Robust techniques for magic state distillation in clifford+t-based quantum computers

Abstract

A quantum computing system providing noise resistance to magic state distillation is provided. The quantum computing system includes a quantum computing device including a plurality of qubits. The quantum computing device is programmed to: a) execute a distillery to distill a plurality of T states to generate one or more distilled magic states; b) measure out a plurality of syndromes from the distillation; c) calculate one or more error rates from the plurality of syndromes; d) estimate infidelity for the distillery based upon the one or more error rates; and e) determine if the infidelity exceeds a threshold, recalibrate the distillery.

Description

ROBUST TECHNIQUES FOR MAGIC STATE DISTILLATION IN CLIFFORD+T- BASED QUANTUM COMPUTERSCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and the benefit of Provisional Patent Application Serial Number 63 / 626,800, entitled ROBUST TECHNIQUES FOR MAGIC STATE DISTILLATION IN CLIFFORD+T-BASED QUANTUM COMPUTERS, filed January 30, 2024, the contents of which are incorporated herein in their entirety.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH & DEVELOPMENT

[0002] This invention was made with government support under a grant‘NSF STAQ Phy-1818914’ awarded by the National Science Foundation (NSF), and a grant ‘DE-SC0020331 ’ awarded by the Department of Energy (DOE). The government has certain rights in the invention.TECHNICAL FIELD

[0003] This disclosure relates generally to quantum computing and, more specifically, to techniques for magic state distillation in Clifford+T-based quantum computers, or fault-tolerant quantum computing architectures.BACKGROUND

[0004] Quantum computing is a revolutionary computational model that leverages quantum mechanical phenomena for solving intractable problems. Quantum computers (“QCs”) evaluate quantum circuits or programs in a manner similar to a classical computer, but quantum information’s ability to leverage superposition, interference, and entanglement is projected to give QCs significant advantage with various particular processing problems, such as in the fields of cryptography, chemistry, optimization, and machine learning.

[0005] The program capacity of early fault-tolerant quantum computers (FTQC) will be defined by their magic state distilleries. Magic state distillation is a key component of FTQC. Magic state distilleries refine low fidelity injected magic states into high fidelity distilled magic states, a critical task in fault- tolerant quantum architectures. Injected magic states are prepared via physical gates and suffer from infidelities matching physical error rates — if physical hardware is of sufficiently low infidelity, output magic states can attain infidelities as low as 1.9 x 10'11on projected superconducting hardware. Furthermore, magic state distilleries are susceptible to a variety of physical noise sources, thereby degrading quantum programs.

[0006] Unfortunately, quantum hardware faces a myriad of noise sources operating at different timescales and with varying magnitudes of severity. Slow noise, like drift caused by fluctuating temperatures of the chip, and fast noise, like the appearance of two-level systems (TLSs), can increase the infidelity of magic states. Research shows that magic state distilleries are vulnerable to vary ing hardware performance and can magnify hardware degradation, producing dangerously low-quality magic states. If used in quantum computers, these high infidelity states can silently corrupt quantum data and programs.

[0007] On near-term devices, distilling magic T states of sufficient fidelity will consume substantive compute, requiring up to > 95% of a program’s qubitcycles. Designing high-fidelity, low-cost distilleries is challenging, in part because distilleries must bridge algorithms and hardware - distilleries must meet algorithmic demands for high fidelity magic states by distilling magic from hardware of a much lower fidelity.

[0008] Historically, parameters for magic state distillation have been chosen by first assuming physical hardware error rates, then analyzing algorithm infidelity requirements. While the required number and fidelity of Ts is known in advance via compilation, assuming consistent physical error rates is dubious: quantum hardware faces a myriad of noise sources, meaning that the infidelity of input magic states can fluctuate or degrade over time. At best, this assumption imposes onerous requirements during device fabrication to meet stringent error rate guarantees; at worst, these guarantees cannot be met, meaning that low-fidelity output states can silently corrupt quantum data and programs. Thus, as demand for quantum computation services grows, it is imperative to efficiently prevent corruption of quantum data and programs.SUMMARY

[0009] In one aspect, a quantum computing system providing noise resistance to magic state distillation is provided. The quantum computing system includes a quantum computing device including a plurality of qubits. The quantum computing device is programmed to: a) execute a distillery to distill a plurality of T states to generate one or more distilled magic states; b) measure out a plurality of syndromes from the distillation; c) calculate one or more error rates from the plurality of syndromes; d) estimate infidelity for the distillery based upon the one or more error rates; and e) determine if the infidelity' exceeds a threshold, recalibrate the distillery. The quantum computing system may have additional, less, or alternate functionalities, including those discussed elsewhere herein.

[0010] In another aspect, a quantum computing system providing noise resistance to magic state distillation is provided. The quantum computing system includes a quantum computing device including a plurality of qubits. The quantum computing device is programmed to: a) execute a plurality of distilleries, each distillery of the plurality of distilleries configured to distill a plurality of / states to generate one or more distilled magic states; b) measure out a plurality of syndromes from the distillation from each of the distilleries; c) calculate one or more error rates for each of the distilleries from the plurality of syndromes from each of the distilleries; d) estimate infidelity for each of the distilleries based upon the corresponding one or more error rates; and e) determine if the infidelity of a distillery exceeds a threshold, recalibrate that distillery. The quantum computing system may have additional, less, or alternate functionalities, including those discussed elsewhere herein.

[0011] In yet another aspect, a quantum computer implemented method for providing noise resistance to magic state distillation id provided. The method is implemented by a quantum computing device including a plurality of qubits. The method includes a) executing a plurality of distilleries, each distillery of the plurality of distilleries configured to distill a plurality of T states to generate one or more distilled magic states; b) measuring out a plurality' of syndromes from the distillation from each of the distilleries; c) calculating one or more error rates for each of the distilleries from the plurality of syndromes from each of the distilleries; d) estimating infidelity for each of the distilleries based upon the corresponding one or more error rates; and e) determining if the infidelity of a distilleryexceeds a threshold, recalibrate that distillery. The method may have additional, less, or alternate functionalities, including those discussed elsewhere herein.

[0012] Various refinements exist of the features noted in relation to the above-mentioned aspects. Further features may also be incorporated in the above-mentioned aspects as well. These refinements and additional features may exist individually or in any combination. For instance, various features discussed below7in relation to any of the illustrated embodiments may be incorporated into any of the above-described aspects, alone or in any combination.BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The Figures described below depict various aspects of the systems and methods disclosed. It should be understood that each Figure depicts an embodiment of a particular aspect of the disclosed systems and methods, and that each of the Figures is intended to accord with a possible embodiment thereof. Further, wherever possible, the following description refers to the reference numerals included in the following Figures, in which features depicted in multiple Figures are designated with consistent reference numerals. There are shown in the drawings arrangements presently discussed, it being understood, however, that the present embodiments are not limited to the precise arrangements.

