Quantum error correction system and quantum error correction process

Abstract

Provided is a quantum error correction system capable of realizing a scheme in which, when a quantum system receives some noise, the quantum system itself can act to correct itself against this noise. This quantum error correction system includes a quantum material and a dichroic recovery drive generator that communicates with the quantum material. The dichroic recovery drive generator transmits a waveform to the quantum material.

Description

Technical Field

[0001] The present invention relates to a quantum error correction system and a quantum error correction process.

Background Art

[0002] Quantum information is very fragile and can be destroyed by virtually any noise that affects a quantum computer or quantum device. One of the important discoveries that showed the world that quantum computers could be built is the invention of quantum error correction technology described in Non-Patent Document 1. In response to this epoch-making discovery, a competition to develop quantum computers has begun, and currently, countries, multinational companies, and startups are challenging the development of quantum computers. The goal is to create a fault-tolerant quantum computer using millions of qubits, where a fault-tolerant quantum computer is one in which the underlying quantum computer and the entire machine with incorrect error correction can operate to perform useful quantum computations even if there are errors in the error correction itself. Many studies have been conducted, such as quantum error correction, design of new codes, and design of methods for removing noise from qubits using complex control pulse sequences or continuous driving. If cleaner qubits (physical systems with less noise) can be designed, the task of performing quantum error correction (QEC) and fault-tolerant QEC (FT QEC) becomes increasingly easier. Designing and building cleaner qubits is a very technology-related problem, such as designing purer materials and designing nearly identical qubits, but there are ways to drive dirty individual qubits to improve them into cleaner individual qubits.

[0003] Decoherence is one of the major obstacles that must be overcome in the development of any quantum technology. Researchers have developed various techniques over the past 30 years to protect quantum information from noise. Recently, Non-Patent Document 2 showed a scheme for overcoming static and inhomogeneous broadening in a spin ensemble.

Prior Art Documents

Non-Patent Literature

[0004]

Non-Patent Literature 1

Non-Patent Literature 2

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, the protocols used to perform the cleaning of individual qubits involve the application of a long sequence of pulses (dynamic decoupling, abbreviated as DD) or continuous driving by electromagnetic radiation (continuous dynamic decoupling, abbreviated as CDD). DD is a complex technique and CDD generates qubits that are often not very convenient for experiments. When attempting to apply to a collection of qubits where there is a slight variation in each qubit, both techniques fail. This is because a pulse / control that works correctly for one qubit does not work correctly for another qubit with a slight variation in parameters.

[0006] Such small variations in the design of individual qubits also pose a problem in quantum computers. Even if a quantum computer is made with clean qubits, if each qubit is slightly different, this can also impair the operation of the quantum computer. Therefore, all current quantum computer designs include a vast amount of hardware related to the adjustment of each and every qubit to make the qubits substantially identical.

[0007] It would be beneficial to provide a quantum error correction system and process capable of realizing a scheme in which, when a quantum system is subject to some noise, the quantum system itself can act to correct itself against this noise.

[0008] A quantum error correction system according to some embodiments comprises: a quantum material; and a dichroic recovery drive generator communicating with the quantum material, the dichroic recovery drive generator transmitting a waveform to the quantum material.

[0009] A quantum error correction process according to some embodiments includes sending a dichroic electromagnetic drive to a quantum system including a non-interacting multi-level spin population.

[0010] According to the present disclosure, a quantum error correction system and process can be provided that can realize a scheme in which, when a quantum system is subject to some noise, the quantum system itself acts to correct itself against this noise.

[0011] This scheme can achieve more and can effectively remove many forms of noise, both static and temporal. This scheme can take in a single or collective dirty spin system and, by applying two appropriate off-resonant drives, can generate a clean spin system in which unwanted static and dynamic fluctuations are significantly suppressed. As an example, the present disclosure mainly shows how this automatic correction scheme can be applied to the nuclear spins coupled to nitrogen-vacancy spins in diamond, and through extensive numerical simulations, shows how the inhomogeneous phase relaxation in a nuclear spin population coupled to a nitrogen-vacancy (NV) center, and the self-phase relaxation of a single nuclear spin coupled to a single NV center, can be continuously reduced in realistic experiments by using the light shift. The simplicity of this scheme will be useful for the preparation and stabilization of highly coherent and homogeneous spin populations or individual spins used in many quantum technologies such as quantum computing, quantum memory, quantum repeaters, and quantum sensors.

Brief Description of the Drawings

[0012]

Figure 1

Figure 2

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Embodiments for Carrying Out the Invention

[0013] First In order to build large-scale quantum information processing devices that go beyond the era of noisy intermediate scale quantum (NISQ) devices, there are still great challenges to overcome [1]. One of the main challenges is the construction of physical qubits with error rates far below the threshold required for fault-tolerant quantum error correction [2]. Another challenge is to fabricate identical qubits in quantum technology so that it is not necessary to add a large number of control circuits to adjust each qubit [3]. In quantum devices using spins in solids that cover applications in quantum memories [4-7], quantum repeaters [8], quantum sensors [9], and quantum computers

[10] , the fabrication and / or design of control schemes that achieve an array of identical spins with extremely low decoherence rates remains a very difficult problem.

[0014] This disclosure considers that realistic spins / qubits are actually multi-level quantum systems each having more than two quantum levels, and each level experiences noise. This disclosure shows that by placing a simple off-resonant continuous wave (CW) drive in this multi-level structure, a dynamics can be designed that automatically corrects any phase relaxation noise of the collective or individual spins. This corrects the phase relaxation arising from the spatial distribution of spins with inhomogeneous energy splittings, and also corrects the time-varying noise of the individual or collective energy splittings of the spins. Furthermore, this disclosure shows that this automatic correction is fault-tolerant and corrects the amplitude noise present in the correction drive field itself. Thus, this automatic self-correction scheme takes in a dirty spin population and creates a nearly identical and long-lived coherent qubit population that can be used for any purpose of a quantum machine.

[0015] Cleaning Dirty Quantum Bits To clean up or reduce the effects of phase relaxation due to spatial inhomogeneities within a population or due to temporal fluctuations in qubit energy, researchers have developed a wide range of techniques. To correct for temporal phase relaxation, quantum error correction (QEC) can be utilized, but this requires important additional capabilities such as encoding logical qubits into multiple physical qubits and the ability to perform fast readout or reset of qubits. However, QEC can operate even if the noise is Markovian. In many realistic cases, the phase relaxation noise is colored or non-Markovian, and researchers have developed three main methods to improve the effects of colored phase relaxation noise from qubits. These are classified as (A) discrete dynamical decoupling (DDD) pulse control triggered by Hahn echo sequences

[11] , (B) continuous dynamical decoupling (CDD) control using CW drive, and (C) decoherence-free subspaces

[12] . Before explaining the self-correcting protocol, first, comment on these existing cleaning protocols.

