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Quantum register

A quantum register is a collection of qubits in quantum computing that together hold a quantum state, serving as the fundamental structure for encoding and processing quantum information. Unlike a classical register composed of bits that store definite 0 or 1 values, a quantum register leverages the principles of quantum mechanics to exist in a superposition of multiple states simultaneously, allowing it to represent up to 2^n possible configurations for n qubits.^[1] This capability enables quantum registers to perform computations that exploit parallelism and interference, far surpassing classical limits for certain problems. Quantum registers can also exhibit entanglement, where the state of one qubit is intrinsically linked to others, facilitating correlated operations essential for algorithms like Shor's factoring or Grover's search.^[2]^[3] In practice, quantum registers are implemented in physical systems such as superconducting circuits, trapped ions, or neutral atoms, where they form the basis of quantum circuits manipulated by unitary gates to execute quantum operations.^[4]^[5] The concept of quantum registers underpins the scalability of quantum computers, with ongoing research focusing on increasing register size while mitigating decoherence and errors through techniques like quantum error correction.^[6] Applications span cryptography, optimization, and molecular simulation, where the exponential information storage of quantum registers promises transformative computational power.^[7]

Fundamentals

Definition and Basic Concepts

A quantum register is a collection of two or more qubits that functions as the quantum analog of a classical processor register, enabling parallel storage and manipulation of quantum states.^[8] A quantum register holds quantum information through superposed states, where it can represent multiple configurations simultaneously, or entangled states, in which the qubits exhibit correlations that have no classical counterpart.^[8] These properties allow the register to serve as the central component in quantum circuits, where unitary operations manipulate the overall state to perform computations.^[8] Qubits form the individual units of this register. For instance, a simple 2-qubit register can store computational basis states denoted as |00\rangle, |01\rangle, |10\rangle, or |11\rangle, or linear superpositions of these states.^[8]

Building Blocks: Qubits

A qubit serves as the fundamental building block of a quantum register, functioning as the quantum analog of a classical bit. It is a two-level quantum mechanical system capable of encoding quantum information. The term "qubit" was introduced by Benjamin Schumacher in his 1995 paper on quantum coding, where it refers to a unit of quantum information analogous to a classical bit.^[9] Mathematically, a qubit is described as a normalized vector in a two-dimensional complex Hilbert space \mathcal{H}_2, with the standard computational basis consisting of the orthonormal states |0\rangle and |1\rangle. This representation originates from early formulations of quantum computation, where such basis states model the simplest quantum systems suitable for information processing. The general state of an isolated qubit is a linear superposition

|\psi\rangle = \alpha |0\rangle + \beta |1\rangle,

where \alpha, \beta \in \mathbb{C} are complex coefficients satisfying the normalization condition |\alpha|^2 + |\beta|^2 = 1. This superposition principle, rooted in the linearity of quantum mechanics, allows a qubit to exist in multiple states simultaneously, providing the potential for parallel computation when scaled to multiple qubits.^[10] Key properties of a qubit include its coherence time, which quantifies the duration over which the quantum superposition remains intact before environmental interactions cause decoherence, typically measured as the decay rate of off-diagonal elements in the density matrix. Coherence times are critical for practical quantum operations, with values ranging from microseconds to seconds depending on the implementation, though the focus here is on the conceptual role in maintaining quantum information. Another essential property is the collapse upon measurement: when a qubit in state |\psi\rangle is measured in the computational basis, it probabilistically projects onto |0\rangle with probability |\alpha|^2 or |1\rangle with probability |\beta|^2, destroying the superposition and yielding a classical outcome. This measurement-induced collapse follows from the projective measurement postulate in quantum mechanics. For visualization, the pure states of a single qubit can be represented on the Bloch sphere, a unit sphere in three-dimensional real space where the north and south poles correspond to |0\rangle and |1\rangle, respectively, and equatorial points represent maximal superpositions; this geometric tool, originally developed for spin-1/2 systems, aids in understanding state evolution under unitary operations. In the context of quantum registers, multiple qubits combine to form larger systems: an assembly of n qubits occupies a $2^n-dimensional Hilbert space, enabling the encoding of exponentially many states through superposition, which underpins the computational power of quantum registers without requiring entanglement for this dimensional scaling.^[10]