[0014] Figure 1 illustrates an exemplary7T gate, in accordance with at least one embodiment.

[0015] Figures 2A and 2B illustrate a 15-1 distillery7in accordance with at least one embodiment.

[0016] Figure 3A illustrates exemplary measurement syndromes that can be traced back to individual faulty7T states.

[0017] Figure 3B illustrates an exemplary distillery syndrome history7that can be used to dynamically recalibrate a distillery.

[0018] Figure 3C illustrates an exemplary7estimator system used by the MSD system described herein.

[0019] Figure 4 illustrates graphs of localized disruptive noise on injected magic states and fault-tolerant surface code patches, in accordance with at least one embodiment.

[0020] Figure 5 illustrates a generalized example of a suitable computing environment 500 in which several of the described embodiments can be implemented.

[0021] Figure 6 illustrates an exemplary system for implementing embodiments of the disclosed technology.

[0022] Figure 7 illustrates a process for distilling magic states with noise resistance, in accordance with at least one embodiment of the disclosure.

[0023] Corresponding reference characters indicate corresponding parts throughout the drawings.DETAILED DESCRIPTION OF THE DISCLOSURE

[0024] The following detailed description illustrates embodiments of the disclosure by way of example and not by way of limitation. It is contemplated that the disclosure has general application to quantum computing, classical computing, and quantum- classical hybrid computing in, for example, client / server or cloud computing architectures.

[0025] The present disclosure introduces a third consideration when designing magic state distilleries, beyond output fidelity7and cost: resilience to hardware noise. To meet algorithm fidelity requirements, distilleries must be resilient to fluctuations in hardware error in both time and space. This requires a new framework to design and test distillery architectures, one that better integrates devices, distilleries, and magic demands. The present disclosure illustrates that hardware noise can reduce quantum program fidelity via distillation, thereby7motivating the design of the presented resiliency framework. Qubitlevel simulations show that hardware fluctuations can significantly reduce program fidelity7and are challenging to counteract without real-time characterizations of device performance. If left unchecked, noise may be amplified through distillation, silently corrupting quantum data and programs.

[0026] Accordingly, the systems and methods recited herein describe a magic state distillation (MSD) computer system. The MSD computer system executes an online kernel which balances fidelity, cost, and resilience. The online kernel is configured to leverage syndrome measurements from magic state distilleries to assess the infidelity of both hardware inputs and magic outputs. This data can be gathered and used at negligible cost to estimate program fidelity and dynamically recalibrate the device. More specifically, the MSD computer system and the online kernel manage distilleries to estimate the infidelity of injected and distilled magic states in real-time or near real-time. The online kernel uses syndrome measurements already produced by distillation to characterize hardware noise. The online kernel estimates can be used to automatically detect and mitigate faulty T states. The online kernel identifies faulty T states and recommends recalibration, which prevents data corruption.

[0027] One advantage of the MSD system with the online kernel is that by reducing noise, less stable hardware is more viable using this system. This is important as some producers area attempting to scale to 1000+ physical qubits spread over multiple chips. Another advantage is that MSD system relaxes hardware requirements. While stable hardware achieves stronger fidelity guarantee. Although less stable hardware is noisier, the MSD system corrects for the noise and thus this hardware becomes viable when used with the MSD system.

[0028] Methodologically, the MSD computer system and its online kernel work towards a more complete characterization of noise on fault-tol erant devices. The MSD computer system analyzes magic state lifecycles to correct their sensitivity to noise disturbances. The MSD computer device executes a qubit-level stabilizer simulator that tracks hardware noise throughout the magic state lifecycle.

[0029] Current quantum devices face a variety of challenging noise sources with few scalable mitigation methods. Some noise sources, such as cosmic rays, are well- studied in small systems, but are costly to mitigate. Other noise sources, such as two-level system (TLS) resonances and 1 / f flux noise, are poorly characterized on large-scale devices and lack clear mitigation methods. This is especially important as quantum computers continue to scale. In both settings, time-varying noise may be costly or challenging to suppress in hardware. Therefore, software mitigation methods are preferred.

[0030] When analyzing the performance per qubit, qubits may exhibit strong, abrupt shifts in error rates on the time scale of minutes. These fluctuation are know n to severely degrade the performance of small-scale quantum programs. Unfortunately, counteracting noise is expensive. Users can mitigate noise at the cost of device time, e.g. by repeating the computation or fully characterizing the device to optimize compilation. Providers can mitigate noise by improving fabrication processes, control electronics, or calibration routines. Typically in quantum hardware, calibration entails characterizing the parameters and behavior of the hardware, then tuning up control pulses to effectively implement qubit gates. For example, some providers fully calibrate their devices on a daily basis and others calibrate immediately before every experiment.

[0031] Unfortunately, these calibrations are expensive, requiring minutes to hours for the calibration of a small (~100qubit) device. In spite of these frequent calibrations, severe noise fluctuation still appear. This potentially corrupts the computations. Calibration can be performed to mitigate current device noise and avoid existing TLS defects, but cannot mitigate the effects of new unexpected noise sources appearing after calibration.

[0032] Both user and provider error mitigation techniques face challenges when scaling to fault-tolerant devices. Modem mitigation techniques are designed for chips with hundreds of qubits, w hile fault-tolerant devices will require hundreds of thousands or millions of qubits. Moreover, many methods are incompatible with error correction or require exponentially more samples as algorithm size increases, eliminating any quantum advantage. Provider strategies, like performing system-wide recalibrations, will be challenging to implement, as some quantum programs are expected to run computations that last hours or even days.

[0033] Hardware noise affects fault-tolerant quantum computers through the error correcting code or through magic states. The MSD system uses the latter, including the distillation of magic T states needed for surface code quantum error correction. Furthermore, the surface code can suppress hardw are errors.

[0034] More generally, quantum error correction (QEC) encodes logical qubits into many physical qubits to reduce the impact of physical errors. Unfortunately,every QEC code (including the surface code) must have operations it cannot implement directly. Thus, every7code has two types of logical operations: transversal fault-tolerant gates which are native to the code and non-transversal gates which are implemented via magic states.

[0035] Figure 1 illustrates an exemplary T gate, in accordance with at least one embodiment. The surface code cannot transversally implement fault-tolerant T gates, a necessary operation for universal computation. Instead, by consuming a T magic state: the MSD system implements a T gate using a CNOT and Sgate as shown in Figure 1 . Both the CNOT and the S gate are native to the surface code. The MSD system injects magic states via physical rotations, distills to improve fidelity, and consumes to reliably implement the gate.

[0036] Injection uses physical gates to produce a raw magic state. Injection is vulnerable to noise. Typically, magic T states are prepared by creating a single qubit T state. Then the physical T state is expanded into a logical patch. Injection is especially sensitive to noise present on the injection site. Injection strategies produce magic states with infidelity comparable to the physical hardware’s error rates. Accordingly, heterogeneous noise from injection qubits directly damages the injected magic state.