[0016] First, the DDD method requires complex pulse sequences and typically involves the application of π pulses. If there are large inhomogeneities in the resonance frequencies of the qubits, the application of a complete π pulse is impossible, and without advanced pulse shaping techniques, DDD control becomes weak

[13] . However, despite its complexity, researchers have demonstrated that DDD can protect single spins and spin populations from the environment [4, 14 - 16].

[0017] The continuous limit of the DDD sequence, i.e., the case where the number of pulses becomes infinite and the time delay between pulses becomes zero, was first considered in important works [17, 18]. To the best of our knowledge, the idea of CDD or the use of CW driving to minimize the effects of decoherence was introduced in reference

[19] . However, this research dealt with protecting unitary operations or gates from the environment. The authors of reference

[20] introduced and demonstrated a CDD scheme to protect diamond qubits (NV centers) from both environmental and control-drive fluctuations. Protection from the environment was achieved by a strong drive resonant with the qubit's energy splitting. On the other hand, protection from drive-intensity fluctuations was achieved by a sequence of orthogonal drives with decreasing intensity. This scheme is called CCDD (concatenated continuous dynamical decoupling), was adopted for sensing

[21] , and was extended to handle the population of NV centers

[22] . The drawback of this method is that the energy splitting of the protected qubit is several orders of magnitude smaller than that of the original qubit, which makes the gate slower and, as a result, the operation may be limited by the qubit's relaxation time. Alternatively, it is possible to design a qubit protected up to first order in the ratio of the inhomogeneity strength to the drive Rabi frequency from environmental noise by resonating a three-level system (NV center ground state) with two CW drives to form a pair of transitions [23, 24]. Also, a so-called hybrid dynamical decoupling (MDD) scheme incorporating discrete and continuous dynamical decoupling has been introduced

[25] .

[0018] A quantum error correction system according to one embodiment utilizes a completely different approach from the above methods by using a shift in the energy levels of a multi-level system by a light shift or an off-resonant drive so that the system automatically compensates for unwanted energy fluctuations. These methods were originally devised to deal with Doppler broadening in atomic gases but can be generalized to other inhomogeneous systems [26 - 29].

[0019] In the present disclosure, a method is shown for extending a Doppler broadening-based scheme originally devised to address spatial inhomogeneities so that it can also address temporal noise. This scheme can incorporate either a population (or individual spins) and generate a homogeneous population (or individual spins) with significantly improved coherence. The present disclosure shows how to implement this scheme on spins associated with color centers in diamond, as shown below, to protect the coherence of a population as well as that of a single spin.

[0020] Configuration FIG. 1 is a block diagram showing the configuration of a quantum error correction system 1 according to an embodiment. As shown in FIG. 1, the quantum error correction system 1 can include a quantum material 10 and a dichroic recovery drive generator 20 communicable with the quantum material 10. In the present disclosure, the term "quantum error correction" is used in a broad sense that includes not only quantum error correction in the strict sense of the term, but also quantum error suppression and quantum error mitigation.

[0021] Any quantum system interacts with the environment. This interaction leads to dissipation and decoherence. Quantum error correction, quantum error suppression, and quantum error mitigation are strategies for counteracting the effects of the environment. Quantum error correction and quantum error suppression are quantum control schemes. Quantum error correction identifies and corrects errors. In essence, it can be regarded as a form of quantum feedback control implemented in a redundant physical system. Redundancy is fundamental for performing checks that reveal the presence of errors. Quantum error suppression includes a series of techniques for reducing the likelihood of errors at the hardware level (for which redundancy is not required). DD belongs to this category. DD can be regarded as an open-loop control technique that effectively decouples the system from the environment by a series of pulses. Finally, quantum error mitigation is a post-processing technique that uses the output from a population of quantum circuits to minimize the influence of the environment on the average value of the measured quantity.

[0022] The quantum material 10 may include spins associated with the color centers of diamond. In the present disclosure, "spins associated with the color centers of diamond" include nuclear spins coupled to NV spins in diamond or NV spins in diamond. The quantum material 10 may include a single or a collective of non-interacting multi-level spins that are qubits. The spins may be spins associated with the color centers of diamond. The quantum material 10 may include at least one of a single or a collective of non-interacting multi-level quantum systems, quantum memories, quantum repeaters, quantum sensors, single or collective defects in diamond, and quantum computers. The quantum material 10 may be subject to the influence of temporally fluctuating noise.

[0023] Each of the spins may have at least three states |1>, |2>, and |3> associated with respective energy levels E1, E2, and E3, where E1 < E2 and E2 < E3, and the spin undergoes an energy shift due to noise such that when one state |2> of the spin undergoes an energy shift of -δ, the state |3> of the same spin undergoes an energy shift of -sδ, where s is a real number and s > 0. s is greater than 4, preferably greater than 6, and more preferably greater than 10. The energy levels may be anharmonic. The noise may be either static spatially inhomogeneous noise or spatially homogeneous or inhomogeneous temporal noise, preferably spatially homogeneous or inhomogeneous temporal noise. The spin may be subject to the influence of temporal noise.

[0024] The dichroic recovery driving generator 20 may include a laser light source and an optical system that guides the light irradiated from the laser light source to the quantum material 10. The dichroic recovery driving generator 20 can transmit the waveform of light to the quantum material 10. The waveform may be either an optical frequency or a microwave frequency. The waveform may include two tones of a continuous electromagnetic field of the same or substantially the same amplitude Ω having frequencies of ω+Δ and ω-Δ, where ω corresponds to the energy separation between states |2> and |3>, Δ is the frequency detuning, and Δ>0. The two tones of the continuous electromagnetic field may be in phase or substantially in phase. The tones may have frequencies detuned in opposite directions from the auxiliary transition. The waveform may be an off-resonant continuous wave drive in a multi-level structure.

[0025] (Ω / Δ) 2 may be equal to or approximately equal to 1 / s in the limit of s>1, typically s>4, more typically s>10, and even more typically s>>1. In the quantum error correction system 1, 0.5Δ / sqrt(s)<Ω<1.5Δ / sqrt(s), more preferably 0.9Δ / sqrt(s)<Ω<1.1Δ / sqrt(s), more preferably 0.99Δ / sqrt(s)<Ω<1.01Δ / sqrt(s), and even more preferably 0.999Δ / sqrt(s)<Ω<1.001Δ / sqrt(s).

[0026] The quantum error correction system 1 functions as an automatic quantum error correction system including the dichroic recovery driving generator 20 that converts a dirty quantum bit population and creates a substantially identical and long-lived coherent quantum bit population. In the automatic quantum error correction system, the dichroic recovery driving generator 20 can shift the energy levels of the multi-level system by off-resonant driving to automatically compensate for the unwanted energy fluctuations of the qubit system.

