before the start of computation. This is necessary for both straightforward computing and quantum error correction, which requires a continuous supply of qubits in a low-entropy state (like the 0 state).

The need for a continuous supply of 0s is a real challenge for many proposed implementations of quantum computers. If the time it takes to initialize a qubit is relatively long compared to the time it takes to perform a gate operation, then the quantum computer will need to be equipped with some kind of “qubit conveyor belt” to move qubits away from the active computation region for initialization.

There are two main approaches to setting qubits to a standard state: “natural” cooling and measurement-based cooling.

1. Natural cooling occurs when the ground state of the system’s Hamiltonian is the state of interest. It is often advocated for electron spin resonance-based techniques, but it can be too slow for the needs of error correction.
2. Measurement-based cooling involves projecting the system into the desired state or another state that can be rotated into it. It can be much faster, but it requires that the measurement scheme be fully implemented.

Figure 2 illustrates a Markovian collision model employed for cooling a two-spin longitudinal Ising model governed by Hamiltonian Equation. The model uses four spin-star quantum refrigerators (labeled as i=1…4) with central qubits acting as refrigerants at an effective inverse temperature βeff. Notably, the central qubits are not resonant with the Ising model qubits but with the transition frequencies ωi (i=1…4) instead. The spin-star model features longitudinal and homogeneous couplings (gi). Image Credits: https://www.nature.com/articles/s41598-021-92258-0/figures/4

In Nuclear Magnetic Resonance (NMR) quantum computers, cooling of the initial state has been foregone altogether. This is acknowledged to be a limitation, and it is not clear whether NMR can ever be a scalable scheme for quantum computing without some of the proposed cooling schemes being implemented.

3. Long “relevant” decoherence times, much longer than the gate operation time

Decoherence times are crucial for understanding the behavior of qubits and quantum systems in relation to their environment. In simplified terms, decoherence time refers to the characteristic time it takes for a qubit state to transform into a mixed state. However, a more accurate description of decoherence involves the decay of the qubit state, potential dependence on the initial state, changes in state amplitudes, and the influence of other quantum states. It is important to consider the correlation of decoherence between neighboring qubits, as this has implications for error correction strategies.

Decoherence is the process where quantum superpositions decay due to interaction with the environment. In the case of an electron spin qubit with eigenstates |↑ and |↓, decoherence refers to transitions from the superposition state to either |↑ or |↓. The main focus is on the schematic decay of |σ+(t)| for a quantum dot electron with significant Zeeman splitting, assuming the nuclear spin bath is prepared in a narrowed state. Image Credits: https://www.researchgate.net/publication/224849182_Prospects_for_Spin-Based_Quantum_Computing_in_Quantum_Dots

For quantum computing, long decoherence times are crucial to maintain the quantum features necessary for computation. Decoherence, if it acts for a significant duration, can undermine the advantages of quantum computers over classical machines. The decoherence time needs to be sufficiently long to allow the quantum properties of the qubit to manifest. Quantum error correction provides insights into the required timescales, helping to determine how long is "long enough" for maintaining the desired quantum behavior. By focusing on the relevant decoherence time for a specific qubit and optimizing its performance, the potential of quantum computation can be realized.

Quantum error correction has revealed that successful fault-tolerant quantum computation requires decoherence times that are around 10^-4 to 10^-5 times the duration of an individual quantum gate operation. [1] Once the required decoherence threshold is attainable, the scalability of quantum computation is ensured. It is important to note that a quantum particle may have multiple decoherence times associated with different degrees of freedom, but not all of these times are relevant to its functioning as a qubit. The choice of qubit basis states determines which decoherence times are pertinent. By understanding and focusing on the relevant decoherence time, quantum computation can be optimized for performance and reliability.

4. A “universal” set of quantum gates

Quantum algorithms are typically defined as sequences of unitary transformations acting on qubits. To physically implement these transformations, a corresponding set of Hamiltonians is required. However, the available types of Hamiltonians that can be turned on and off are often limited, posing a challenge for certain quantum computations. One common approach is to express multi-qubit unitary transformations in terms of one- and two-qubit interactions, such as the “quantum XOR” or “cNOT” gate. While some implementations allow for direct multi-qubit gates, additional work is needed to design and implement suitable refocusing sequences. The choice of interaction profile and the classicality of the control apparatus are also important considerations for successful gate operations.

