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Breakthroughs in physics, engineering, and classical computing were prerequisites for building a quantum computer, which is why for many decades the task was, and in some cases remains, beyond the limits of available technology. IonQ Annual Report FY 21

The last 6 words of the quote above should be etched into the minds of every potential and existing IonQ (NYSE:IONQ) investor.

Figure 1: IONQ Stock Price Performance (Yves Sukhu)

I certainly hope most long investors in IONQ understand that the stock, even at ~$5/share, must be, by every definition, speculative given that (extrapolating from their own words) practical quantum computing systems may never exist. If so, presumably those investors were and are prepared for steep losses, as with the stocks ~(71%) decrease so far this year.

Figure 2: IONQ and Selected Competitor Performance (Yves Sukhu)

Yet, it must be acknowledged that IONQ, along with their true peers in the quantum computing space, is trying to build, what appears to be, the next great leap in computing systems. On that point, the company may merit a value that is somewhat independent of what might be deserved on mere financial performance alone. After all, the combined economic and societal value of practical quantum computing if it could be realized may be almost unimaginable.

Trading at just over $5/share as of market close June 17, 2022, IONQ may appear as something of a bargain considering its 2021 high over $30. But, is it?

I couldnt resist going a bit nerdy in the title of this section. For readers who dont get the reference, I will explain at the end of the article. For readers who do get the reference, yes, I know it was corny . But, back to business.

I think there are a few reasons to be excited about IonQs prospects, which I outline as follows.

1. The market for quantum computing hardware, software, and services could exceed several billion dollars in a few years.

Figure 3: IonQ Company and Market Overview (IonQ Investor Updates Presentation March 2022)

As I write this, IonQs market capitalization is a hair below $1B. That might seem reasonable against a projected total addressable market (TAM) of $65B, as offered in Figure 3. At first glance this forecast may strike as realistic, given the many potential applications for practical quantum computing; these applications vary from new drug discovery to options pricing within the finance industry to network and loading optimization for shipping and logistics carriers. If the forecast is accurate, it might be argued that IonQ is actually undervalued based on the potential of the market. Although, in making that statement, investors should keep in mind the quantum computing space is fairly crowded with both large and small public players, including IONQ, Rigetti (RGTI), IBM (IBM), Alphabet (GOOG, GOOGL), and Honeywell (HON), as well as a growing number of start-ups. In other words, the pie hardly belongs exclusively to IonQ. Still, the riches of quantum computing are expected to grow exponentially as true quantum advantages (i.e. quantum computers with provable advantages over classical computers) hopefully emerge in the future.

Figure 4: Expected Phases of Quantum Computing Maturity (IonQ Investor Updates Presentation March 2022)

2. IONQs technological path could be the right path that allows them to win the race. As mentioned in the introduction, a practical (or useful) quantum computer is the ultimate prize being chased after by the various major quantum computing players. I imagine most IONQ investors are aware that the company differentiates itself (largely) on the basis of its particular approach to quantum computing hardware, which is trapped-ion technology pioneered by IONQ co-founders Chris Monroe and Jungsang Kim. This stands in contrast to competing quantum computing hardware approaches being explored by other players who use fundamentally different technologies to implement physical qubits, such as photon-based systems and superconducting circuits. IONQ notes a number of advantages with respect to trapped-ion technology, including its error-resilient characteristics and ability to operate at room temperature.

Figure 5: IonQ Unique Technological Advantages (IonQ Investor Updates Presentation March 2022)

In regard to the latter, certain competing technologies such as superconducting circuits can only operate at very, very low temperatures. The former is an important point as well since individual logical qubits in a quantum computing system must be composed of several individual physical qubits due to decoherence and other error-inducing aspects of maintaining and manipulating physical qubit systems. The reduced error correction overhead required by IONQs hardware suggests that the firms technology may ultimately yield to smaller, more practical systems. If you have read about quantum computing firms introducing quantum computing machines with larger and larger amounts of qubits, that is in part driven by the need to compensate for a single logical qubit with many physical qubits.

Figure 6: Expected Phases of Quantum Computing Maturity (IonQ Investor Updates Presentation March 2022)

Finally, the company also details that they have solved, or may be on the path to solving, certain engineering and manufacturing challenges typically associated with trapped-ion technology, thus affording the firm something of a competitive moat versus other players seeking to build competing quantum computing systems based on trapped ion technology.