[0027] The waveform from the dichroic recovery drive generator 20 may be an electromagnetic field that applies a light shift to automatically correct for fluctuating unknown energy shifts that act on the dirty qubits. The dirty qubit(s) may be at least one of a plurality of dirty qubits, and the waveform can remove phase relaxation noise from each of the at least one dirty qubit(s) of the plurality of dirty qubits. The waveform can correct for static noise, temporal noise, or phase noise. The waveform can remove inhomogeneous phase relaxation of a non-interacting multi-level spin ensemble. The waveform can convert a dirty qubit into a clean qubit. The waveform can homogenize a group of at least one of a plurality of dirty qubits and at least one of a plurality of clean qubits. The resulting clean qubits can be protected from spatial and temporal energy fluctuations.

[0028] FIG. 2 is a flowchart for explaining an operation example of the quantum error correction system 1 of FIG. 1. A process according to an embodiment performed using the quantum error correction system 1 shown in FIG. 1 will be described with reference to FIG. 2.

[0029] In step S101, the quantum error correction system 1 executes sending a dichroic electromagnetic drive to the quantum system of the quantum material 10 including a non-interacting multi-level spin ensemble by the dichroic recovery drive generator 20.

[0030] In addition to step S101, the process may further include evaluating the power spectrum (including frequency and intensity) of noise, typically temporal noise. The process may further include adjusting the dichroic electromagnetic drive based on the power spectrum of the noise. The process may further include determining Ω and / or Δ based on the power spectrum of the noise. In this case, the quantum error correction system 1 may further include an evaluation system that evaluates the temporal noise of the quantum material 10. The waveform of the dichroic recovery drive generator 20 can be adjusted based on the evaluation of the temporal noise in order to correct errors related to the temporal noise of the quantum material 10.

[0031] Light shift As briefly described above, in order to achieve auto self-correction, the quantum error correction system 1 requires that the atomic system cancel out the fluctuations in its own energy level structure. This cancellation is achieved by a quantum atom optics process known as the light shift. In the present disclosure, the light shift refers to the shift of the energy levels of a two-level system (TLS) due to continuous driving by an off-resonant classical field. These energy shifts are also called ac-Stark shifts. In the present disclosure, we adhere to the former nomenclature. Below, the present disclosure will perform these simple derivations.

[0032] TIFF2025524074000002.tif7170

[0033]

Number

[0034] Where ω2 corresponds to the energy splitting of the TLS, and in the present disclosure, it is assumed that the energy of the ground state |1> is the same as zero. Next, in the present disclosure, a transverse drive is considered.

[0035]

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[0036] Amplitude Ω, frequency ω d , and phase φ. Henceforth, this disclosure is limited to a phase of φ = 0. Therefore, the total Hamiltonian of the driven TLS is as follows.

[0037]

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[0038] In a frame rotating at the driving frequency and the rotating wave approximation (RWA), the latter Hamiltonian is simplified as follows.

[0039]

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[0040] Δ = ω2 - ω d is the detuning between the qubit and the drive. RWA is valid as long as ω2 >> Ω. The eigenenergies of the Hamiltonian (4) are as follows.

[0041]

Number

[0042] In the limit of large detuning (|Δ| >> Ω), the drive hardly dresses the energy levels. In that case, the eigenenergies correspond to the bare energies E1 and E2 (corresponding to Ω = 0) with small corrections added. Up to second order in the ratio Ω / |Δ|, the eigenenergies are given by the following equation.

[0043]

Number

[0044]

Number

[0045] Here, in the present disclosure, it is considered that E2 > E1. These actual values depend on the sign of the detuning. When Δ > 0, E1 = 0 is the ground state energy and E2 = Δ, and when Δ < 0, the ground state energy is E1 = Δ and E2 = 0. This is a small correction ±Ω 2 / (4|Δ|). In the present disclosure, it is shown below how to cancel additional shifts in the energy level structure of a multi-level system using these light shifts.

[0046] In the present disclosure, first, a heterogeneous spin population without temporal noise is considered, and it is shown how self-correction can clean up heterogeneous phase relaxation. Next, the present disclosure considers a single spin with temporal noise and shows that self-correction can also clean up non-Markovian temporal noise.

[0047] Continuous off-resonance protection from heterogeneous phase relaxation using light shifts Heterogeneous phase relaxation, that is, the relative loss of quantum coherence of an emitter population due to heterogeneous characteristics, is ubiquitous in solid-state applications. Common causes of heterogeneous phase relaxation are the Doppler effect in gases, spatial variations in the local environment of emitters in crystals, and lack of reproducibility in artificial atoms

[30] .

[0048] The idea of correcting heterogeneous Doppler phase relaxation using light shifts was first introduced in reference

[26] . This idea was later extended in reference

[27] to handle systems close to the ground state. More recently, very relevant research has been carried out on a more rigorous mathematical treatment that includes the effects of higher-order corrections and considers the driving field near resonance

[29] .

[0049] The above method is not limited to spin ensembles. As shown in the latter half of this section of the present disclosure, it can also be applied to situations where a single spin interacts with a slowly fluctuating bath. The goal is to treat spins as multi-level systems and generate TLSs or qubits protected from ensemble or single inhomogeneities. In the present disclosure, first, the methods of references [27, 29] are reviewed.

[0050] A. Spin Ensemble Correction In the present disclosure, it is limited to the case of non-interacting spins. Theoretically, inhomogeneous dephasing can be modeled as a spin ensemble with a static statistical distribution of the resonance frequencies of individual spins within the ensemble. This statistical distribution of frequencies limits the collective operation of the spins, and since individual spins precess at different frequencies in the initial coherent superposition, it ultimately leads to the decay of coherent oscillations in Ramsey-type experiments. Therefore, different types of inhomogeneous systems can be described by the same formalism.

[0051] Let's start by considering each spin as a TLS. Ignoring the interactions, each is described by the Hamiltonian

Equation

Equation

[0052] The authors of reference

[27] showed that it is actually possible to obtain an ensemble with a non-zero inhomogeneity-dependent light shift by introducing auxiliary levels that are susceptible to the same inhomogeneous source. In the remaining discussion, this disclosure focuses on the scheme of reference

[29] .

[0053] FIG. 3 is a first diagram for explaining an operation example of the quantum error correction system 1 of FIG. 1. FIG. 3 shows a continuous protection scheme using a light shift. (a) shows a three-level system {|1>, |2>, |3>}. The lower two levels {|1>, |2>} constitute a qubit for protecting against inhomogeneous phase relaxation δ. Therefore, the quantum error correction system 1 uses a third sensor quantum level |3> that is s-fold more sensitive to inhomogeneity / noise by continuously applying two off-resonant driving electromagnetic fields as shown in (b).