Classical vs. Quantum Registers

Functional Similarities

Quantum registers function analogously to classical registers by serving as temporary storage units for data during computational processes. In classical computing, a register holds a sequence of bits that represent numerical values or instructions processed by the central processing unit (CPU). Similarly, a quantum register consists of an array of qubits, which act as the quantum counterparts to classical bits, enabling the storage of quantum states that can be manipulated within quantum algorithms. This parallel allows quantum registers to hold input data for operations in a manner akin to how classical registers manage binary data in arithmetic logic units (ALUs).^[11] Operationally, quantum registers exhibit parallels to classical ones in initialization and readout procedures. Classical registers are typically reset to a default state, such as all zeros, to prepare for new computations. Quantum registers are initialized to a standard state, often |0⟩ for all qubits, using preparation techniques that ensure a known starting point for subsequent operations. Likewise, readout in classical systems involves directly accessing bit values without altering the register's state, while in quantum systems, measurement of the register yields classical bit outcomes, effectively retrieving the processed information into a classical format for further use or output. These steps bridge the workflow between classical and quantum paradigms, facilitating hybrid computations where quantum results are integrated into classical processing.^[11]^[12] In terms of processing, quantum registers parallel classical registers by acting as inputs and outputs for algorithmic steps, much like how classical registers feed data into logic operations within a CPU. For instance, in arithmetic tasks, a classical 3-bit register can perform addition by propagating carries through bit-wise operations in a ripple-carry adder. Analogously, a 3-qubit quantum register can execute addition using a quantum ripple-carry circuit, where qubits represent the binary inputs and the operation produces the summed output encoded in the quantum state, mirroring the classical adder's function but adapted to quantum gates. This similarity underscores the quantum register's role in emulating familiar computational primitives while extending to quantum-specific algorithms.^[11]

Fundamental Differences

Unlike classical registers, which store a single definite state out of 2^n possible configurations for n bits, a quantum register of n qubits can exist in a superposition of all 2^n basis states simultaneously, enabling parallel exploration of multiple computational paths.^[13] This capability, formalized in the quantum Turing machine model, underpins the potential for exponential speedup in certain algorithms by processing superposed inputs coherently.^[14] Entanglement introduces non-local correlations among qubits in a register, where the state of one qubit cannot be described independently of the others, even at arbitrary distances, allowing computations that exploit these correlations for tasks infeasible with classical separable states. Originating from the Einstein-Podolsky-Rosen paradox, such multi-partite entanglement in quantum registers facilitates resource states for advanced protocols, contrasting with classical registers' lack of inherent non-local dependencies.^[15] The no-cloning theorem prohibits the perfect replication of an arbitrary unknown quantum state in a register, a direct consequence of quantum linearity, unlike classical bits that can be copied indefinitely without loss of fidelity.^[16] This limitation profoundly affects quantum error correction and information processing, requiring alternative strategies like encoding into larger entangled subspaces rather than simple duplication.^[13] Quantum operations on registers are inherently unitary transformations, ensuring all computations are reversible and preserve the information content of the system, in stark contrast to classical irreversible gates that can erase information and generate entropy.^[17] This reversibility, modeled via quantum mechanical Hamiltonians for Turing machines, eliminates thermodynamic dissipation in principle and enables the recovery of intermediate states, a feature absent in standard classical register manipulations.^[13]

Physical Implementations

Superconducting and Solid-State Systems

Superconducting qubits form the basis of many solid-state quantum registers, leveraging the nonlinear inductance provided by Josephson junctions to encode quantum information in superconducting circuits. These junctions, typically composed of two superconductors separated by a thin insulating barrier, enable the creation of qubit types such as transmons and flux qubits. Transmon qubits, which use a capacitor shunted by a Josephson junction, suppress charge noise for improved coherence, while flux qubits rely on a superconducting loop interrupted by junctions to store information in circulating currents. These systems require operation at millikelvin temperatures, achieved through dilution refrigerators, to maintain superconductivity and minimize thermal noise.^[18]^[19]^[20] Quantum registers in superconducting implementations are typically arranged in two-dimensional grid layouts on lithographically fabricated chips, allowing for scalable connectivity via nearest-neighbor coupling. For instance, IBM's Eagle processor features a 127-qubit register in such a 2D configuration, enabling complex multi-qubit operations within a compact planar architecture, while more recent systems like IBM's Nighthawk processor (as of 2025) incorporate 120 qubits with 218 connections for enhanced circuit complexity.^[21]^[22]^[23] This chip-based design facilitates integration with classical control electronics, where microwave pulses are used to manipulate qubit states through resonant cavities.^[21]^[23] Key advantages of these systems include fast gate operation times, typically ranging from 10 to 100 nanoseconds, which support high-speed quantum computations. Single-qubit gate fidelities often exceed 99.9%, and two-qubit gates achieve over 99%, reflecting precise control via microwave pulses. The compatibility with semiconductor fabrication techniques further aids scalability and integration with readout resonators.^[24]^[4] Despite these strengths, challenges persist, including coherence times ranging from tens to over 1000 microseconds in recent devices, limited by material defects and environmental coupling, which constrain the depth of quantum circuits. Crosstalk between adjacent qubits, arising from unintended electromagnetic interactions in the dense 2D layout, can degrade gate performance and introduce errors.^[25]^[26]^[27] A prominent example is Google's Sycamore processor, which utilized a 53-qubit superconducting register in 2019 to demonstrate quantum supremacy by completing a random circuit sampling task in 200 seconds—a computation estimated to take classical supercomputers thousands of years. This achievement highlighted the potential of superconducting registers for tasks beyond classical simulation, using a 2D array of transmon qubits coupled via tunable couplers.^[28]