3. IONQs backing includes leading academic and governmental research entities, as well as premier technology investors. IONQ as a business entity was born in 2015 with $2M in seed funding from New Enterprise Associates, with enabling technologies based on its founders research activities at Duke University and University of Maryland. The companys subsequent funding rounds included Google Ventures, Amazon Web Services, and Samsung as investors. I think we can all agree that the prior entities hardly seem like the type that would suffer fools; and therefore IONQs investor base lends credence to the (potential) viability of their technological approach as discussed in the point above, although these investors are likely to bet on multiple approaches versus a single one. Nonetheless, IONQ more recently announced they were selected by the Defense Advanced Research Projects Agency (DARPA) as the only quantum computing hardware vendor to participate on a multi-million dollar quantum benchmark project with the intent to establish reliable metrics by which to compare the power of different quantum computing systems. This too, I think, must say something (positive) about the firms technological path.

Of course, I would be remiss not to discuss negative points and observations; and I thus offer the following counter-arguments against a play in the firm.

1. No one knows what technology might win. While IONQ lays out a compelling story around their trapped-ion technology for quantum computing, no one really knows what technology (or technologies) will win in the end. After all, if it was obvious that trapped-ion technology is a superior path, every other player would have switched to that approach by now.

2. IONQ has virtually non-existent revenues as compared to its market cap. IONQs net revenue for FY 21 stood at just over ~$2M. The good news is that sales growth is trending in the right direction, with the company recording $2M in net sales in Q1 FY 22 alone, along with $4.2M in total bookings. The revenue forecast for FY 22 is in the range of $10.2M to $10.7M. Readers can do the math: with ~198M shares outstanding, the high end of the FY 22 forecast range produces a P/S multiple above 90 using the current share price.

3. Forecasts for the quantum computing market are questionable at best. IONQ references a Prescient and Strategic Intelligence report from February 2020 when identifying their TAM forecast of $65B by 2030 in Figure 3. The actual report, which I believe to be this one, appears to offer a different forecast for the quantum computing market; so, I am not exactly clear how IONQ derived the estimate listed in the prior graphic. Regardless, with no one even sure if practical quantum computing is even possible, any forecast must obviously be taken with a grain of salt.

IONQ is attempting to tackle what may ultimately prove impossible: practical quantum computing may be prohibited by nature itself, which I noted in a prior article on the subject.

As I mentioned, IONQs market capitalization is just below $1B as I write this. Is this valuation fair? This is going to sound like a cop-out, but I honestly have no idea. How do you value something that could be worth $0, if practical quantum computing proves infeasible, or be worth an amount beyond your wildest dreams if practical quantum computing is feasible and IONQ happens to have the technology that is going to win?

I hypothesized in the introduction that most investors in IONQ must know that their investment is necessarily speculative. On that basis, I would think a Hold recommendation is logical since we, as investors, can only sit back and watch how the story in quantum computing unfolds. A word of caution, however. I was reading an article some time ago by Scott Aaronson, another leading mind in the world of quantum computing, who said (paraphrasing) that it would be a shame to find out that any given scientist (like him) spent most of their life chasing a computing paradigm (i.e. practical quantum computing) and that paradigm turns out to be impossible. But, lest I end this analysis on a bad note, Mr. Aaronson offered in that same article that scientific evidence hints that practical computing may be possible.

I concede that IONQ does not fit my personal investing strategy as I am hesitant to jump on a firm whose future is somewhat binary (i.e. worth nothing or worth everything). That being said, I find their story and technology compelling. Should the stock suffer another steep drop for whatever reason I might be inclined to buy a few shares, but purely on a speculative basis.

P.S. If you got this far, thanks for reading. The nerdy title reference I made in the second section was with respect to bra-ket notation, which is used within quantum computing and quantum mechanics to describe quantum states.

More here:
IonQ Stock: Building The Future Of Computing And Is Only $5/Share - Seeking Alpha

If the future influenced the past, that would be retrocausality. As Victor Bhaura puts it,

Retrocausality means that, when an experimenter chooses the measurement setting with which to measure a particle, that decision can influence the properties of that particle (or another one) in the past, even before the experimenter made their choice. In other words, a decision made in the present can influence something in the past.