[0037] Distillation produces higher fidelity magic states by consuming many lower fidelity magic states. Distillation is critical for fault-tolerant computation. If the raw magic state were immediately consumed, the overall computation would be limited by the physical error rate, rather than the code-suppressed error rate. Thus, by spending greater spacetime costs on distillation, magic state infidelities can be suppressed below hardware error rates, enabling fault-tolerant computation.

[0038] Consumption of T states occurs via the circuit shown in Figure 1. The program fidelity is reduced by the infidelity of the T state.

[0039] Figures 2A and 2B illustrate a 15-1 distillery7in accordance with at least one embodiment. Figure 2A illustrates a successful round of distillation. Figure 2B illustrates a rejected distillation.

[0040] Distillation produces higher fidelity magic states, but the procedure is probabilistic and can fail. When it fails, no state is produced, but a syndrome describing the faulty T states is given. This syndrome can be used to perform error estimation.

[0041] T states are typically distilled via triorthogonal codes. These distilleries build a second layer of error correction on the surface code, then transversally consume T states, and finally measure out syndromes shown in Figures 2 A and 2B. If the syndrome is all 0s, there is no error and the distilled magic state is accepted. If the syndrome has any Is, there is an error and the output is discarded. Figures 2A and 2B use the 15-1 protocol, which consumes 15 T states and outputs 1 higher fidelity state.

[0042] Figure 2A illustrates a successful round of distillation in a first distillery 200. The distillery 200 includes surface code logical qubits 205, inactive routing space 210, and active routing space 215. Active routing space 215 is used to apply noisy T gates. In the top step 220 of the distillation process, three noisy T states are injected and noisy jr / 8 rotations are applied to the logical qubits 205. In the bottom step 225, are 15 noisy rotations are applied in six layers, the four syndrome qubits 230 are measured. If all are 0, then the distilled magic state is accepted.

[0043] Figure 2B illustrates a rejected distillation. If one injected T state is faulty, then that causes a faulty logical rotation. In bottom step 235, the faulty rotation causes a non-zero syndrome measurement 240. The magic state is discarded and the distillation is run again to obtain a distilled magic state.

[0044] Many systems simply post-selects on the no-syndrome case and discard the syndrome data. The MSD system takes a different approach. Each syndrome bit pattern uniquely corresponds to one faulty input magic state in the 15-to-l distillery 200. The MSD system uses these syndromes as a real-time source of information to estimate the underlying error rate as described below.

[0045] Currently, distillery architectures are designed with three parameters in mind: 1) f the desired program fidelity; 2) Nr, the number of T states required for the program; and 3) p. the infidelity of injected magic states. For chemistry applications f > 0.99. For factoring, / > 0.66. Estimates for NT range from a minimum of 2xl06T states tomore than 1011T states for large programs. Estimates for p range from 10‘4to 10‘3on superconducting qubits. Accordingly, the maximal infidelity pr of a T state is thus bounded by:

[0046] The MSD system uses this inequality to estimate maximum program capacities for a given distillation architecture. For example, the 15-1 distillery consumes 15 T magic states with infidelity p to produce one output T state with infidelity 0(35p3). Accordingly, the MSD system may be used to support programs with billions of T gates.

[0047] Furthermore, EQ. 1 can be made time dependent. By denoting pk as the infidelity of the th consumed T state, the bound is:^ ^ < 1 - / EQ. 2

[0048] This can be considered an infidelity budget, where every consumed T spends infidelity from the 1 - / 'budget.

[0049] When T states overspend the infidelity budget, programs may lose accuracy or require additional sampling over-head. Distilleries are incredibly sensitive to the fidelity of raw T states provided. Even minor fluctuations in hardware performance aggregate into significant deviations in program fidelity. For example, the output infidelity of a 15- 1 distillery scales as O(p A 50% increase in input infidelities corresponds to a >3x increase in output infidelities. By EQ. (2), this also corresponds to a 3x decrease in program capacity'.

[0050] Furthermore, the bound in EQ. (2) is program-level and applies when there are multiple distilleries. Degradations from any individual distillery' count against the program infidelity budget. Thus, T states across distilleries must all be high fidelity, requiring noise mitigation techniques for all distilleries. This may be especially challenging as devices are scaled, as distilleries may be located on different chips with different environmental and fabrication properties.

[0051] One significant advantage of the MSD system described herein is taking into account noise variations to improve over baseline mitigation strategies. Three common mitigation strategies include frequent periodic recalibrations, periodic tomography driving dynamic recalibration, and overdistillation. Frequent calibrations only counteract slow noise when the drift rate is known. As fast noise and random variability increase, periodic recalibrations can no longer guarantee T quality. Furthermore, recalibrations may be unnecessarily triggered if the recalibration period is underestimated. Alternatively, recalibrations could be guided by periodic characterization experiments (such as tomography or randomized benchmarking) at the hardware or logical level. This reduces unnecessary calibrations. However, characterization is expensive, incurring significant overhead even when the device is operating normally. Multiple rounds of distillation can be used, i.e. feeding output states of lower level distilleries into another distillery. Existing resource studies estimate that stacked distilleries result in final logical T states with infidelities rates in the 2 x 1015to 6 x I O25range, so even l OO-lOOOx increases in error from hardware fluctuations are tolerable. However, hierarchical distilleries are costly, with the most conservative two-level distilleries requiring 5x more qubit cycles and 8x more qubits.

[0052] To counteract these issues, the MSD system estimates output magic state infidelities by analyzing distillation syndromes in near-real time. Using these estimates, the MSD system can dynamically recalibrate distilleries to mitigate the impact of timevarying noise. The MSD system uses two tunable parameters: the window size IF used to perform online infidelity estimation and the output infidelity threshold T that triggers recalibration. This is shown in Figures 3A-3C.

[0053] The MSD system uses the syndrome bits of distilleries to estimate the fidelity of the input and output T magic states. Because tnorthogonal distilleries are error correcting codes, greater syndrome rates imply that there are more errors in the consumed magic states and lower fidelity in the output magic state. Furthermore, the syndrome measured can indicate which input magic state was defective. The MSD system leverages these syndrome bits to estimate the underlying performance of the device.

[0054] Each of the injected T states i corresponds to a specific syndrome bitstring oi G {0, I }4\ 0000. If multiple states have faults, the measured syndrome is the bitwise XOR of the syndromes. For example, if rotations z, j, k are faulty, the syndrome iso, © Gj ® o*. The distillery output is only accepted if the measured syndrome is 0000, which occurs with probability 1 - 0(15p) (if all input states have error rate p). The syndrome structure explains why the distillery has error reduction in 0(35 / ?): the output state will be accepted if o;© o7© o / f= 0000, even though three input states z, j, k all had errors. There are 35 such three-state combinations, so the output infidelity is 0(35 / ?) to leading order. Finally, note that distillation occurs in superposition, so output states are a mix of faulty and sound T states. Each output T state thus has some error probability, which must be sufficiently low so that all of a program’s T states succeed.