[0054] Now, consider the three-level system {|1>, |2>, |3>} in FIG. 3(a). Levels |1> and |2> constitute a TLS for protecting from the environment, and level |3> is an auxiliary level with frequency ω3. In this disclosure, here, consider two driving fields with the same amplitude Ω and opposite detunings ±Δ (when Δ > 0) from the transition between level |2> and level |3>. In the double-rotating frame of frequencies ω2 and ω3, the total Hamiltonian of the system is given by the following equation:

Equation

Equation

Equation

[0055] In other words, the effective Hamiltonian of the TLS is [Equation] becomes. In the large off-resonance region Ω / Δ<<1, due to the auxiliary level that is very sensitive to inhomogeneity, i.e., s>>1, [Equation] so that [Equation] the inhomogeneous shift can be compensated by setting. In the present disclosure, it is emphasized that this is an approximate result because there are higher-order corrections to the light shift.

[0056] Single spin correction In the previous section, the present disclosure showed how the light shift can be used to correct the inhomogeneous phase relaxation in a spin ensemble. As an alternative, the quantum error correction system 1 can use them to correct the phase relaxation of single spins due to the distribution of phases obtained in measurements repeated over time. The origin of this distribution is a slowly fluctuating environment such as weakly interacting nuclear spins.

[0057] Similar to the previous subsection, a doubly driven single spin is described by a Hamiltonian of the following form [Equation] where H 駆動 (t) is given by Equation (9). The difference from the previous case is that the inhomogeneous Hamiltonian is time-dependent:

Number

[0058] To explain the effectiveness of the light shift method for a fluctuating environment, in the present disclosure, two typical examples of noise in a solid-state system: random telegraph noise (RTN) and Ornstein-Uhlenbeck (OU) noise are considered.

[0059] A. Random telegraph noise (RTN) First, in the present disclosure, a TLS with time-dependent noise of energy splitting modeled by random telegraph noise (RTN) is considered. This model explains the low-frequency fluctuations in microwave qubits and resonators [31, 32], and is also implemented through the modulation of a flux qubit to study the motional narrowing phenomenon in superconducting circuits

[33] . The starting point of the present disclosure is the Hamiltonian in the laboratory frame

Number

Number

[0060] B. Ornstein-Uhlenbeck (OU) noise As a second example, the present disclosure examines the case of Ornstein-Uhlenbeck (OU) noise

[34] . This corresponds to a Gaussian stochastic process that accurately models the effect of the spin bath on a central spin such as the NV center in diamond. In this case, the fluctuations in the NV center frequency are the result of fluctuations in the effective magnetic field it experiences, which is in turn also the result of the reorientation of spins in the spin bath due to magnetic dipole-dipole interactions.

[0061] The effect of the slowly fluctuating spin bath on the coherence of the central spin has been studied in two types of experiments inspired by NMR: free induction decay (FID) or simply the free evolution of the central spin and the Hahn echo (HE) refocusing pulse sequence. In the first case, the central spin is initialized in its ground state |1>, and then, by a π / 2 pulse (instantaneous), a coherent superposition of the ground state and the excited state on the equator of the Bloch sphere, i.e., [Number] (omitting the normalization factor) is prepared. This superposition acquires a random relative phase φ after a free evolution time τ due to the influence of the fluctuating spin bath. That is,

Number

[0062] The HE refocusing technique can cancel decoherence caused by the slowly fluctuating spin bath. Similar to the FID, the spins are initialized on the equator of the Bloch sphere, evolve freely for a time τ, and then acquire a relative phase φ due to the low-field:

Number

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[0063] As an extension of the HE re-convergence technique, there are Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences containing more π pulses and free evolution periods of different durations [35, 36]. In fact, for optimized pulse sequences, it has been shown in

[15] that at the limit of an infinite number of pulses, the coherence time of the NV center is proportional to the number of pulses. The latter time is limited only by the relaxation of the NV center.

[0064] In numerical simulations, the present disclosure can mimic the effect of the spin bath on the central spin by a time-dependent Hamiltonian

Number

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Number

[21] . Thus, the static component δ r models the FID, and the OU process δ ou (t) models the influence of spin bath correlation in the central spin dynamics.

[0065] Compatibility of single qubit gates and schemes The ability to extend the coherence lifetime of a quantum system is desirable, but the quantum error correction system 1 operates while protecting this system from the environment. Therefore, in this section of the present disclosure, it is examined whether the described protection scheme is compatible with the application of coherent gates. Here, the present disclosure is limited to the case of single qubit gates. As an example, the present disclosure considers the π pulse U Xπ and the Hadamard gate U H . Representing the general rotation by an angle θ around the A axis of the Bloch sphere as

Number

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[0066] The present disclosure applies these gates via coherent pulses on the TLS, and for simplicity, the present disclosure considers rectangular pulses. The general rotation R A (θ) corresponds to a pulse of the form

Number

Number

Number

[42] .

[0067] A quantum process is mathematically represented by a completely positive linear map ε. The purpose of QPT is to estimate ε from experimental measurements. A quantum process acting on an arbitrary quantum state ρ can be represented in the Kraus representation.

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[0068] Explanation of the electron-nuclear spin system of diamond In the present disclosure, the nearby 13Consider a diamond sample containing NV defects that couple to C nuclei spins. NV defects are perhaps the only example of room-temperature qubits, and researchers are studying NV defects for use in quantum memories, quantum interconnects, and quantum computers. Such systems are being intensively studied, and researchers have discovered ways to polarize and control large ensembles of adjacent individual 13 C nuclear spins using NV electrons. The hyperfine coupling to nearby 13 C nuclear spins is strong and can range from 1.3 MHz to 130 MHz

[43] . The nuclear spins of diamond, especially 13 C spins, usually have very long coherence times because they couple less strongly to the environment than electron spins [43, 45]. In the present disclosure, next, the coupling system between the NV electron spin S and 13 C nuclear spin I will be studied.

[0069] In the present disclosure, consider applying a static magnetic field of magnitude B0 along the NV axis that defines the z direction. The Hamiltonian of the electron-nuclear spin coupling system under the secular approximation can be written as follows:

Equation

[0070] A. Types of noise for both electrons and atomic nuclei For simplicity, first focus on a pair of a single 13 C nuclear spin and an NV electron spin. 13 Considering that the C nuclear spin is close to the electron spin, both will experience the same environment constituted by nearby weakly interacting nuclear spins in the sample that hosts them. Since the electron spin has a large gyromagnetic ratio (i.e., γ e / γ c ~3000), it interacts more strongly with the magnetic field B r (t) created by the slowly fluctuating nearby spins. This means that electron transitions are more sensitive to the environment than nuclear transitions, which is the key to implementing protection protocols.