Atomic and Ionic Traps

Atomic and ionic traps provide a platform for realizing quantum registers by confining individual atoms or ions in electromagnetic fields, enabling precise manipulation of their quantum states for qubit encoding. In trapped ion systems, charged atoms such as ytterbium (Yb⁺) or calcium (Ca⁺) ions are confined in Paul traps, which use oscillating radiofrequency electric fields to create stable potential wells. Qubits are typically encoded in the hyperfine energy levels of the ions' ground electronic state, offering long-lived coherence due to their insensitivity to environmental magnetic field fluctuations. These qubits are manipulated using laser pulses for state preparation, single-qubit rotations, and two-qubit entangling operations via phonon-mediated coupling in the ion chain.^[29]^[30] Neutral atom quantum registers, in contrast, employ uncharged atoms like rubidium or cesium trapped in optical lattices formed by interfering laser beams, which create periodic potential wells for array arrangement. Qubits are encoded in ground-state hyperfine levels, with strong interactions induced by exciting atoms to Rydberg states—highly excited orbitals that enable dipole-dipole coupling for entanglement over micrometer distances. A notable achievement is the demonstration of a 3,000-atom register in continuous operation, using optical tweezers and lattices to reload atoms and maintain density, showcasing scalability for large-scale quantum simulation (as of September 2025).^[31] These platforms offer key advantages, including coherence times on the order of seconds for hyperfine qubits, far exceeding those of many solid-state alternatives and supporting extended quantum operations. All-to-all qubit connectivity is achievable through global laser addressing in ion traps or reconfigurable optical potentials in neutral atom arrays, with ion shuttling in segmented traps enabling dynamic reconfiguration for arbitrary interactions. However, challenges persist, such as two-qubit gate speeds ranging from microseconds to milliseconds—typically 30–600 μs—limited by laser addressing precision and motional state control, which slows computation compared to faster electronic-based systems. Scaling to larger registers relies on microfabricated surface-electrode traps for ions or advanced optical systems for atoms, addressing fabrication uniformity and crosstalk issues.^[30]^[33]^[34] A practical example is IonQ's 32-qubit quantum register, which utilizes barium (Ba⁺) ions in a linear Paul trap for commercial quantum computing applications, leveraging barium's favorable optical transitions for higher gate fidelities exceeding 99.99% in two-qubit operations (as of October 2025). Another recent system is Quantinuum's Helios, featuring 98 barium ion qubits in an ion trap, announced in November 2025, which advances scalability and error correction in trapped ion hardware. This system demonstrates the transition from research prototypes to deployable hardware, with barium ions enabling improved error rates and integration potential.^[35]^[36]^[37]

Operations and Manipulation

Quantum Gates on Registers

Quantum gates are unitary operations applied to quantum registers to manipulate qubit states during computation. In a multi-qubit register, single-qubit gates act independently on individual qubits via the tensor product structure of the Hilbert space, while multi-qubit gates couple qubits to enable interactions essential for quantum algorithms. These operations preserve the norm of the state vector, ensuring reversibility, and form the basis of quantum circuits.^[38] Single-qubit gates operate on one qubit within the register, transforming its state while leaving others unchanged. The Hadamard gate (H) creates superposition from basis states, for example, applying H to the |0⟩ state yields H|0\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}}, enabling parallel exploration of multiple computational paths.^[39] The Pauli-X gate performs a bit flip, mapping |0⟩ to |1⟩ and |1⟩ to |0⟩, analogous to a classical NOT operation but acting on superpositions coherently.^[39] These gates, represented by 2×2 unitary matrices, extend to n-qubit registers by tensoring with identity matrices on other qubits, such as H \otimes I^{\otimes (n-1)} for the first qubit.^[38] Multi-qubit gates, such as the controlled-NOT (CNOT), act on pairs of qubits in the register to introduce correlations. The CNOT gate flips the target qubit if the control qubit is |1⟩, with the transformation |x, y⟩ → |x, x ⊕ y⟩, where ⊕ denotes modulo-2 addition; this operation can generate entanglement when applied to superposed states.^[38] For larger registers, CNOTs connect qubits selectively, forming controlled operations that underpin entanglement in quantum protocols.^[38] Any unitary operation on an n-qubit register can be decomposed into elementary single- and two-qubit gates, establishing universality for quantum computation. Seminal results show that the set comprising all single-qubit gates (U(2)) and the CNOT suffices to approximate any n-qubit unitary U(2^n) with polynomial overhead in n, where circuit depth—the number of sequential gate layers—impacts coherence times and scalability.^[38] Decompositions often use techniques like the cosine-sine decomposition to break down multi-qubit unitaries into controlled rotations and local gates, minimizing the number of two-qubit interactions required.^[38] To extract classical information from a quantum register, projective measurement is performed, collapsing the superposition to a basis state with probabilities given by the Born rule. For an n-qubit register in state ρ, measuring in the computational basis projects onto eigenstates |k⟩ (k = 0 to 2^n - 1) with projectors P_k = |k⟩⟨k|, yielding outcome k with probability tr(P_k ρ) and updating the state to P_k ρ P_k / tr(P_k ρ).^[40] This irreversible process interfaces quantum computation with classical outputs, essential for reading results from registers.^[40]