[0055] Given the input magic state infidelities (p(,>the syndrome probabilities and output fidelity can be computed. Further-more, because each syndrome oz uniquely corresponds to an injected state, a sufficiently large collection of past observed syndromes allows for estimating the underlying p(i>via maximum likelihood estimation. This is the goal of the MSD system: to utilize a past window of observed syndromes to estimate input and output T infidelities and intelligently trigger recalibrations based on these estimated error rates.

[0056] To summarize the MSD system estimation technique, each distillation attempt produces a single syndrome. The MSD system stores a window of the most recent W syndromes. Using these syndromes, the MSD system estimates input accuracy of these predictions. Because the syndrome data is streaming and stochastic, error rates can be misestimated, causing unnecessary calibrations (false positives) or consumption of low-fidelity magic states (false negatives). Thus, device providers will need to tune true positive I false negative rates to be consistent with their reliability and cost guarantees as described further herein.

[0057] More specifically as shown in Figures 3A-3C. Figure 3A illustrates exemplary measurement syndromes 305 that can be traced back to individual faulty T states. In this Figure, the syndromes 305 for final four rotations 310 of a 15-1 distillation circuit 200 (shown in Figure 2) are shown. The third to last rotation 310 consumes a faulty’ T. The measured syndrome 305 uniquely corresponds to that specific T state that was consumed. The MSD system uses these syndromes 305 to estimate the individual T fidelities.

[0058] Figure 3B illustrates an exemplary distillery syndrome history that can be used to dynamically recalibrate a distillery 200. The first section 315 uses the same distillery layout as in Figure 2. The MSD system uses the rates of nonzero syndromes (black dots) to estimate errors online. In the second section 320, the MSD system inspects the past window of syndromes 305, reducing the memory' and computing requirements while also enabling rapid response to degradations. In the third section 325, when syndromes suggest a severe degradation in output states, the distillery 200 is recalibrated.

[0059] Figure 3C illustrates an exemplary estimator system used by the MSD system described herein. First, the MSD system sets the parameters are set to ensure some reliability and cost guarantees. During runtime, the MSD system consumes syndromes automatically produced by a distillery 200. The MSD system optimizes the raw error rates to match the observed syndrome counts. Then, the MSD system estimates infidelity using these raw error rates. If the infidelity exceeds thresholds, the MSD system recommends recalibration.

[0060] The MSD system’s implementation cost is minimal, especially versus QEC decoding. Devices would need a classical infrastructure to store syndromes and dynamically recalibrate. In some embodiments, window sizes never exceed 1,000,000 four bit syndromes, <500 kilobytes. Furthermore, in some embodiments, the ideal window size is 3,162 (1.6 kilobytes). The estimation procedure is also computationally lightweight, taking ~lms in practice in a Python implementation, which is a similar timescale to one distillation in superconducting hardware.

[0061] In addition to the window size, the second parameter is the output infidelity threshold T used to trigger recalibration. The MSD system triggers a distillerylevel recalibration when the window-estimated output error rate o, > T. In many embodiments, estimated error rates are not necessarily distributed symmetrically, so a specific threshold value does not necessarily correspond to guaranteeing the same true output error rate. Lower thresholds correspond to more sensitive estimators, which are useful for stricter infidelity guarantees.

[0062] More generally, recalibrations could be triggered with a cost function that accounts for the length and severity of the degradation. For example, noisefluctuations may be highly transient. If noise events are much shorter than the duration of a recalibration, the MSD system could be tuned to less aggressively recalibrate. Instead, the MSD system could be used to trigger a ‘waiting’ period of duration B, during which the factory continues to operate but the outputs are discarded rather than used in the program. To the program, the factor}' is effectively offline, but the MSD system has notyet committed to a recalibration. The MSD system can then continue to analyze output fidelity. If the fidelity recovers before the end of the waiting period, the MSD system turns the factory back online, and if not, the MSD system begins the recalibration.

[0063] In this scenario, one of two cases occurs: either the noise persists for less than B cycles, and the factory is offline for the duration of the noise event, or the noise event continues for longer than B and a recalibration triggers, requiring R additional cycles. In the exemplary embodiment, the MSD system chooses B to minimize the cost function:where p(t) is the probability that the transient event lasts for duration i. The distribution of degraded noise durations p(t) can either be characterized ahead of time or can be tuned insitu using the MSD system’s infidelity estimates, allowing B to betuned on real devices with minimal cost.

[0064] The MSD system can detect high infidelity states, regardless of the infidelity distributions on the different patches. The signals that the MSD system uses (nonzero syndromes) are proportional to the injection infidelities (P[tr = z] oc p;). This follows theoretically because the syndrome rate is proportional to the raw infidelity in the first order. This signal is informative, i.e. can identify high infidelity outputs. Furthermore, there is alignment between estimated and true infidelity. The accuracy of the estimator increases as the window size increases.

[0065] In addition, the MSD system ensures fidelity guarantees across noise regimes. In one embodiment, across different noise regimes, the MSD system with a (W, T) settings of (3162, 3.25 x 10’8) consistently performs by providing a balance between recalibrations and output error rate. Across different noise model s / regimes. these settings estimator maintains infidelity guarantees at minimal recalibration cost.In many embodiments, there is a trade-off between the number of recalibrations and the achieved output infidelity guarantee. There is also flexibility regarding the particular choice of estimator parameters; for example, different pairs, such as, but not limited to, (316227, 10-8), (100000, 10-8), (3162. 3.25 x io-8). (1000, 10-7) have similar performance.

[0066] Furthermore, the MSD system can accurately predict program fidelity across noise regimes. This functionality can be useful to post-process output results or as a baseline characterization of device performance in time. To produce a program-level estimate, the MSD system averages the output infidelity estimate produced across all of the T states, then compares this to the true average output infidelity. While the mean estimated outputs may exhibit a bias, this can be corrected by performing a linear fit and shifting the data to lie on the identity. The modified predictions strongly correlate with the true program infidelity, with an J?2= 0.993. Accordingly, the MSD system may accurately predict program performance as a side effect, without requiring any additional data collection. This prediction could be used as a post-run check to improve confidence in the results.

[0067] FTQC demands a scalable stack which is noise-resilient at all levels. While magic state distillation protocols are highly sensitive to fluctuation in device noise, the MSD system addresses and corrects this vulnerability.

[0068] In further enhancements, the MSD system is configured to provide additional responses to hardware degradations. For example, in some of these enhancements, the MSD system discard previously distilled states with estimated low fidelity. In still further enhancements, the MSD system could change the distillery to more aggressively suppress errors. This could include changing the distillery from 15-1 to a 20-4 distillery.