Bhaura reminds us of a limerick called Relativity from 1923:

There was a young lady named BrightWhose speed was far faster than light;She set out one dayIn a relative wayAnd returned on the previous night.

Now, if Bright was exceeding the speed of light, she was already violating the laws of physics for entities as large as ourselves and she could well end up going backward in time, according to philosopher of mathematics Sam Baron.

But, as Bhaura has noted, quantum particles do not follow such rules. In 2019, scientists showed that time travel is theoretically possible by sending a simulated particle back in time via a quantum computer. A quantum computer doesnt use 1s and 0s (bits) but rather qubits, which are simultaneously 1s and 0s. Thats much faster. Yes, quantum systems can do that. Its why Albert Einstein called them spooky.

Since quantum mechanics is about probability (not certainty), success was no guarantee. However, in a two-qubit quantum computer, the algorithm managed a time jump an impressive 85 percent of the time. When it was upped to three qubits, the success rate dropped to about 50 percent, which the authors attributed to imperfections in current quantum computers.

The particle was simulated because the amount of force required to send an actual particle back in time exceeded natural capabilities:

This experiment also shows us that sending even a simulated particle back in time requires serious outside manipulation. To create such an external force to manipulate even one physical particles quantum waves is well beyond our abilities.

We demonstrate that time-reversing even ONE quantum particle is an unsurmountable task for nature alone, study author Vinokur wrote to the New York Times in an email [emphasis original]. The system comprising two particles is even more irreversible, let alone the eggs comprising billions of particles we break to prepare an omelet.

Thats the reason that time travel into the past, as in H. G. Wellss The Time Machine, is impractical. It may also be futile if the object is to change anything because that is unlikely to be possible.

Meanwhile, in 2021, another team of physicists offered calculations proposing that quantum particles can move forward as well as backward in time again because of quantum superposition:

According to the principle of quantum superposition, individual units ( for instance, of light) can exist in two states at once, both as waves and particles, manifesting as one or the other depending on what youre testing. Rubinos team looked at a quantum superposition with a state that evolves both backward and forward in time. Measurements showed that more often than not, the system ended up moving forward in time. But for small entropy changes, the system could actually continue to evolve both forward and backward in time.

The paper is open access.

Team leader Giulia Rubio stresses, that still wouldnt move us. But there may be another way, as we shall see Christian apologist C.S. Lewis (18981963), who read and wrote science fiction, pointed out that the present and future can change the past. If we assume that God exists and God is not in time, an action taken now could influence an event in the past. He offers an illustration:

When we are praying about the result, say, of a battle or a medical consultation the thought will often cross our minds that (if only we knew it) the event is already decided one way or the other. I believe this to be no good reason for ceasing our prayers. The event certainly has been decided in a sense it was decided before all worlds. But one of the things taken into account in deciding it, and therefore one of the things that really cause it to happen, may be this very prayer that we are now offering.

Thus, shocking as it may sound, I conclude that we can at noon become part causes of an event occurring at ten oclock. (Some scientists would find this easier than popular thought does.) The imagination will, no doubt, try to play all sorts of tricks on us at this point. It will ask, Then if I stop praying can God go back and alter what has already happened? No. The event has already happened and one of its causes has been the fact that you are asking such questions instead of praying. It will ask, Then if I begin to pray can God go back and alter what has already happened? No. The event has already happened and one of its causes is your present prayer. Thus something does really depend on my choice. My free act contributes to the cosmic shape. That contribution is made in eternity or before all worlds; but my consciousness of contributing reaches me at a particular point in the time-series.

There is another way in which the present can change the past. Suppose a woman has made rather a mess of her life and reaches a crisis point. Two possibilities: 1. She gives up and sinks further into misery and despair. 2. She decides to seek help and, on getting it, turns her life around becoming, in time, a support to others.

As she looks back on her life in the first scenario, she will see a bleak, grim born to lose picture, punctuated by disasters, the worst of which was perhaps that crisis point, after which she just gave up

In the second scenario, looking back from some years distance, she sees a very different past: That crisis point is the moment I decided, I to do whatever it takes to free myself! All the other events of note are now remembered as steps, forward or backward, on a journey to a more meaningful life.