Entanglement and Multi-Qubit States

In a quantum register comprising multiple qubits, the overall state resides in a Hilbert space of dimension $2^n for n qubits, allowing the register to be described by a superposition \sum_{i=0}^{2^n-1} c_i |i\rangle, where |i\rangle denotes the computational basis states represented as binary strings, and the coefficients satisfy \sum |c_i|^2 = 1 to ensure normalization.^[41] If the qubits evolve independently, the register state factors as a tensor product |\psi\rangle = \bigotimes_{k=1}^n |\psi_k\rangle, reflecting no correlations between subsystems.^[41] However, quantum registers generally occupy entangled states that defy such factorization, enabling collective behaviors essential to quantum information processing. Entanglement arises when the joint state of the register cannot be expressed as a product of individual qubit states, a phenomenon first highlighted in the Einstein-Podolsky-Rosen (EPR) paradox as a challenge to the completeness of quantum mechanics.^[42] For two qubits, a canonical example is the Bell state \frac{1}{\sqrt{2}} (|00\rangle + |11\rangle), which exhibits perfect correlations between measurements on the qubits despite their spatial separation.^[43] These states violate Bell inequalities, confirming non-local correlations beyond classical limits, as derived in Bell's seminal analysis.^[44] In larger registers, multi-qubit entanglement extends this, such as in Greenberger-Horne-Zeilinger (GHZ) states of the form \frac{1}{\sqrt{2}} (|0\rangle^{\otimes n} + |1\rangle^{\otimes n}), which capture genuine n-party correlations not reducible to pairwise links. Entanglement in quantum registers is typically generated by applying controlled operations to initially separable superpositions; for instance, a controlled-NOT (CNOT) gate acting on the state |+\rangle |0\rangle—where |+\rangle = \frac{1}{\sqrt{2}} (|0\rangle + |1\rangle)—produces the Bell state \frac{1}{\sqrt{2}} (|00\rangle + |11\rangle).^[43] To quantify entanglement, measures like concurrence are used for bipartite systems, defined for a pure two-qubit state |\psi\rangle as C(|\psi\rangle) = |\langle \psi | \sigma_y \otimes \sigma_y | \psi^* \rangle|, where \sigma_y is the Pauli-Y matrix and |\psi^*\rangle is the complex conjugate; this yields values from 0 (separable) to 1 (maximally entangled). For multipartite cases, the von Neumann entropy of a reduced density matrix \rho_A for subsystem A provides a general quantifier: S(\rho_A) = -\operatorname{Tr}(\rho_A \log_2 \rho_A), with maximum entropy indicating strong entanglement across the partition.^[43] Such entangled states, including EPR pairs akin to Bell states and GHZ configurations, underpin multi-qubit correlations in registers, facilitating phenomena like quantum teleportation through shared EPR pairs and distributed entanglement for n-party protocols.^[42] These properties distinguish quantum registers from classical ones, harnessing superposition and inseparability for enhanced information capacity.

Applications

Role in Quantum Algorithms

Quantum registers form the foundational computational units in quantum algorithms, enabling the manipulation of multi-qubit states to achieve speedups over classical counterparts. By serving as the primary data structures for encoding inputs, performing operations, and extracting outputs, these registers leverage quantum superposition and interference to process information in ways unattainable classically.^[45] In Shor's algorithm for integer factorization, quantum registers play a central role in period-finding, where an n-qubit register encodes the input modular exponentiation function, and the quantum Fourier transform (QFT) applied to this register extracts the period with high probability, yielding an exponential speedup over the best known classical algorithms. This process relies on the register's ability to maintain superposition across exponentially many states during the computation.^[46] Grover's search algorithm utilizes quantum registers to perform amplitude amplification on an unsorted database of size N, employing an oracle implemented on the register to mark target states and diffusion operators to amplify their amplitudes, achieving a quadratic speedup (O(√N queries) compared to classical exhaustive search. The register here acts as the search space, with iterative operations rotating the state vector toward the solution.^[47] For quantum simulation of physical systems, quantum registers encode molecular Hamiltonians, allowing algorithms like the variational quantum eigensolver (VQE) to approximate ground-state energies by optimizing parameterized circuits on the register. In practice, VQE has been applied to small molecules using 10-20 qubit registers, with recent demonstrations on up to 25-qubit registers on quantum hardware as of 2025, demonstrating feasibility for near-term devices in modeling quantum chemistry problems.^[48]^[49]^[50] Within the quantum circuit model, registers provide the input space for universal gate sets, where algorithms are expressed as sequences of single- and multi-qubit gates applied to initialize, evolve, and measure the register, enabling universal quantum computation. Entanglement generated across the register during these operations underpins the parallelism inherent to quantum algorithms.^[45]