[0069] In other enhancements, the MSD system could also use finer-grained recalibrations, that target specific input magic states instead of recalibrating the entire distillery. This would reduce the average time cost because distilleries can still function even when patches have been disabled.

[0070] In still further enhancements, the MSD system may further refine the abstraction barriers for a noise-resilient stack. For example, a surface code ISA may only provide T fidelities and logical operation error rates while abstracting distillery kernels.Alternatively, the MSD system could also exploit distillery syndromes to dynamically recompile algorithms to degraded hardware. These compilations also need to account for patches which may go offline.

[0071] In some embodiments, the MSD system program fidelity estimation may be useful for compilation or post-processing. High program fidelity indicates the quality of program outputs. While error mitigation techniques have already shown promise, these techniques rely on hardware-level signals which will be too expensive to gather on large systems and are less relevant in an error-corrected setting. However, the MSD system provides a useful estimator on a key determinant of program fidelity (magic state fidelity and can support FTQC versions of these techniques. For example, variational algorithms like the Variational Quantum Eigensolver (VQE) can use fidelity signals to counteract noise. On NISQ devices, mitigation methods attempt to counteract noise by ignoring transient errors during gradient evaluation or randomizing correlated errors. The estimators provided by the MSD system can be used as signals to extend both of these methods to FTQC, whether to skip shots with poor fidelity or to randomize the consumption of low-fidelity T states.

[0072] Figure 4 illustrates graphs of localized disruptive noise on injected magic states and fault-tolerant surface code patches, in accordance with at least one embodiment. Graph 400 illustrates line 405 of a distance 5 inj ection experiment. In Graph 400, the appearance of a TLS defect drastically reduces the Ti time of just a single qubit, doubling the infidelity of injected magic states from around 1 x 103to around 2 x | ()3. Higher distances suffer even worse infidelities. Graph 410 includes a line 415 for a distance 5 rotated surface code patch and a line 420 for a distance 7 rotated surface code patch. Line 415 illustrates that the effect of a single bad qubit is far less significant than shown by line 405 in graph 400. Line 420 shows no noticeable effect at all. Accordingly, increasing the distance further suppresses the impact of a single bad qubit.

[0073] Furthermore, local noise only minorly degrades fault-tolerant logical operations used in distillation. Surface code patches are much more resilient to noise than injection / distillation as shown in Figure 4. While magic state injection is constrained by physical gate error rates, modest increases in distance can wholly suppress logical error rate increases due to local physical qubit noise. Accordingly, the MSD system may provide surface code patches and increased distance.

[0074] Figure 5 illustrates shows an example embodiment of suitable computing environment 500 for implementing several of the described embodiments.

[0075] Quantum computing technology exhibits some key differences over classical computing technology. For example, quantum computing devices are typically more prone to error than classical computing devices. Thus, maximizing execution fidelity in quantum processing is a first-order constraint and a primary concern, where the greater reliability and predictability of classical processing allows focus more on performance and energy efficiency. Further, the execution of quantum applications are substantially dependent on and sensitive to the target quantum computing device and its characteristics, some of which may vary through time, where classical computing devices typically provide more stable characteristics.

[0076] The term “classical,” as used herein, refers to conventional transistor-based computing technology or other non-quantum based processing technologies (e.g., analog computing, superconducting computing). This term, where necessary, is used to distinguish such computing devices or associated hardware, software, algorithms, and such, from “quantum” computing. Quantum computing devices, or just “quantum computers” (“QCs”) and associated hardware, software, algorithms, and such, are typically distinguished from classical computing devices based on their reliance on quantum phenomena of quantum mechanics to perform processing operations (e.g., using “qubits,” or quantum bits). Example classical computing devices include conventional personal computers, servers, tablets, smartphones, x86-based processors, random access memory (“RAM”) modules, and so forth. Example quantum computing devices include “IBM Q” devices from International Business Machines (IBM), “Bristlecone” quantum computing device from Google, “Tangle Lake” quantum computing device from Intel, and “2000Q” from D-Wave. The term “classical bit” or “cbif ’ may be used herein to refer to a bit within classical computing. The term “qubit” may be used herein to refer to a quantum bit in quantum computing. While QCs include quantum computing hardware that relies upon quantum mechanics for processing, it should be understood that such QCs and associated QIP systems typically rely upon various classical computing devices for normal operation (e.g., job scheduling, preparation, compilation, signal generation, and the like).

[0077] Quantum programming languages and compilers use a quantum assembly language composed of 1- and 2-qubit gates. Quantum compiler frameworks translate this quantum assembly into control pulses, typically electric signals that implement the specified computation on a specific quantum computing device. A quantum circuit represents a list of instructions bound to some registers that has a number of gates and is spread out over a number of qubits. Compilation of a quantum circuit involves a sequence of steps to enable the quantum circuit to be executed on a particular QC. A quantum job (“QC job." or just “job,” depending on context) encapsulates a single circuit or a batch of circuits that executes on a QC. The circuits within a batched job may be treated as a single task such that all quantum circuits are executed successively, and each circuit in a job may be rapidly re-executed for a particular number of “shots.”

[0078] Figure 5 illustrates a generalized example of a suitable computing environment 500 in which several of the described embodiments can be implemented. The computing environment 500 is not intended to suggest any limitation as to the scope of use or functionality of the disclosed technology, as the techniques and tools described herein can be implemented in diverse general-purpose or special-purpose environments that have computing hardware.

[0079] With reference to Figure 5, the computing environment 500 includes at least one processing device 510 and memory’ 520. In Figure 5, this most basic configuration 530 is included within a dashed line. The processing device 510 (e.g, a CPU or microprocessor) executes computer-executable instructions. In a multi-processing system, multiple processing devices execute computer-executable instructions to increase processing power. The memory 520 may be volatile memory’ (e.g., registers, cache. RAM, DRAM, SRAM), non-volatile memory (e.g., ROM, EEPROM, flash memory), or some combination of the two. The memory’ 520 stores software 580 implementing tools for implementing the quantum circuit (e.g., the Magic state distillation circuits and associated techniques) as described herein.

[0080] The computing environment 500 can have additional features. For example, the computing environment 500 includes storage 540, one or more input devices 550, one or more output devices 560, and one or more communication connections 570. An interconnection mechanism (not shown), such as a bus, controller, or network, interconnectsthe components of the computing environment 500. Typically, operating system software (not shown) provides an operating environment for other software executing in the computing environment 500. and coordinates activities of the components of the computing environment 500.

[0081] The storage 540 can be removable or non-removable, and includes one or more magnetic disks (e.g.. hard drives), solid state drives (e.g. , flash drives), magnetic tapes or cassettes, CD-ROMs, DVDs, or any other tangible non-volatile storage medium which can be used to store information and which can be accessed within the computing environment 500. The storage 540 can also store instructions for the software 580 implementing the quantum circuits and techniques described herein.