Perhaps thats one of the roles that free will plays in our lives. It changes the past not by changing the events but by making them mean different things. And after all, the main reason we care about the past is its meaning. So there is a sense this sense in which we can really travel back and change the past, by changing its meaning.

You may also wish to read:

A form of time travel that might be possible In world of entropy, time runs in one direction and reversing it would create impossible contradictions, physicists say. The time travel that is likely to be possible would be like having a very good four-dimensional memory it recreates events but it doesnt change them.

See original here:
Can the Future Reach Back and Affect the Past? - Walter Bradley Center for Natural and Artificial Intelligence

QuantLR Ltd, an Israel-based Quantum Key Distribution (QKD) company, and MedOne, a leading Israeli data center service provider, have announced the successfuloperationofQuantLRs QKD system with MedOnes Data Centerinfrastructurebetween the cities ofTel Aviv andPetah Tikva.

Quantum Key Distribution (QKD) is the onlyproven technology that provides the ultimate level of security fordata in transit, includingsecurity against any attack or eavesdropping attempts by contemporary, future, classical or quantum-based computers. Another threat that is secured by QKD is a hack now- decrypt later attack where the attacker collects the data now and decrypt in a later stage. This puts a sense of urgency in the implementation of QKD.

This quantum-based technology isespeciallyimportant in a data center environment to secure the information to and from the data center, between data centers, and within the data center itself.

The announcement comes following the recent successful testthat was conducted between the MedOne Tel Aviv and MedOne Petah Tikva facilities, over a distance of more than 35km (21.7 miles). Earlier this year QuantLR managed to exchange keys over longer distances.

The test was led by Dr. Nitzan Livneh, QuantLRs CTO, and Eli Saig, MedOnes CTO.

A single fiber strand was used to carry the quantum information as well as C-band data channels, enabling quantum-safe communication for clients without dark fiber. The system created more than ten 256bit symmetric encryption keys per second, without any flaws.

A QKD solution at an affordable price is critical to solve a major upcoming problem: todays networksecurityrelies on public keycryptographythatishighly vulnerable to cracking. The vast majority of encryption keys in the commercial world are distributed via PKI, but new algorithms and advances in quantum computing will soon provide the capabilities to crack most PKI instances, including RSAand Diffie Hellman methods. This issue is well-known, and Quantum Key Distribution is widely considered the most secure solution for long-term data security, as conventional security solutions approach their end-of-life.

We are delighted to collaborate with a leading data center service provider such as MedOne. Data Centers are a very important use case for QKD and we see an increasing demand from leading players in this market, notesDr. Nitzan Livneh, CTO of QuantLR

Data security has become the most important aspect in a data center offering, and we are planning to be the first data center service provider worldwide that will offer a QKD solution to secure its clients data noted Ronnie Sadeh, CEO of MedOne.

AboutQuantLR:Headquartered in Israel, QuantLRaims to provide versatile cost-effective quantum cryptographic solutions based on quantum key distribution (QKD)technology to protect communicated data. This solution is proven to provide the ultimate level of security against any attack by contemporary, future, classical or quantum-based computers. QuantLRs solutions will be offered to the market as a component embedded within communication hardware vendor products, as well as stand-alone products.

About MedOne:MedOne leads Israels data center market, providing comprehensive hosting services to Israels largest organizations. With several underground data centers spanning over 16,000 square meters (172,000 square feet), MedOne provides hosting, backup and business continuity services with the highest SLA, resiliency and the best standard of security.

QuantLR Contact

Shlomi Cohen, shlomi[at]quantlr.com

Original post:
QuantLR Partners With MedOne to Test and Validate a QKD Solution to Protect Against Quantum Computer Attacks - StartupHub.ai

Proposed quantum computer implementation

A trapped ion quantum computer is one proposed approach to a large-scale quantum computer. Ions, or charged atomic particles, can be confined and suspended in free space using electromagnetic fields. Qubits are stored in stable electronic states of each ion, and quantum information can be transferred through the collective quantized motion of the ions in a shared trap (interacting through the Coulomb force). Lasers are applied to induce coupling between the qubit states (for single qubit operations) or coupling between the internal qubit states and the external motional states (for entanglement between qubits).[1]