[0071] In the present disclosure, a decoherence model is reached in which the coherent excitation exchange between the electron spin and nuclear spin and the environmental spin is ignored, and the environment induces a random fluctuation in the transition frequencies of the NV center and the nuclear spin, resulting in the loss of their quantum coherence. This is described by the Hamiltonian

Number

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[0072] Here 13 Let's consider the population of the C nuclear-NV electron spin pairs. The local environments they experience are not uniform throughout the sample. Therefore, the frequency fluctuations experienced by individual pairs depend on their specific locations. This can be modeled as the sum of non-interacting Hamiltonians,

Number

[0073] Explanation of the self-protection protocol A. Overview The coherence protection protocol summarized here by the present disclosure belongs to a class of continuous dynamical decoupling methods. Its purpose is to protect transitions between two energy levels (referred to in the present disclosure as qubit or two-level system (TLS) transitions) from environmentally induced fluctuations that ultimately lead to the loss of quantum coherence. To achieve this goal, the present disclosure utilizes a secondary transition between one of the qubit levels and a third auxiliary level. This auxiliary energy level is also affected by the same noise source, but is still more sensitive to noise than the qubit transition, i.e., the magnitude of the frequency change as a result of small fluctuations in the environmental configuration is much larger for the auxiliary level (with respect to the ground state) than for the qubit transition.

[0074] It is well known that off-resonance driving of an energy transition results in a small shift in its frequency, also known as the Stark or light shift. As the present disclosure will detail below, by driving both the red and blue of the qubit and the auxiliary transition far off resonance simultaneously, the quantum error correction system 1 can generate a Stark shift on the qubit transition and, by carefully selecting the amplitude and detuning of the driving field, can accurately compensate for the environmentally induced frequency fluctuations. This is possible because of the high sensitivity of the auxiliary energy level to noise.

[0075] As the present disclosure will show later, 13 All of the above requirements are met by both the C nuclear spin and the electron spin of the NV defect hosted in the diamond sample. Since the electron spin has a large gyromagnetic ratio and high sensitivity to magnetic noise, it is possible to use the electron transition to protect the nuclear spin from decoherence induced by magnetic noise. In the following subsections, the present disclosure introduces the mathematical details of the protection scheme for any multi-level quantum system.

[0076] TIFF2025524074000051.tif26170

Number

[0077] Now, in the present disclosure, two CW drives that couple the energy levels |1> and |2> are introduced. Both drives have the same Rabi frequency Ω and are detuned from the transition between the two levels to the red and blue. [Number] Here, Δ>0 is the detuning. As shown in references [44, 29], the total Stark shift of the qubit transition frequency by the two drive fields in the off-resonance limit (Δ≫Ω, sσ) is as follows. [Number] This is proportional to the frequency fluctuation δ. Therefore, the total qubit Hamiltonian is as follows. [Number] The term in the angular brackets is proportional to δ and can be eliminated by setting (Ω / Δ) 2 = 1 / s. These results correspond to the limit of s≫1 that is relevant to the subsequent discussion in the present disclosure. A more general treatment for any value of the sensitivity s is in the appendix of reference

[29] .

[0078] C.NV- 13 Detailed application of the scheme to the C system In the present disclosure, the C nuclear spin system that is coupled to the NV center via the hyperfine interaction and is described by the Hamiltonian (19) is considered. According to the selection rules, in the present disclosure, as the qubit transition |0>←→|1>, the nuclear transition |m 13 = -1, m s = -1 / 2>←→|m I = -1 / 2> is considered.s = -1, m I = +1 / 2> is selected. On the other hand, the electronic transition |m s = -1, m I = +1 / 2> ←→ |m s = 0, m I = +1 / 2> functions as an auxiliary transition |1> ←→ |2>.

[0079] The goal is to protect the qubit transition from magnetic noise in the environment using the protection protocol introduced above. This is possible because the gyromagnetic ratio of the electron is large, so the electron transition is more sensitive to magnetic noise than the nuclear transition. In fact, in Equation (19), the frequency fluctuations of both transitions are not independent.

Number

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[0080] In the system we selected, the above equation is simplified as follows.

Number

Number

[0081] In diamond 13 Simulation of protection protocols for C nuclear spins The present disclosure will next describe the simulation of the protection of a population of 1000 C nuclear spins, each hyperfine-coupled to a neighboring NV center. Further, in the present disclosure, interactions between different nuclear-electron spin pairs are ignored. With this non-interaction assumption, the concentration of NVs in diamond is preferably limited to less than 1 ppm

[48] . To simulate the time-dependent frequency fluctuations, the present disclosure uses the Ornstein-Uhlenbeck (OU) process. In particular, the present disclosure executes the algorithm developed in reference

[49] . The OU process is characterized by the following two time correlation functions. 13 This is in turn defined by two parameters, the effective coupling strength b to the environment and the correlation time τ of the environment. From these perspectives, the present disclosure considers the free (inductive) decay time

Equation

Equation

Equation

[0082] C, the Larmor precession motion due to the magnetic fields B0 and A can be ignored. However, to obtain a relatively large Zeeman splitting for the electronic transition, it is necessary to perform the experiment in the medium to low magnetic field region of 200 - 500 G. This allows the system to be driven off-resonance without the risk of dealing with higher energy levels. 13 This enables the system to be driven off-resonance without the risk of dealing with higher energy levels.

[0083] In the simulation, a simple Ramsey measurement is performed on the spin qubit to measure the coherence time. The qubit is initialized in an equal superposition of |0> and |1>. Then, the present disclosure evolves it under a noise process and a protection driving scheme for a time t. Next, the present disclosure projects it onto the ground state, measures the expectation value of σ z and repeats the process at various time intervals t. As a result, in the simulation, the present disclosure defines the coherence as <σ z >(t)> normalized to 1.

[0084] The present disclosure describes a specific application of a general self-protection scheme

[44] previously developed by some of us. In the present disclosure, a method for enhancing the nuclear spin coherence of 13 C tightly coupled to the electronic system of neighboring NV defects is described in detail. The correction scheme can operate in the same way for individual NV- 13 C pairs as well as for collective pairs. The protection protocol should be relatively sensitive to the exact value of the hyperfine coupling A zz and thus 13The protection should work even when C is not in the first coordination shell of NV. Based on simulations, for any physical coupling system of nuclear-electron spins that can be described by Equation (18) (regardless of the presence or absence of the ZFS term), an autonomous protection scheme should be applicable to extend the coherence time of the nuclear spin. Such electron-nuclear spin systems have been the focus of many implementations of quantum information retention technologies, such as the SiV defect in diamond [53, 54], nuclear spins in silicon donors [55 - 57], or silicon carbide

[58] , to name a few. The protection protocol is expected to be applicable to such nuclear-electron spin systems when 1) the main noise is magnetic noise, 2) the Zeeman shift of all energy levels is linear with respect to the magnetic field, and 3) the transition selection rules between levels allow for non-resonantly driving the protection transition strongly. Applying the autonomous protection protocol involves applying a CW drive between the upper state (|1>) and the sensor state (|2>) of the TLS. Therefore, all coherent quantum operations on the TLS {|0>, |1>} are not affected, and thus quantum technologies containing nuclear spins can be improved by applying the autonomous protection protocol.