[0082] The input device(s) 550 can be a touch input device such as a keyboard, touchscreen, mouse, pen, trackball, a voice input device, a scanning device, or another device that provides input to the computing environment 500. The output device(s) 560 can be a display device (e.g., a computer monitor, laptop display, smartphone display, tablet display, netbook display, or touchscreen), printer, speaker, or another device that provides output from the computing environment 500.

[0083] The communication connection(s) 570 enable communication over a communication medium to another computing entity. The communication medium conveys information such as computer-executable instructions or other data in a modulated data signal. A modulated data signal is a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media include wired or wireless techniques implemented with an electrical, optical, RF, infrared, acoustic, or other carrier.

[0084] As noted, the various methods for generating the disclosed circuits (e.g., for compiling / synthesizing the circuits) can be described in the general context of computer-readable instructions stored on one or more computer-readable media. Computer- readable media are any available media (e.g. , memory or storage device) that can be accessed within or by a computing environment. Computer-readable media include tangible computer-readable memory or storage devices, such as memory 520 and / or storage 540, anddo not include propagating carrier waves or signals per se (tangible computer-readable memory or storage devices do not include propagating carrier waves or signals per se).

[0085] Various embodiments of the methods disclosed herein can also be described in the general context of computer-executable instructions (such as those included in program modules) being executed in a computing environment by a processor. Generally, program modules include routines, programs, libraries, objects, classes, components, data structures, and so on, that perform particular tasks or implement particular abstract data types. The functionality of the program modules may be combined or split between program modules as desired in various embodiments. Computer-executable instructions for program modules may be executed within a local or distributed computing environment.

[0086] Figure 6 illustrates an exemplary system for implementing embodiments of the disclosed technology. The exemplar}' system for implementing embodiments of the disclosed technology includes computing environment 600. In computing environment 600, a compiled quantum computer circuit description, including a circuit description for one or more magic state distillation circuits as disclosed herein, can be used to program (or configure) one or more quantum processing units such that the quantum processing unit(s) implement the circuit described by the quantum computer circuit description. The quantum computer circuit description can implement any of the magic state distillation circuits discussed herein.

[0087] The environment 600 includes one or more quantum processing units 602 and one or more readout device(s) 608. The quantum processing unit(s) 602 execute quantum circuits that are precompiled and described by the quantum computer circuit description. The quantum processing unit(s) 602 can be one or more of, but are not limited to: (a) a superconducting quantum computer; (b) an ion trap quantum computer; (c) a fault-tolerant architecture for quantum computing; and / or (d) a topological quantum architecture (e.g., a topological quantum computing device using Majorana zero modes). The precompiled quantum circuits can be sent into (or otherwise applied to) the quantum processing unit(s) 602 via control lines 606 at the control of quantum processor controller (QP controller) 620. The QP controller 620 can operate in conjunction with a classical processor 610 (e.g., having an architecture as described above with respect to Figure 5) to implement the desired quantum computing process.

[0088] In the illustrated example, the QP controller 620 further implements the desired quantum computing process via one or more QP subcontrollers 604 that are specially adapted to control a corresponding one of the quantum processor(s) 602. For instance, in one example, the quantum controller 620 facilitates implementation of the compiled quantum circuit by sending instructions to one or more memories (e.g., lower- temperature memories), which then pass the instructions to low-temperature control unit(s) (e.g., QP subcontroller(s) 604) that transmit, for instance, pulse sequences representing the gates to the quantum processing unit(s) 602 for implementation. In other examples, the QP controller(s) 620 and QP subcontroller(s) 604 operate to provide appropriate magnetic fields, encoded operations, or other such control signals to the quantum processor(s) to implement the operations of the compiled quantum computer circuit description. The quantum controller(s) can further interact with readout devices 608 to help control and implement the desired quantum computing process (e.g., by reading or measuring out data results from the quantum processing units once available, etc.)

[0089] With reference to Figure 6, compilation is the process of translating a high-level description of a quantum algorithm into a quantum computer circuit description comprising a sequence of quantum operations or gates, which can include any of the magic state distillation circuits as disclosed herein. The compilation can be performed by a compiler 622 using a classical processor 610 (e.g. , as shown in Figure 5) of the environment 600 which loads the high-level description from memory or storage devices 612 and stores the resulting quantum computer circuit description in the memory or storage devices 612.

[0090] In other embodiments, compilation can be performed remotely by a remote computer 660 (e.g., a computer having a computing environment as described above with respect to Figure 5) which stores the resulting quantum computer circuit description in one or more memory or storage devices 662 and transmits the quantum computer circuit description to the computing environment 600 for implementation in the quantum processing unit(s) 602. Still further, the remote computer 660 can store the high-level description in the memory or storage devices 662 and transmit the high-level description to the computing environment 600 for compilation and use with the quantum processor(s) 602. In any of these scenarios, results from the computation performed by the quantum processor(s) 602 can be communicated to the remote computer 660 after and / or during the computation process. Stillfurther, the remote computer 660 can communicate with the QP controller(s) 620 such that the quantum computing process (including any compilation and / or QP processor control procedures) can be remotely controlled by the remote computer 660. In general, the remote computer 660 communicates with the QP controller(s) 620 and / or compiler / synthesizer 622 via communication connections 650.

[0091] In particular embodiments, the environment 600 can be a cloud computing environment, which provides the quantum processing resources of the environment 600 to one or more remote computers (such as remote computer 660) over a suitable network (which can include the Internet).

[0092] Figure 7 illustrates a process 700 for distilling magic states with noise resistance, in accordance with at least one embodiment of the disclosure. In the exemplary embodiment, the steps of process 700 are performed by one or more of processing device 510 (shown in Figure 5), quantum processor 602, and / or classical processor 610 (both shown in Figure 6).

[0093] In the exemplary embodiment, the quantum processor 602 executes 705 a distillery' 200 (shown in Figure 2) to distill a plurality of T states to generate one or more distilled magic states.

[0094] In the exemplary embodiment, the quantum processor 602 measures 710 out a plurality' of syndromes 230 (shown in Figure 2) from the distillation.

[0095] In the exemplary embodiment, the quantum processor 602 calculates 715 one or more error rates from the plurality of syndromes 230. In some embodiments, the error rates include faulty' magic states.

[0096] In the exemplary embodiment, the quantum processor 602 estimates 720 infidelity7for the distillery 200 based upon the one or more error rates.

[0097] In the exemplary embodiment, the quantum processor 602 determines 735 if the infidelity exceeds a threshold, recalibrate the distillery 200.

[0098] In further embodiments, the quantum processor 602 determines if the infidelity exceeds the threshold based upon a cost function. The cost function includes a time to recalibrate the distillery 200.