Quantum Memory and Storage

Quantum registers serve as quantum memories by storing superpositions of quantum states, enabling the preservation of quantum information for later retrieval or use in networked protocols. Unlike classical memory, which stores bits sequentially, a quantum register of n qubits spans a Hilbert space of dimension 2^n, theoretically allowing the encoding of exponentially many states in superposition for efficient storage. However, practical capacity is constrained by environmental noise and decoherence, which degrade the fidelity of stored states over time, limiting usable storage to durations on the order of milliseconds in current superconducting systems as of 2023; recent advances, such as a 2025 Caltech method using sound waves in mechanical oscillators, have extended lifetimes by up to 30 times.^[51]^[52] In quantum random access memory (qRAM), registers facilitate exponential storage by addressing data in superposition, where classical or quantum information is encoded in the amplitudes of register states. For instance, amplitude-encoded data allows a single n-qubit register to represent 2^n data points compactly, accessed via quantum queries without collapsing the superposition. This approach, proposed in seminal works, enables logarithmic-time access to large datasets, pivotal for quantum-enhanced data processing.^[53]^[54] Preserving coherence in quantum registers relies on techniques such as dynamical decoupling, which applies sequences of rapid π-pulses to refocus dephasing effects and extend storage times. These pulses average out low-frequency noise, maintaining qubit coherence for applications requiring stable memory, with demonstrations achieving coherence extensions by factors of 10 to 100 in solid-state systems.^[55]^[56] Quantum registers also function as memory nodes in quantum repeaters, storing entangled states to enable entanglement distribution over long distances in quantum networks. By purifying and swapping stored entanglement between register pairs, repeaters overcome photon loss in optical fibers, facilitating secure quantum communication across hundreds of kilometers. Experimental protocols have demonstrated entanglement storage and retrieval in register-based memories with fidelities exceeding 80%.^[57]^[58]

Challenges and Future Directions

Decoherence and Error Correction

Decoherence in quantum registers arises from unavoidable interactions between the qubits and their environment, leading to the rapid loss of quantum coherence and fidelity. The dominant mechanisms include T1 relaxation, or amplitude damping, where a qubit in the excited state (|1⟩) spontaneously decays to the ground state (|0⟩) by dissipating energy, characterized by the relaxation time T1. Complementing this is T2 dephasing, or phase damping, which preserves the qubit's energy populations but randomizes the relative phase in superpositions, often resulting from fluctuating magnetic fields or charge noise; T2 is typically shorter than T1 and related by the formula \frac{1}{T_2} = \frac{1}{2T_1} + \frac{1}{T_\phi}, where T_\phi is the pure dephasing time. These processes degrade the register's ability to maintain coherent multi-qubit states, limiting gate fidelities to milliseconds or less in current systems. Such decoherence manifests as probabilistic errors on individual qubits, modeled by quantum channels that propagate to affect the entire register. The bit-flip channel, corresponding to T1 relaxation, applies a Pauli X operator with probability p, flipping |0⟩ to |1⟩ or vice versa, while the phase-flip channel, linked to T2 dephasing, applies a Pauli Z operator, altering the phase of |1⟩ relative to |0⟩. In entangled registers, these local errors can correlate through joint operations, amplifying decoherence and making the system vulnerable to information leakage.^[59] Quantum error correction (QEC) mitigates these errors by encoding a logical qubit across a redundant array of physical qubits, enabling error detection and correction via non-demolition measurements of stabilizers without disturbing the encoded state. The surface code, a stabilizer-based topological code, arranges physical qubits on a 2D lattice to form logical registers, where data qubits store information and ancillary qubits measure parity syndromes to identify bit- or phase-flip errors as localized defects; this locality allows efficient correction using minimum-weight matching algorithms. The threshold theorem establishes that fault-tolerant computation is achievable if the physical error rate remains below a code-specific threshold (approximately 1% for surface codes), as increasing the lattice distance d suppresses logical error rates exponentially, p_L \approx (p/p_{th})^{d}.^[60]^[61]^[62] Implementing fault-tolerant logical registers incurs significant resource overhead, with surface code schemes requiring roughly 1000 physical qubits per logical qubit to achieve logical error rates below 10^{-10} for practical algorithms, due to the need for ancillary qubits and repeated syndrome extractions. This redundancy, while enabling scalability in principle, underscores the engineering challenges in building large-scale quantum registers.^[63]