[0085] Effect The scheme described in this disclosure is very robust and can extract (T2 time is short) individual dirty qubits and clean them (significantly reducing the phase relaxation noise from their local environment and increasing T2). It can also operate on a population of dirty qubits and remove the phase relaxation noise from each qubit in the population. This same control can also homogenize a set of dirty (or clean) qubits, where each qubit has slightly different energies. Thus, this simple continuous drive can take in a set of dirty qubits, each prepared in a slightly different way, and generate a set of nearly identical clean qubits without complex pulses, additional hardware, or the need to tune or address individual qubits.

[0086] This disclosure numerically shows that the method introduced in references [27, 29] to correct the Doppler width and thermal width in an atomic ensemble can also suppress the temporal variation of the frequency of a single spin due to a slowly fluctuating environment. In particular, this disclosure shows how this scheme can be implemented in a realistic experiment using spins associated with color centers in diamond.

Example

[0087] Example 1 FIG. 4 is a first graph for explaining an operation example of the quantum error correction system 1 of FIG. 1. FIG. 4 shows the correction of inhomogeneous phase relaxation for a population of 500 atoms. Here, this disclosure shows the average coherence of qubits (graph A) a single homogeneous qubit, (graph B) a population of qubits with inhomogeneous phase relaxation given by a normal distribution, and (graph C) qubits under the same as described above but continuous protection using a pair of drives with opposite detuning from an auxiliary transition.

[0088] FIG. 4 shows the variance σ δ = 10 2 (unit: qubit relaxation rate γ) The average response of a population of 500 atoms with inhomogeneous phase relaxation modeled as random detuning obtained from a normal distribution is compared without the above continuous protection scheme (graph B) and with (graph C) using the auxiliary level with a scaling factor s = 10.

[0089] Example 2 Figure 5 is a second diagram for explaining an operation example of the quantum error correction system 1 of FIG. 1. FIG. 5 shows the performance of an automatic correction scheme for cleaning up non-Markovian temporal noise in a single spin system: (a) The excitation state probability of a two-level system subject to longitudinal random telegraph noise (RTN) with an amplitude ξ = 43 as a function of the detuning δω of a weak probe from a qubit transition and the RTN rate χ. Without automatic correction, the coherence of the TLS is poor when exposed to this type of noise. (b) The excitation state probability when automatic correction is applied. Here, two off-resonance transitions between the excited state of the qubit and a higher level s = 10 times more sensitive to the RTN are simultaneously driven. The corresponding Rabi frequencies and detuning magnitudes are Ω = 927 and |Δ| = 3000, respectively. All parameters are given in units of the qubit relaxation rate γ. Applying automatic correction significantly improves the coherence characteristics of the TLS and essentially makes it immune to the influence of noise.

[0090] The response of the TLS <|1><2|> as a function of the probe detuning δω = ω - ω2 and the RTN jump rate χ for a single realization of the noise is shown in Fig. 5(a). In the limit of slow jump rates (χ << ξ), the TLS responds at both ω2 ± ξ, as is clearly seen from the two peaks at the bottom of the plot. On the other hand, in the fast jump limit (χ >> ξ), the individual frequencies cannot be resolved and only the response of the TLS at the mean frequency ω2 (δω = 0) is witnessed.

[0091] To refocus the TLS, the present disclosure here includes a third level that experiences a non-uniform frequency shift [ω3 - sδ RTN |3> <3|. By coupling the levels |2> and |3> to two off-resonant drives below and above the corresponding transition energy ω3 - ω2, Fig. 5(b) shows how a non-uniform drift in frequency can be removed.

[0092] Example 3 FIG. 6 is a second graph diagram for explaining an operation example of the quantum error correction system 1 of FIG. 1. FIG. 6 shows a Ramsey-type experiment of a TLS under Ornstein-Uhlenbeck noise due to interaction with a spin bath.

[0093] The decay envelopes of the FID and HE are shown in graphs a and b of FIG. 6, respectively. These are simulated using the probability field (14) and correspond to the average over 3000 realizations of the noise. In the present disclosure, the slow limit of the bath (τc >> 1 / b) that faithfully describes the NV center experiment [15, 37] is considered. The parameters selected for this simulation are b = 3.6 μs -1 and τ c = 23.7 μs

[15] . Further, spin relaxation is ignored in the present disclosure. Again, considering the auxiliary level of s = 10, the present disclosure shows that the spin can be decoupled from the environment by two driving schemes, and the initial coherence measured by the population difference of the states {|1>, |2>} in the Ramsey experiment and shown in graph c is preserved far beyond the decay times of the FID and HE. The observed high-frequency oscillations are the result of using off-resonant driving. It can be shown that increasing the value of s further reduces the amplitude of these oscillations.

[0094] Example 4 Experimental Proposal Using an NV Center Example 4 relates to a secondary example of NV spins in diamond, which are included in the spins associated with color centers in diamond. So far, in this disclosure, we have considered a three-level system where the second and third levels experience opposite frequency shifts due to static or time-dependent inhomogeneities. Furthermore, in numerical simulations, it was considered in this disclosure that the frequency shift at the third level is s = 10 times the frequency shift at the second level. The authors of references [29, 38, 39] have shown that it is actually possible to find this kind of configuration in atomic ensembles troubled by Doppler broadening or motional phase relaxation. Beyond these examples, this disclosure clearly shows how such a large sensitivity to inhomogeneities can be achieved in magnetically sensitive systems such as diamond nitrogen-vacancy (NV) centers

[40] .

[0095] According to reference

[41] , the ground state Hamiltonian of the NV center is given by the following equation.

Number

[0096] TIFF2025524074000064.tif60170

[0097] TIFF2025524074000065.tif28170

[0098] TIFF2025524074000066.tif32170

Number

Number

Number

Number

[0099] TIFF2025524074000071.tif63170

[0100] Example 5 FIG. 8 is a third diagram for explaining an operation example of the quantum error correction system 1 of FIG. 1. FIG. 8 shows the X when there is a low-speed RTN with ξ = 8 / τ and χ = 1 / τ π quantum process matrices of the pulse (upper row) and the Hadamard gate (lower row). For both processes, the left column represents the ideal gate when there is no noise, the middle column corresponds to the case where the gate is applied in the presence of noise but not protected, and the right column represents the case where the gate is applied in the presence of noise and at the same time the TLS with s = 80 is protected using a two-drive scheme with detuning Δ = 4000 / τ.

[0101] The scaling time in units of 1 / τ, the correlation time of the environment, and the reconstruction chi matrix of the gate process when the present disclosure selects an RTN with amplitude ξ = 8 / τ, jump rate χ = 1 / τ, an emitter with sensitivity s = 80, and a drive detuning Δ = 4000 / τ are shown in FIG. 8. The upper row corresponds to U Xπ and the lower row corresponds to U H . In both cases, the left column corresponds to the ideal process matrix, that is, the case where a pulse that realizes the gate is applied to the TLS in the absence of RTN. The middle column corresponds to the process matrix when the pulse is applied in the presence of RTN and the protection function is not effective. In the case of a slowly drifting environment, since the gate pulse hardly resonates with the TLS, the process fidelity becomes quite low, F = 0.08 for U Xπ and F = 0.25 for U H . Finally, the right column corresponds to the gate realized through the pulse when there is an RTN and a two-drive protection scheme. It can be easily seen that the process matrix in the ideal case is almost restored. This is confirmed by the fact that a very high process fidelity F = 0.99 is achieved for both U Xπ and U H .