[0099] In some further embodiments, the quantum processor 602 waits a delay period before recalibrating the distillery 200. In these embodiments, the quantum processor 602 continues to execute the distillery 200 during the delay period. In further embodiments, the quantum processor 602 discards output magic states from the distillery 200 during the delay period. In additional embodiments, the quantum processor 602 estimates infidelity for the generated output magic states during the delay period. Then the quantum processor 602 cancels the recalibration if the estimated infidelity no longer exceeds the threshold.

[0100] In some further embodiments, the quantum processor 602 analyzes historical syndromes and corresponding historical error rates to recognize one or more trends.

[0101] In some further embodiments, the quantum processor 602 uses distance injection with the distillery. In these embodiments, the quantum processor 602 injects rotated a surface code patch with a predetermined distance.

[0102] In some further embodiments, the quantum processor 602 stores the plurality of syndromes 230. The plurality of syndromes 230 include a predetermined number of sets of syndromes 230, such as W syndromes 230 as described herein.

[0103] In some further embodiments, the quantum processor 602 performs the steps of process 700 on a plurality of distilleries 200 simultaneously or nearly simultaneously, such as when solving a problem. In these embodiments, one or more distilleries 200 may be recalibrated or taken offline from the problem while those distilleries 200 have infidelity exceeding the thresholds. Furthermore, the thresholds for different distilleries 200 may be different. These thresholds may be tailored to hardware or other factors. Furthermore, these thresholds may be calculated based upon historical performance of the corresponding distilleries 200 and / or hardware.ADDITIONAL CONSIDERATIONS

[0104] Example embodiments of compressor systems and methods, such as refrigerant compressors, are described above in detail. The systems and methods are not limited to the specific embodiments described herein, but rather, components of the system and methods may be used independently and separately from other components described herein. For example, the cooling circuits described herein may be used in compressors other than centrifugal compressors, including, for example and without limitation, scroll compressors, rotary compressors, and reciprocating compressors.

[0105] Example embodiments of compressor systems and methods, such as refrigerant compressors, are described above in detail. The systems and methods are not limited to the specific embodiments described herein, but rather, components of the system and methods may be used independently and separately from other components described herein. For example, the cooling circuits described herein may be used in compressors other than centrifugal compressors, including, for example and without limitation, scroll compressors, rotary compressors, and reciprocating compressors.

[0106] As will be appreciated based upon the foregoing specification, the abovedescribed embodiments of the disclosure may be implemented using computer programming or engineering techniques including computer software, firmware, hardware or any combination or subset thereof. Any such resulting program, having computer-readable code means, may be embodied or provided within one or more computer-readable media, thereby making a computer program product, i.e., an article of manufacture, according to the discussed embodiments of the disclosure. The computer-readable media may be, for example, but is not limited to, a fixed (hard) drive, diskette, optical disk, magnetic tape, semiconductor memory such as read-only memory (ROM), and / or any transmitting / receiving medium, such as the Internet or other communication network or link. The article of manufacture containing the computer code may be made and / or used by executing the code directly from one medium, by copying the code from one medium to another medium, or by transmitting the code over a network.

[0107] These computer programs (also known as programs, software, software applications, “apps,” or code) include machine instructions for a programmable processor,and can be implemented in a high-level procedural and / or object-oriented programming language, and / or in assembly / machine language. As used herein, the terms “machine- readable medium” and “computer-readable medium” refer to any computer program product, apparatus and / or device (e.g., magnetic discs, optical disks, memory, Programmable Logic Devices (PLDs)) used to provide machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. The “machine-readable medium” and “computer-readable medium,” however, do not include transitory signals. The term “machine-readable signal” refers to any signal used to provide machine instructions and / or data to a programmable processor.

[0108] As used herein, a processor may include any programmable system including systems using micro-controllers, reduced instruction set circuits (RISC), application specific integrated circuits (ASICs), logic circuits, and any other circuit or processor capable of executing the functions described herein. The above examples are example only and are thus not intended to limit in any way the definition and / or meaning of the term “processor.”

[0109] As used herein, the terms “software” and “firmware” are interchangeable, and include any computer program stored in memory' for execution by a processor, including RAM memory, ROM memory. EPROM memory, EEPROM memory, and non-volatile RAM (NVRAM) memory. The above memory types are example only, and are thus not limiting as to the ty pes of memory' usable for storage of a computer program.

[0110] As used herein, the term “database” can refer to either a body of data, a relational database management system (RDBMS), or to both. As used herein, a database can include any collection of data including hierarchical databases, relational databases, flat file databases, object-relational databases, object-oriented databases, and any other structured collection of records or data that is stored in a computer system. The above examples are example only, and thus are not intended to limit in any way the definition and / or meaning of the term database. Examples of RDBMS’ include, but are not limited to including, Oracle® Database, MySQL, IBM® DB2, Microsoft® SQL Server, Sybase®, and PostgreSQL. However, any database can be used that enables the systems and methods described herein. (Oracle is a registered trademark of Oracle Corporation, Redwood Shores,California; IBM is a registered trademark of International Business Machines Corporation, Armonk, New York; Microsoft is a registered trademark of Microsoft Corporation, Redmond, Washington; and Sybase is a registered trademark of Sybase. Dublin, California.)[01 1 1] In another example, a computer program is embodied on a computer- readable medium. In an example, the system is executed on a single computer system, without requiring a connection to a serv er computer. In a further example, the system is being run in a Windows® environment (Windows is a registered trademark of Microsoft Corporation, Redmond, Washington). In yet another example, the system is run on a mainframe environment and a UNIX® server environment (UNIX is a registered trademark of X / Open Company Limited located in Reading, Berkshire, United Kingdom). In a further example, the system is run on an iOS® environment (iOS is a registered trademark of Cisco Systems. Inc. located in San Jose, CA). In yet a further example, the system is run on a Mac OS® environment (Mac OS is a registered trademark of Apple Inc. located in Cupertino, CA). In still yet a further example, the system is run on Android® OS (Android is a registered trademark of Google, Inc. of Mountain View-, CA). In another example, the system is run on Linux® OS (Linux is a registered trademark of Linus Torvalds of Boston, MA). The application is flexible and designed to run in various different environments without compromising any major functionality.

[0112] As used herein, an element or step recited in the singular and proceeded with the word '‘a” or “an” should be understood as not excluding plural elements or steps, unless such exclusion is explicitly recited. Furthermore, references to “example” or “one example” of the present disclosure are not intended to be interpreted as excluding the existence of additional examples that also incorporate the recited features. Further, to the extent that terms “includes,” “including,” “has,” “contains,” and variants thereof are used herein, such terms are intended to be inclusive in a manner similar to the term “comprises” as an open transition w ord without precluding any additional or other elements.