Scalability and Recent Advances

The development of quantum registers has progressed significantly since the demonstration of the first 2-qubit register using trapped beryllium ions in 1995, where a controlled-NOT quantum logic gate was implemented with fidelity around 90% using internal hyperfine and motional states in a single ion.^[64] This foundational milestone laid the groundwork for multi-qubit systems, evolving to more complex registers over decades. By 2024, neutral atom platforms achieved scalability milestones exceeding 1000 qubits, with systems like Atom Computing's 1225-qubit array demonstrating stable operation for quantum simulations.^[65] A key recent advance in 2024 involved the continuous operation of a 1200-atom quantum register using neutral strontium atoms in an optical lattice, maintained for over one hour through periodic replenishment to counter atom loss, enabling prolonged quantum simulations.^[31] Hybrid approaches combining superconducting and photonic elements have also emerged, such as superconducting qubits interfaced with photonic metamaterials for distributed quantum processing, improving connectivity and scalability beyond monolithic designs. These developments highlight cross-platform integration as a pathway to practical registers. Looking ahead, modular architectures are projected to enable million-qubit scales by interconnecting smaller processor modules via photonic links, as outlined in industry roadmaps targeting fault-tolerant systems by 2030.^[66] Simulations have confirmed that fault-tolerant thresholds—error rates below approximately 1% per gate—can be reached with current hardware fidelities when combined with quantum error correction, supporting scalable logical qubit operations.^[67] Accompanying metrics include two-qubit gate fidelities exceeding 99.9% in trapped-ion and superconducting systems, essential for reducing error accumulation in large registers.^[68] Additionally, coherence times in diamond nitrogen-vacancy (NV) centers have been extended to microseconds (up to approximately 80 μs) through core-shell nanostructures and dynamical decoupling, mitigating decoherence in solid-state registers.^[69]