Figure shows the hand which can be seen as a quantum computer, and the picture can be seen as a quantum state. The act of drawing the picture can be seen as the process of applying quantum gates to the quantum state. Hence, the phrase “hand drawing itself” can be seen as a metaphor for the process of applying universal gates to a quantum state! Image Credits: https://www.researchgate.net/publication/227998692_Life-Span_Development

Implementing quantum gates introduces errors, both systematic and random. These errors contribute to decoherence and can impact the reliability of computations. Error correction techniques aim to mitigate these errors and enable reliable computations. Tolerable levels of unreliability due to random errors are on the order of 10^-4 to 10^-5 per gate operation [1]. Systematic errors, on the other hand, require careful calibration and depend on the specific quantum computation. The use of error correction codes, such as stabilizer codes, allows gate operations to be performed on coded qubits without requiring a new repertoire of elementary gates. In some cases, coding can even simplify the gate repertoire required for quantum computation, such as with decoherence-free subspaces and subsystems.

5. A qubit-specific measurement capability

The fifth criterion of the DiVincenzo criteria for quantum computing is the requirement for a qubit-specific measurement capability. In the context of this criterion, “specific” refers to the ability to perform measurements on individual qubits without affecting the state of the rest of the quantum computer or nearby qubits. This means that the measurement process should be independent of system parameters, including the presence of neighboring qubits.

In quantum computing, it is essential to extract information from qubits through measurements. Ideally, these measurements should be non-demolition, meaning that they leave the measured qubit in its initial state after reporting the measurement outcome. This capability allows researchers and engineers to gather data about the quantum state of individual qubits without disturbing the overall computation. It enables precise control and manipulation of individual qubits, facilitating the implementation of quantum algorithms and error correction techniques.

Figure demonstrates the qubit measurement process (a) Probability distributions wj(q) depict the detector output q for qubit states |j, where j = 0, 1. (b) A schematic representation of the measurement setup utilizing a QPC detector to measure the mesoscopic ‘charge’ qubit. In this setup, the qubit states |j vary depending on the position of an elementary charge, which influences the transmission properties of the QPC. Consequently, the applied voltage V drives the current I in the contact. Image Credits: https://www.researchgate.net/publication/45874292_Tunneling_without_tunneling_Wavefunction_reduction_in_a_mesoscopic_qubit

Developing specific measurement capabilities involves overcoming technical challenges and optimizing measurement processes. Quantum efficiency, which measures the fidelity of a quantum measurement, plays a role in determining the reliability of the obtained outcomes. While perfect quantum efficiency is not necessary, achieving high efficiency is desirable for reliable quantum computation. Quantum efficiency reflects the tradeoff between the fidelity of measurements and the allocation of resources. By understanding and exploring these tradeoffs, researchers can design rational plans for future experiments and advance the field of quantum computing.

Additional Conditions

The advantages of quantum information processing go beyond straightforward computation, encompassing tasks that involve both computation and communication. To meet the requirements of these tasks, two additional criteria are necessary. These are the following:

1. The ability to interconvert stationary and flying qubits: This allows for allowing the conversion of quantum information between qubits at rest (stationary qubits) and those being transmitted (flying qubits). Different tasks may require either stationary or flying qubits, such as quantum cryptography, which only requires direct transmission of flying qubits.
2. The ability faithfully to transmit flying qubits between specified locations: This involves the intact transmission of qubits from one place to another. Photon states, encoded in the polarization or spatial wavefunction of photons, are commonly used as flying qubits, utilizing technologies like optical fibers.

Conclusion

In conclusion, the DiVincenzo criteria serve as fundamental guidelines in quantum information processing, providing a comprehensive framework for efficient computation through physical realization. As we navigate the future of quantum technology, fulfilling these criteria remains a significant challenge. The study of quantum effects in complex artificial systems is in its early stages, and unforeseen tradeoffs and experimental discoveries may shape new paths of investigation. By remaining open to advancements, the DiVincenzo criteria will guide us toward harnessing the remarkable computational power of quantum systems for groundbreaking applications.

References

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[1] DiVincenzo, D. P. (2000). The Physical Implementation of Quantum Computation. Fortschritte Der Physik, 48(9–11), 771–783. https://doi.org/10.1002/1521-3978(200009)48:9/11<771::aid-prop771>3.0.co;2-e

[2] O. Arısoy and Ö. E. Müstecaplıoğlu, ‘Few-qubit quantum refrigerator for cooling a multi-qubit system’, Scientific Reports, vol. 11, no. 1, p. 12981, Jun. 2021.

[3] C. Kloeffel and D. Loss, “Prospects for Spin-Based Quantum Computing in Quantum Dots,” Annual Review of Condensed Matter Physics, vol. 4, no. 1, pp. 51–81, Apr. 2013, doi: 10.1146/annurev-conmatphys-030212–184248.

[4] J. A. Nesteroff and D. V. Averin, “Tunneling without tunneling: wavefunction reduction in a mesoscopic qubit,” Physica Scripta, vol. T137, p. 014002, Dec. 2009, doi: 10.1088/0031–8949/2009/t137/014002.