[0113] As used herein, the terms “software” and “firmware” are interchangeable and include any computer program stored in memory for execution by a processor, including RAM memory7, ROM memory7, EPROM memory7, EEPROM memory7, and non-volatile RAM (NVRAM) memory. The above memory types are example only, and are thus not limiting as to the types of memory usable for storage of a computer program.

[0114] Furthermore, as used herein, the term '‘real-time” refers to at least one of the time of occurrence of the associated events, the time of measurement and collection of predetermined data, the time to process the data, and the time of a system response to the events and the environment. In the examples described herein, these activities and events occur substantially instantaneously.

[0115] In some embodiments, the system includes multiple components distributed among a plurality of computer devices. One or more components may be in the form of computer-executable instructions embodied in a computer-readable medium. The systems and processes are not limited to the specific embodiments described herein. In addition, components of each system and each process can be practiced independent and separate from other components and processes described herein. Each component and process can also be used in combination with other assembly packages and processes. The present embodiments may enhance the functionality and functioning of computers and / or computer systems.

[0116] The computer-implemented methods discussed herein can include additional, less, or alternate actions, including those discussed elsewhere herein. The methods can be implemented via one or more local or remote processors, transceivers, servers, and / or sensors (such as processors, transceivers, servers, and / or sensors mounted on vehicles or mobile devices, or associated with smart infrastructure or remote servers), and / or via computer-executable instructions stored on non-transitory computer-readable media or medium. Additionally, the computer systems discussed herein can include additional, less, or alternate functionality, including that discussed elsewhere herein. The computer systems discussed herein can include or be implemented via computer-executable instructions stored on non-transitory computer-readable media or medium.

[0117] As used herein, the term “non-transitory computer-readable media” is intended to be representative of any tangible computer-based device implemented in any method or technology for short-term and long-term storage of information, such as, computer-readable instructions, data structures, program modules and sub-modules, or other data in any device. Therefore, the methods described herein can be encoded as executable instructions embodied in a tangible, non-transitory, computer readable medium, including, without limitation, a storage device and / or a memoiy device. Such instructions, when executed by a processor, cause the processor to perform at least a portion of the methodsdescribed herein. Moreover, as used herein, the term “non-transitory computer-readable media” includes all tangible, computer-readable media, including, without limitation, non- transitory computer storage devices, including, without limitation, volatile and nonvolatile media, and removable and non-removable media such as a firmware, physical and virtual storage, CD-ROMs, DVDs, and any other digital source such as a network or the Internet, as well as yet to be developed digital means, with the sole exception being a transitory, propagating signal.

[0118] The patent claims at the end of this document are not intended to be construed under 35 U.S.C. § 112(f) unless traditional means-plus-function language is expressly recited, such as “means for” or “step for” language being expressly recited in the claim(s).

[0119] This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.

Claims

WHAT TS CLAIMED IS:

1. A quantum computing system providing noise resistance to magic state distillation, the quantum computing system comprising: a quantum computing device including a plurality of qubits, the quantum computing device programmed to: execute a distillery to distill a plurality of T states to generate one or more distilled magic states; measure out a plurality of syndromes from the distillation; calculate one or more error rates from the plurality of syndromes; estimate infidelity for the distillery based upon the one or more error rates; and determine if the infidelity exceeds a threshold, recalibrate the distillery.

2. The quantum computing system of Claim 1, wherein the quantum computing device is further programmed to determine if the infidelity exceeds the threshold based upon a cost function.

3. The quantum computing system of Claim 2, wherein the cost function includes a time to recalibrate the distillery.

4. The quantum computing system of Claim 1, wherein the quantum computing device is further programmed to wait a delay period before recalibrating the distillery.

5. The quantum computing system of Claim 4, wherein the quantum computing device is further programmed to continue to execute the di sti 11 ery during the delay period.

6. The quantum computing system of Claim 5, wherein the quantum computing device is further programmed to discard output magic states from the di sti 11 ery during the delay period.

7. The quantum computing system of Claim 5, wherein the quantum computing device is further programmed to: estimate infidelity for the generated output magic states during the delay period; and cancel the recalibration if the estimated infidelity no longer exceeds the threshold.

8. The quantum computing system of Claim 1, wherein the quantum computing device is further programmed to analyze historical syndromes and corresponding historical error rates to recognize one or more trends.

9. The quantum computing system of Claim 1, wherein the error rates include faulty magic states.

10. The quantum computing device of Claim 1, wherein the quantum computing device is further programmed to use distance injection with the distill ery.

11. The quantum computing device of Claim 1, wherein the quantum computing device is further programmed to inject rotated a surface code patch with a predetermined distance.

12. The quantum computing device of Claim 1, wherein the quantum computing device is further programmed to store the plurality of syndromes, wherein the plurality of syndromes includes a predetermined number of sets of syndromes.

13. A quantum computing system providing noise resistance to magic state distillation, the quantum computing system comprising: a quantum computing device including a plurality of qubits, the quantum computing device programmed to:execute a plurality of distilleries, each distillery of the plurality of distilleries configured to distill a plurality of T states to generate one or more distilled magic states; measure out a plurality of syndromes from the distillation from each of the distilleries; calculate one or more error rates for each of the distilleries from the plurality of syndromes from each of the distilleries; estimate infidelity for each of the distilleries based upon the corresponding one or more error rates; and determine if the infidelity of a distillery exceeds a threshold, recalibrate that distillery.

14. The quantum computing system of Claim 13, wherein the quantum computing device is further programmed to take the recalibrating distillery offline from any executing program while that distillery is recalibrating.

15. The quantum computing system of Claim 13, wherein the quantum computing device is further programmed to determine if the infidelity’ exceeds the threshold based upon a cost function.

16. The quantum computing system of Claim 15, wherein the cost function includes a time to recalibrate the selected distillery.

17. The quantum computing system of Claim 13, wherein the quantum computing device is further programmed to: wait a delay period before recalibrating the selected distillery’; continue to execute the selected di sti 11 ery during the delay period; discard output magic states from the distillery during the delay period;estimate infidelity for the generated output magic states during the delay period; and cancel the recalibration if the estimated infidelity’ no longer exceeds the threshold.

18. The quantum computing device of Claim 13, wherein the quantum computing device is further programmed to use distance injection with the distillery.

19. The quantum computing device of Claim 13, wherein the quantum computing device is further programmed to inject rotated a surface code patch with a predetermined distance.

20. A quantum computer implemented method for providing noise resistance to magic state distillation, the method implemented by a quantum computing device including a plurality’ of qubits, the method comprises: executing a plurality of distilleries, each distillery of the plurality of distilleries configured to distill a plurality of T states to generate one or more distilled magic states; measuring out a plurality of syndromes from the distillation from each of the distilleries; calculating one or more error rates for each of the distilleries from the plurality of syndromes from each of the distilleries; estimating infidelity for each of the distilleries based upon the corresponding one or more error rates; and determining if the infidelity of a distillery’ exceeds a threshold, recalibrate that distillery.

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