The fundamental operations of a quantum computer have been demonstrated experimentally with the currently highest accuracy in trapped ion systems. Promising schemes in development to scale the system to arbitrarily large numbers of qubits include transporting ions to spatially distinct locations in an array of ion traps, building large entangled states via photonically connected networks of remotely entangled ion chains, and combinations of these two ideas. This makes the trapped ion quantum computer system one of the most promising architectures for a scalable, universal quantum computer. As of April 2018, the largest number of particles to be controllably entangled is 20 trapped ions.[2][3][4]

The first implementation scheme for a controlled-NOT quantum gate was proposed by Ignacio Cirac and Peter Zoller in 1995,[5] specifically for the trapped ion system. The same year, a key step in the controlled-NOT gate was experimentally realized at NIST Ion Storage Group, and research in quantum computing began to take off worldwide.[citation needed]

In 2021, researchers from the University of Innsbruck presented a quantum computing demonstrator that fits inside two 19-inch server racks, the world's first quality standards-meeting compact trapped ion quantum computer.[7][6]

The electrodynamic ion trap currently used in trapped ion quantum computing research was invented in the 1950s by Wolfgang Paul (who received the Nobel Prize for his work in 1989[8]). Charged particles cannot be trapped in 3D by just electrostatic forces because of Earnshaw's theorem. Instead, an electric field oscillating at radio frequency (RF) is applied, forming a potential with the shape of a saddle spinning at the RF frequency. If the RF field has the right parameters (oscillation frequency and field strength), the charged particle becomes effectively trapped at the saddle point by a restoring force, with the motion described by a set of Mathieu equations.[1]

This saddle point is the point of minimized energy magnitude, | E ( x ) | {displaystyle |E(mathbf {x} )|} , for the ions in the potential field.[9] The Paul trap is often described as a harmonic potential well that traps ions in two dimensions (assume x ^ {displaystyle {hat {x}}} and y ^ {displaystyle {widehat {y}}} without loss of generality) and does not trap ions in the z ^ {displaystyle {widehat {z}}} direction. When multiple ions are at the saddle point and the system is at equilibrium, the ions are only free to move in z ^ {displaystyle {widehat {z}}} . Therefore, the ions will repel each other and create a vertical configuration in z ^ {displaystyle {widehat {z}}} , the simplest case being a linear strand of only a few ions.[10] Coulomb interactions of increasing complexity will create a more intricate ion configuration if many ions are initialized in the same trap.[1] Furthermore, the additional vibrations of the added ions greatly complicate the quantum system, which makes initialization and computation more difficult.[10]

Once trapped, the ions should be cooled such that k B T z {displaystyle k_{rm {B}}Tll hbar omega _{z}} (see Lamb Dicke regime). This can be achieved by a combination of Doppler cooling and resolved sideband cooling. At this very low temperature, vibrational energy in the ion trap is quantized into phonons by the energy eigenstates of the ion strand, which are called the center of mass vibrational modes. A single phonon's energy is given by the relation z {displaystyle hbar omega _{z}} . These quantum states occur when the trapped ions vibrate together and are completely isolated from the external environment. If the ions are not properly isolated, noise can result from ions interacting with external electromagnetic fields, which creates random movement and destroys the quantized energy states.[1]

The full requirements for a functional quantum computer are not entirely known, but there are many generally accepted requirements. David DiVincenzo outlined several of these criterion for quantum computing.[1]

Any two-level quantum system can form a qubit, and there are two predominant ways to form a qubit using the electronic states of an ion:

Hyperfine qubits are extremely long-lived (decay time of the order of thousands to millions of years) and phase/frequency stable (traditionally used for atomic frequency standards).[10] Optical qubits are also relatively long-lived (with a decay time of the order of a second), compared to the logic gate operation time (which is of the order of microseconds). The use of each type of qubit poses its own distinct challenges in the laboratory.