References

[1]
Hybrid Quantum Computing Concepts - Azure - Microsoft Learn
Sep 16, 2024 · A quantum register is a system comprised of multiple qubits. Quantum computers excel at performing complex calculations by manipulating ...
[2]
Vibrating atoms make robust qubits, physicists find | MIT News
Jan 26, 2022 · In so doing, they achieved a new “quantum register,” or system of qubits, that appears to be robust over relatively long periods of time.
[3]
[1010.3242] 5-qubit quantum error correction in a charge ... - arXiv
Oct 15, 2010 · We implement the DiVincenzo-Shor 5 qubit quantum error correcting code into a solid-state quantum register. The quantum register is a multi ...
[4]
Quantum Computing - Stanford Encyclopedia of Philosophy
Dec 3, 2006 · ... computation, however, the quantum register must be measured. Measurement is represented as a non-unitary gate that “collapses” the quantum ...
[5]
Simulating physics with computers | International Journal of ...
Cite this article. Feynman, R.P. Simulating physics with computers. Int J Theor Phys 21, 467–488 (1982). https://doi.org/10.1007/BF02650179. Download citation.
[6]
Quantum theory, the Church–Turing principle and the universal ...
It is shown that quantum theory and the 'universal quantum computer' are compatible with the principle.
[7]
Quantum coding | Phys. Rev. A - Physical Review Link Manager
Quantum coding. Benjamin Schumacher. Department of Physics, Kenyon College, Gambier, Ohio ... A 51, 2738 – Published 1 April, 1995. DOI: https://doi.org/ ...
[8]
[PDF] Quantum Computation and Quantum Information
1 Introduction and overview. 1. 1.1 Global perspectives. 1. 1.1.1 History of quantum computation and quantum information. 2. 1.1.2 Future directions.
[9]
[PDF] Introduction to Quantum Computing
An n-bit classical register holds an n-bit integer in binary, e.g. 11001. An n-bit quantum register holds a nonzero C-linear ... That is where the similarity ...
[10]
[PDF] quantum-computation-and-quantum-information-nielsen-chuang.pdf
This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography, and quantum error- ...
[11]
[PDF] The church–turing principle and the universal quantum computer
Oct 28, 2003 · 'universal quantum computer' are compatible with the principle. ... I have described elsewhere (Deutsch 1985; cf. also Albert 1983) how ...
[12]
[PDF] Quantum entanglement - arXiv
Jun 13, 2015 · One can thus conclude with EPR that Quantum Mechanics is not complete.” It was Bell [B64, B] who real- ized that even without specifying the ...
[13]
A single quantum cannot be cloned - Nature
Oct 28, 1982 · We show here that the linearity of quantum mechanics forbids such replication and that this conclusion holds for all quantum systems.
[14]
A Microscopic Quantum Mechanical Hamiltonian Model of ...
In this paper a microscopic quantum mechanical model of computers as represented by Turing machines is constructed. It is shown that for each.
[15]
New material platform for superconducting transmon qubits ... - Nature
Mar 19, 2021 · We fabricate two-dimensional transmon qubits that have both lifetimes and coherence times with dynamical decoupling exceeding 0.3 milliseconds.
[16]
Superconducting flux qubit with ferromagnetic Josephson π-junction ...
Oct 11, 2024 · We report the realization of a zero-flux-biased flux qubit based on three NbN/AlN/NbN Josephson junctions and a NbN/PdNi/NbN ferromagnetic π-junction.
[17]
Superconducting Qubits and the Physics of Josephson Junctions
In summary, Josephson qubits are nonlinear resonators whose critical element is the nonlinear inductance of the Josephson junction. The three types of ...
[18]
IBM Unveils Breakthrough 127-Qubit Quantum Processor
Nov 16, 2021 · 'Eagle' is IBM's first quantum processor developed and deployed to contain more than 100 operational and connected qubits.Missing: superconducting register
[19]
Superconducting quantum computers: who is leading the future?
Aug 19, 2025 · ... superconducting qubits [110, 351]. Their two-dimensional layout aligns well with the physical architecture of superconducting qubit arrays ...
[20]
A quantum engineer's guide to superconducting qubits
Jun 17, 2019 · Since the fidelity of gates is bounded from above by the coherence times of the qubits, short gate times are desirable.232 This presents a ...<|separator|>
[21]
Experimental comparison of two quantum computing architectures
Quantum gate operation fidelities, qubit numbers, primitive gate speeds, and coherence times are obviously important low-level metrics in a large-scale ...
[22]
Materials challenges and opportunities for quantum computing ...
Apr 16, 2021 · ... coherence times T1 and T2 can also affect the gate fidelity. The coherence times can drift or change suddenly over hours and days, even ...
[23]
Practical Guide for Building Superconducting Quantum Devices
Nov 18, 2021 · Consequently, this lowers the actual gate fidelity as compared to the naive estimate based only on the gate time over coherence time ...
[24]
Quantum supremacy using a programmable superconducting ...
Oct 23, 2019 · Our largest random quantum circuits have 53 qubits, 1,113 single-qubit ... A blueprint for demonstrating quantum supremacy with superconducting ...
[25]
High-fidelity quantum logic gates using trapped-ion hyperfine qubits
Dec 14, 2015 · We demonstrate laser-driven two-qubit and single-qubit logic gates with fidelities 99.9(1)% and 99.9934(3)% respectively, significantly above ...
[26]
Trapped-ion quantum computing: Progress and challenges
May 29, 2019 · We review the state of the field, covering the basics of how trapped ions are used for QC and their strengths and limitations as qubits.
[27]
Quantum register reaches 1200 neutral atoms in continuous operation
Oct 9, 2024 · The researchers succeeded in setting up a register of 1200 atoms in an optical lattice of laser light and keeping it in continuous operation for one hour.
[28]
Quantum register reaches 1,200 neutral atoms in continuous operation
Oct 9, 2024 · The atoms are trapped individually using optical tweezers, tightly focused laser beams, or optical lattices, extremely precise periodic arrays ...
[29]
Quantum Computing 101: Introduction, Evaluation, and Applications
Jan 8, 2025 · In a trapped-ion system, like IonQ's, coherence time is usually measured in seconds to minutes; in solid state systems, it's microseconds to ...
[30]
[PDF] Engineering of microfabricated ion traps and integration of ...
Trapped atomic ions are a highly versatile tool for a wide variety of fields from fundamental physics to quantum technologies. Ion traps use electric and ...