[0102] TIFF2025524074000072.tif83170

[0103] TIFF2025524074000073.tif53170

[0104] Furthermore, at lower driving fields, a nominal improvement in T2 is obtained, and there is still some fluctuation in the coherence curve. On the other hand, at higher driving, the coherence curve is smooth and is observed to extend for a longer period. This is as expected because the quality of the protection provided by this scheme depends on how strongly detuned the present disclosure is compared to the noise experienced by the system (the stronger the Rabi drive Ω, the stronger the detuning Δ, and consequently the better the protection). An important point to note is that the simulation performed in this scheme is equivalent to performing multiple measurements using a single qubit. Therefore, this scheme naturally extends to the case of a single qubit as a matter of course.

[0105] TIFF2025524074000074.tif38170

[0106] Deformed form Although the present disclosure has been described based on the drawings and examples, it should be noted that those skilled in the art can easily make deformations and modifications based on the present disclosure. Therefore, it should be noted that such deformations and modifications are also included in the scope of the present disclosure. For example, as long as there is no logical contradiction, the functions and the like included in each structure and step can be rearranged, a plurality of structures and steps can be combined into one, or divided.

[0107] In the above-described embodiment, the quantum material 10 has been described as including spins associated with the color centers of diamond, but the quantum material 10 is not limited thereto. The quantum material 10 can include any superconducting qubit such as fractionalonium or brachionium as long as it exhibits the desired characteristics discussed herein.

[0108] This disclosure may be implemented on many types of quantum hardware systems. Constructing an array of identical clean quantum systems is useful not only for quantum computing, but also for quantum memory, quantum repeaters (for building a quantum internet), and quantum sensors. The quantum error correction system 1 can be used in a quantum computer or any other device.

[0109] Some embodiments of this disclosure are illustrated below. However, it should be noted that the embodiments of this disclosure are not limited to the following examples.

[0110] [Appendix 1] Quantum material and; A quantum error correction system comprising the quantum material and a dichroic recovery drive generator that communicates with the quantum material, The dichroic recovery drive generator transmits a waveform to the quantum material, a quantum error correction system.

[0111] [Appendix 2] The quantum error correction system according to Appendix 1, wherein the quantum material includes a non-interacting multi-level spin population.

[0112] [Appendix 3] Each of the spins has at least three states |1>, |2>, and |3> associated with respective energy levels E1, E2, and E3, where E1 < E2 and E2 < E3, and the spin is such that when one of the states |2> of the spin undergoes an energy shift of -δ, the state |3> of the same spin undergoes an energy shift of -sδ due to noise, where s is a real number and s > 0. The quantum error correction system according to Appendix 2.

[0113] [Appendix 4] The waveform includes two tones of a continuous electromagnetic field having frequencies of ω + Δ and ω - Δ and the same or substantially the same amplitude Ω, where ω corresponds to the energy separation between states |2> and |3>. The quantum error correction system according to Appendix 3.

[0114] [Appendix 5] The quantum error correction system according to Appendix 4, wherein two tones of the continuous electromagnetic field are in the same phase or substantially in the same phase.

[0115] [Appendix 6] (Ω / Δ) 2 The quantum error correction system according to Appendix 4, which is equal to or substantially equal to 1 / s.

[0116] [Appendix 7] The quantum error correction system according to Appendix 3, wherein the noise is static spatially inhomogeneous noise or spatially homogeneous or inhomogeneous temporal noise.

[0117] [Appendix 8] The quantum error correction system according to Appendix 2, wherein the waveform removes inhomogeneous phase relaxation of a non-interacting multi-level spin ensemble.

[0118] [Appendix 9] The quantum error correction system according to Appendix 1, wherein the waveform corrects static noise, temporal noise, or phase noise.

[0119] [Appendix 10] The quantum error correction system according to Appendix 2, wherein the spin is a qubit.

[0120] [Appendix 11] The quantum error correction system according to Appendix 1, wherein the waveform converts a dirty qubit into a clean qubit.

[0121] [Appendix 12] The quantum error correction system according to Appendix 1, wherein the waveform is off-resonant continuous wave driving in a multi-level structure.

[0122] [Appendix 13] The quantum error correction system according to Appendix 11, wherein the dirty qubit is at least one of a plurality of dirty qubits, and the waveform removes phase relaxation noise from each qubit of at least one of the plurality of dirty qubits.

[0123] [Appendix 14] The quantum error correction system according to Appendix 11, wherein the waveform equalizes a group of at least one of a plurality of dirty qubits and at least one of a plurality of clean qubits.

[0124] [Appendix 15] The quantum material includes at least one of: a single or collective non-interacting multi-level quantum system, a quantum memory, a quantum repeater, a quantum sensor, single or collective defects in diamond, a single or collective multi-level superconducting quantum system, and a quantum computer, and the quantum error correction system according to Appendix 1.

[0125] [Appendix 16] The waveform is two tones of a continuous electromagnetic field with substantially the same amplitude and substantially the same phase, and the tones have frequencies detuned in opposite directions from an auxiliary transition, and the quantum error correction system according to Appendix 1.

[0126] [Appendix 17] The waveform is either light or a microwave frequency, and the quantum error correction system according to Appendix 1.

[0127] [Appendix 18] The waveform is an electromagnetic field that exerts a light shift to automatically correct a fluctuating unknown energy shift acting on a dirty qubit, and the resulting clean qubit is protected from spatial and temporal energy fluctuations, and the quantum error correction system according to Appendix 11.

[0128] [Appendix 19] An automatic quantum error correction system with a dichroic recovery drive that converts a dirty qubit population and creates a substantially identical and long-lived coherent qubit population.

[0129] [Appendix 20] An automatic quantum error correction system with a dichroic recovery drive that shifts the energy levels of a multi-level system by an off-resonant drive to automatically compensate for unwanted energy fluctuations in a qubit system.

[0130] [Appendix 21] A quantum error correction process including sending a dichroic electromagnetic drive to a quantum system including a non-interacting multi-level spin population.

[0131] [Appendix 22] Each of the spins has at least three states |1>, |2>, and |3> associated with respective energy levels E1, E2, and E3, where E1 < E2 and E2 < E3, and the spin undergoes an energy shift due to noise such that when one state |2> of the spin undergoes an energy shift of -δ, the state |3> of the same spin undergoes an energy shift of -sδ, where s is a real number and s > 0, the process according to Appendix 21.

[0132] [Appendix 23] The process according to Appendix 22, where s is greater than 4, preferably greater than 6, and more preferably greater than 10.