Ionic qubit states can be prepared in a specific qubit state using a process called optical pumping. In this process, a laser couples the ion to some excited states which eventually decay to one state which is not coupled to the laser. Once the ion reaches that state, it has no excited levels to couple to in the presence of that laser and, therefore, remains in that state. If the ion decays to one of the other states, the laser will continue to excite the ion until it decays to the state that does not interact with the laser. This initialization process is standard in many physics experiments and can be performed with extremely high fidelity (>99.9%).[11]

The system's initial state for quantum computation can therefore be described by the ions in their hyperfine and motional ground states, resulting in an initial center of mass phonon state of | 0 {displaystyle |0rangle } (zero phonons).[1]

Measuring the state of the qubit stored in an ion is quite simple. Typically, a laser is applied to the ion that couples only one of the qubit states. When the ion collapses into this state during the measurement process, the laser will excite it, resulting in a photon being released when the ion decays from the excited state. After decay, the ion is continually excited by the laser and repeatedly emits photons. These photons can be collected by a photomultiplier tube (PMT) or a charge-coupled device (CCD) camera. If the ion collapses into the other qubit state, then it does not interact with the laser and no photon is emitted. By counting the number of collected photons, the state of the ion may be determined with a very high accuracy (>99.9%).[citation needed]

One of the requirements of universal quantum computing is to coherently change the state of a single qubit. For example, this can transform a qubit starting out in 0 into any arbitrary superposition of 0 and 1 defined by the user. In a trapped ion system, this is often done using magnetic dipole transitions or stimulated Raman transitions for hyperfine qubits and electric quadrupole transitions for optical qubits. The term "rotation" alludes to the Bloch sphere representation of a qubit pure state. Gate fidelity can be greater than 99%.

The rotation operators R x ( ) {displaystyle R_{x}(theta )} and R y ( ) {displaystyle R_{y}(theta )} can be applied to individual ions by manipulating the frequency of an external electromagnetic field from and exposing the ions to the field for specific amounts of time. These controls create a Hamiltonian of the form H I i = / 2 ( S + exp ( i ) + S exp ( i ) ) {displaystyle H_{I}^{i}=hbar Omega /2(S_{+}exp(iphi )+S_{-}exp(-iphi ))} . Here, S + {displaystyle S_{+}} and S {displaystyle S_{-}} are the raising and lowering operators of spin (see Ladder operator). These rotations are the universal building blocks for single-qubit gates in quantum computing.[1]

To obtain the Hamiltonian for the ion-laser interaction, apply the JaynesCummings model. Once the Hamiltonian is found, the formula for the unitary operation performed on the qubit can be derived using the principles of quantum time evolution. Although this model utilizes the rotating wave approximation, it proves to be effective for the purposes of trapped-ion quantum computing.[1]

Besides the controlled-NOT gate proposed by Cirac and Zoller in 1995, many equivalent, but more robust, schemes have been proposed and implemented experimentally since. Recent theoretical work by JJ. Garcia-Ripoll, Cirac, and Zoller have shown that there are no fundamental limitations to the speed of entangling gates, but gates in this impulsive regime (faster than 1 microsecond) have not yet been demonstrated experimentally. The fidelity of these implementations has been greater than 99%.[12]

Quantum computers must be capable of initializing, storing, and manipulating many qubits at once in order to solve difficult computational problems. However, as previously discussed, a finite number of qubits can be stored in each trap while still maintaining their computational abilities. It is therefore necessary to design interconnected ion traps that are capable of transferring information from one trap to another. Ions can be separated from the same interaction region to individual storage regions and brought back together without losing the quantum information stored in their internal states. Ions can also be made to turn corners at a "T" junction, allowing a two dimensional trap array design. Semiconductor fabrication techniques have also been employed to manufacture the new generation of traps, making the 'ion trap on a chip' a reality. An example is the quantum charge-coupled device (QCCD) designed by D. Kielpinski, C. Monroe, and D.J. Wineland.[13] QCCDs resemble mazes of electrodes with designated areas for storing and manipulating qubits.