[31]
In Industry First, IonQ to Use Barium Ions for Computation
Dec 10, 2021 · IonQ has started the work to advance the technology of trapped ion quantum computing beyond the ytterbium ions that we and other researchers have used for ...
[32]
IonQ Achieves 99.9% Gate Fidelity on Barium Platform, a Step on ...
Sep 12, 2024 · IonQ achieves 99.9% two-qubit gate fidelity on barium platform, progress towards IonQ Tempo to provide commercial quantum advantages.
[33]
[PDF] Elementary gates for quantum computation - arXiv
Elementary gates for quantum computation include one-bit quantum gates (U(2)) and a two-bit exclusive-or gate, which can express all unitary operations.
[34]
[PDF] A Short Introduction to Quantum Computing for Physicists - arXiv
Aug 22, 2024 · So far we have seen the Pauli matrices, rotations and the Hadamard gate. Let us introduce a couple of other useful single-qubit gates. We know ...
[35]
None
Summary of each segment:
[36]
Multiple-qubit Operations - Azure Quantum - Microsoft Learn
Feb 13, 2025 · This article reviews the rules used to build multi-qubit states out of single-qubit states and discusses the gate operations needed to include in a gate set.
[37]
Can Quantum-Mechanical Description of Physical Reality Be ...
Feb 18, 2025 · Einstein and his coauthors claimed to show that quantum mechanics led to logical contradictions. The objections exposed the theory's strangest ...
[38]
Quantum Computation and Quantum Information
This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error- ...Missing: definition | Show results with:definition
[39]
On the Einstein Podolsky Rosen paradox | Physics Physique Fizika
On the Einstein Podolsky Rosen paradox. JS Bell. Department of Physics, University of Wisconsin, Madison, Wisconsin.Missing: URL | Show results with:URL
[40]
https://arxiv.org/pdf/2404.05679
[41]
Algorithms for quantum computation: discrete logarithms and factoring
This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is ...
[42]
A fast quantum mechanical algorithm for database search - arXiv
Nov 19, 1996 · Authors:Lov K. Grover (Bell Labs, Murray Hill NJ). View a PDF of the paper titled A fast quantum mechanical algorithm for database search, by ...
[43]
A variational eigenvalue solver on a photonic quantum processor
Jul 23, 2014 · The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution.
[44]
Chemical applications of variational quantum eigenvalue-based ...
Jul 1, 2025 · This review aims to further bridge the knowledge gap between quantum chemistry and quantum computation by surveying the uses of VQE-based ...B. Quantum Computing... · 3. Qubit Encodings For The... · A. Ground State Calculations
[45]
[PDF] Reliability of Noisy Quantum Computing Devices - arXiv
Jul 13, 2023 · Consider an idealized quantum computer composed of an n-qubit register that encodes a 2n-dimensional Hilbert space ... in the Hilbert space ...
[46]
[PDF] Quantum Random Access Memory For Dummies - arXiv
May 2, 2023 · QRAM uses quantum computing principles to store and modify quantum or classical data efficiently, greatly accelerating a wide range of computer ...
[47]
Circuit-Based Quantum Random Access Memory for Classical Data
Mar 8, 2019 · We present a circuit-based flip-flop quantum random access memory to construct a quantum database of classical information in a systematic and flexible way.
[48]
Noise-resilient quantum evolution steered by dynamical decoupling
Aug 5, 2013 · Here we demonstrate non-trivial quantum evolution steered by dynamical decoupling control, which simultaneously suppresses noise effects.
[49]
Universal Dynamical Decoupling of a Single Solid-State Spin from a ...
Because pulse errors can severely degrade the coherence, universal decoupling requires robustness to pulse errors for all possible quantum states. In contrast, ...
[50]
A quantum router architecture for high-fidelity entanglement flows in ...
Jun 29, 2022 · Key to these applications is the sharing of entanglement between many users over large distances, allowing quantum key distribution, distributed ...
[51]
[PDF] arXiv:2309.04151v3 [quant-ph] 24 Apr 2025
Apr 24, 2025 · We present a quantum repeater protocol for distributing entanglement over long distances, where a dedicated communication stage enables ...
[52]
[PDF] Chapter 7 Quantum Error Correction
If there is one bit flip and one phase flip (either on the same qubit or different qubits) then recovery will be successful. 7.8 Some Constraints on Code ...
[53]
[quant-ph/0110143] Topological quantum memory - arXiv
Oct 24, 2001 · We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array.
[54]
Surface codes: Towards practical large-scale quantum computation
Aug 4, 2012 · This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer.
[55]
An Introduction to Quantum Error Correction and Fault-Tolerant ...
Apr 16, 2009 · The threshold theorem states that it is possible to create a quantum computer to perform an arbitrary quantum computation provided the error ...
[56]
IBM Tackles New Approach to Quantum Error Correction
Jun 10, 2025 · One of the most popular approaches is known as a surface code, which requires roughly 1,000 physical qubits to make up one logical qubit.
[57]
[PDF] Demonstration of a Fundamental Quantum Logic Gate
Dec 18, 1995 · The demonstration is of a two-bit 'controlled-NOT' quantum logic gate, a fundamental gate using two qubits stored in a trapped atom.
[58]
Atom Computing Announces Record-Breaking 1,225-Qubit ... - Forbes
Oct 24, 2023 · Today, Atom Computing fulfilled that objective with its announcement of the 2024 release of a second-generation neutral atom quantum computer ...<|control11|><|separator|>
[59]
The Future of Quantum Computing Is Modular - IEEE Spectrum
Feb 27, 2025 · The focus is now shifting to linking multiple quantum processors together to build computers large enough to tackle real-world problems.
[60]
Quantum error correction below the surface code threshold - Nature
Dec 9, 2024 · Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, ...
[61]
IonQ Achieves Landmark Result, Setting New World Record in ...
Oct 21, 2025 · IonQ Achieves Landmark Result, Setting New World Record in Quantum Computing Performance. October 21, 2025. World record 99.99% two-qubit gate ...
[62]
Engineering spin coherence in core-shell diamond nanocrystals
In this work, we utilize engineered core-shell structures to achieve a drastic increase in qubit coherence times (T2) from 1.1 to 35 μs in bare nanodiamonds to ...