[0133] [Appendix 24] The process according to Appendix 22, where the dichroic electromagnetic drive includes two tones of continuous electromagnetic fields of the same or substantially the same amplitude Ω having frequencies ω + Δ and ω - Δ, where ω corresponds to the energy separation between states |2> and |3>, and Δ > 0.

[0134] [Appendix 25] The process according to Appendix 24, where the two tones of the continuous electromagnetic field are in phase or substantially in phase.

[0135] [Appendix 26] (Ω / Δ) 2 is equal to or approximately equal to 1 / s, the process according to Appendix 24.

[0136] [Appendix 27] The process according to Appendix 22, where the noise is static spatially non-uniform noise or spatially uniform or non-uniform temporal noise, preferably spatially uniform or non-uniform temporal noise.

[0137] [Appendix 28] The process according to Appendix 21, where the non-interacting multi-level spin is a qubit.

[0138] [Appendix 29] The process according to Appendix 21, further including evaluating the power spectrum (including frequency and intensity) of the noise, typically temporal noise.

[0139] [Appendix 30] The process according to Appendix 29, further comprising adjusting the dichroic electromagnetic drive based on the power spectrum of the noise.

[0140] [Appendix 31] The process according to Appendix 29, further comprising determining Ω and / or Δ based on the power spectrum of the noise.

[0141] [Appendix 32] The quantum error correction system according to Appendix 1, wherein the quantum material includes single or collective non-interacting multi-level spins.

[0142] [Appendix 33] The quantum error correction system according to Appendix 1, further comprising an evaluation system configured to evaluate the temporal noise of the quantum material.

[0143] [Appendix 34] The error correction system according to Appendix 33, wherein the waveform of the dichroic recovery drive generator is adjusted based on the evaluation of the temporal noise to correct errors related to the temporal noise of the quantum material.

[0144] [Appendix 35] The quantum error correction system according to Appendix 3, wherein s is greater than 4, preferably greater than 6, more preferably greater than 10.

[0145] [Appendix 36](Ω / Δ) 2 is equal to or approximately equal to 1 / s in the limit where s > 1, typically s > 4, more typically s > 10, and even more typically s >> 1, for the quantum error correction system according to Appendix 6.

[0146] [Appendix 37] The quantum error correction system according to Appendix 1, wherein the quantum material is a time quantum system.

[0147] [Appendix 38] An apparatus comprising the quantum error correction system according to Appendix 1.

[0148] [Appendix 39] A quantum computer comprising the quantum error correction system according to Appendix 1.

[0149] [Appendix 40]. The quantum error correction system according to Appendix 1, wherein the spin is under the influence of temporal noise.

[0150] [Appendix 41]. The quantum error correction system according to Appendix 4, wherein Δ is the frequency detuning.

[0151] [Appendix 42]. The quantum error correction system according to Appendix 1, wherein the spin is a spin related to the color center of diamond.

[0152] [Appendix 43]. The quantum error correction system according to Appendix 1, wherein the spin is a fluxonium qubit or a bropium qubit.

[0153] [Appendix 44]. The quantum error correction system according to Appendix 3, wherein the energy levels are anharmonic.

[0154] [Appendix 45]. The process according to Appendix 21, wherein the spin is related to the color center of a spin diamond or is a fluxonium qubit or a bropium qubit.

[0155] [Appendix 46]. The process according to Appendix 22, wherein the energy levels are anharmonic.

[0156] [Appendix 47]. The process according to Appendix 21, further comprising measuring the decay rate of the coherent superposition of the states of the spin, typically using a Ramsey pulse sequence.

[0157] [Appendix 48]. The process according to Appendix 47, further comprising adjusting Ω and / or Δ based on the measured decay rate.

[0158] [Appendix 49] The quantum error correction system described in Appendix 4, where 0.5Δ / sqrt(s) < Ω < 1.5Δ / sqrt(s), more preferably 0.9Δ / sqrt(s) < Ω < 1.1Δ / sqrt(s), even more preferably 0.99Δ / sqrt(s) < Ω < 1.01Δ / sqrt(s), and still more preferably 0.999Δ / sqrt(s) < Ω < 1.001Δ / sqrt(s).

[0159] [Appendix 50] The quantum error correction system described in Appendix 24, where 0.5Δ / sqrt(s) < Ω < 1.5Δ / sqrt(s), more preferably 0.9Δ / sqrt(s) < Ω < 1.1Δ / sqrt(s), even more preferably 0.99Δ / sqrt(s) < Ω < 1.01Δ / sqrt(s), and still more preferably 0.999Δ / sqrt(s) < Ω < 1.001Δ / sqrt(s).

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Claims

1. A quantum material; A quantum error correction system comprising the quantum material and a dichroic recovery driving generator that communicates with the quantum material, The dichroic recovery driving generator transmits a waveform to the quantum material, the quantum error correction system.

2. The quantum error correction system according to claim 1, wherein the quantum material includes single or collective non-interacting multi-level spins.

3. Each of the spins has at least three states |1>, |2> and |3> associated with respective energy levels E1, E2 and E3, where E1 < E2 and E2 < E3, and the spin is such that when one of the states |2> of the spin undergoes an energy shift of -δ, the state |3> of the same spin undergoes an energy shift of -sδ, where s is a real number and s > 0, the quantum error correction system according to claim 2.

4. The waveform includes two tones of a continuous electromagnetic field having the same or substantially the same amplitude Ω with frequencies ω + Δ and ω - Δ, where ω corresponds to the energy separation between states |2> and |3>, and Δ > 0, the quantum error correction system according to claim 3.

5. The quantum error correction system according to claim 4, wherein the two tones of the continuous electromagnetic field are in phase or substantially in phase.

6. (Ω / Δ) ２ The quantum error correction system according to claim 4, wherein (Ω / Δ) is equal to or approximately equal to 1 / s in the limit of s > 1, typically s > 4, and more typically s > 10.

7. The quantum error correction system according to claim 3, wherein the noise is static spatially inhomogeneous noise or spatially homogeneous or inhomogeneous temporal noise.

8. The quantum error correction system according to claim 1, wherein the waveform corrects static noise, temporal noise or phase noise.

9. The quantum error correction system according to claim 2, wherein the spin is a qubit.

10. The quantum error correction system according to claim 9, wherein the waveform converts a dirty qubit to a clean qubit.

11. The quantum error correction system according to claim 1, wherein the waveform is an off-resonant continuous wave drive in a multi-level structure.

12. The quantum error correction system according to claim 2, wherein the spin is a nuclear spin coupled to a nitrogen-vacancy spin in diamond.

13. The quantum error correction system according to claim 3, wherein the energy levels are non-harmonic.

14. A quantum error correction process including sending a dichroic electromagnetic drive to a quantum system including a non-interacting multi-level spin ensemble.

15. The process of claim 14, further comprising measuring a decay rate of a coherent superposition of the states of the spins, typically using a Ramsey pulse sequence.

Images