The variable electric potential created by the electrodes can both trap ions in specific regions and move them through the transport channels, which negates the necessity of containing all ions in a single trap. Ions in the QCCD's memory region are isolated from any operations and therefore the information contained in their states is kept for later use. Gates, including those that entangle two ion states, are applied to qubits in the interaction region by the method already described in this article.[13]

When an ion is being transported between regions in an interconnected trap and is subjected to a nonuniform magnetic field, decoherence can occur in the form of the equation below (see Zeeman effect).[13] This is effectively changes the relative phase of the quantum state. The up and down arrows correspond to a general superposition qubit state, in this case the ground and excited states of the ion.

| + | exp ( i ) | + | {displaystyle left|uparrow rightrangle +left|downarrow rightrangle longrightarrow exp(ialpha )left|uparrow rightrangle +left|downarrow rightrangle }

Additional relative phases could arise from physical movements of the trap or the presence of unintended electric fields. If the user could determine the parameter , accounting for this decoherence would be relatively simple, as known quantum information processes exist for correcting a relative phase.[1] However, since from the interaction with the magnetic field is path-dependent, the problem is highly complex. Considering the multiple ways that decoherence of a relative phase can be introduced in an ion trap, reimagining the ion state in a new basis that minimizes decoherence could be a way to eliminate the issue.

One way to combat decoherence is to represent the quantum state in a new basis called the decoherence-free subspaces, or DFS., with basis states | {displaystyle left|uparrow downarrow rightrangle } and | {displaystyle left|downarrow uparrow rightrangle } . The DFS is actually the subspace of two ion states, such that if both ions acquire the same relative phase, the total quantum state in the DFS will be unaffected.[13]

Trapped ion quantum computers theoretically meet all of DiVincenzo's criteria for quantum computing, but implementation of the system can be quite difficult. The main challenges facing trapped ion quantum computing are the initialization of the ion's motional states, and the relatively brief lifetimes of the phonon states.[1] Decoherence also proves to be challenging to eliminate, and is caused when the qubits interact with the external environment undesirably.[5]

The controlled NOT gate is a crucial component for quantum computing, as any quantum gate can be created by a combination of CNOT gates and single-qubit rotations.[10] It is therefore important that a trapped-ion quantum computer can perform this operation by meeting the following three requirements.

First, the trapped ion quantum computer must be able to perform arbitrary rotations on qubits, which are already discussed in the "arbitrary single-qubit rotation" section.

The next component of a CNOT gate is the controlled phase-flip gate, or the controlled-X gate (see quantum logic gate). In a trapped ion quantum computer, the state of the center of mass phonon functions as the control qubit, and the internal atomic spin state of the ion is the working qubit. The phase of the working qubit will therefore be flipped if the phonon qubit is in the state | 1 {displaystyle |1rangle } .

Lastly, a SWAP gate must be implemented, acting on both the ion state and the phonon state.[1]

Two alternate schemes to represent the CNOT gates are presented in Michael Nielsen and Isaac Chuang's Quantum Computation and Quantum Information and Cirac and Zoller's Quantum Computation with Cold Trapped Ions.[1][5]

Link:
Trapped ion quantum computer - Wikipedia

Quantum Computing Inc.

QAmplify Maximizes End-User Investment in Quantum Computing

LEESBURG, Va., June 07, 2022 (GLOBE NEWSWIRE) -- Quantum Computing Inc. (QCI'' or the Company) (NASDAQ: QUBT), a leader in accessible quantum computing, today unveiled QAmplify, a suite of quantum software technologies that expands the processing power of any current quantum computer by as much as 20x. QAmplify is capable of supercharging any quantum computer to solve real-world realistic business problems today. The Company is actively working with customers and partners in scaling the amplification capabilities of its ready-to-run Qatalyst software, which is designed to eliminate the need for complex quantum programming and runs seamlessly across a variety of quantum computers. QCI has filed for patents on QAmplify technology.

Currently there are two primary technology approaches that deliver a wide range of capabilities spanning the current Quantum Processing Unit (QPU) hardware landscape; gate model (e.g. IBM, IonQ, Rigetti, OQC, etc.) and annealing (e.g. D-Wave) quantum computers. Both are limited in the size of problems (i.e., number of variables and complexity of computations) they can process. For example, gate models can typically process from 10-120 data variables, and annealing machines can process approximately 400 variables in a simple problem set. These small problem sets restrict the size of the problems that can be solved by todays QPUs, limiting businesses ability to explore the value of quantum computing.

QCIs patent-pending QAmplify suite of powerful QPU-expansion software technologies overcomes these challenges, dramatically increasing the problem set size that each can process. The QAmplify gate model expansions demonstrated capabilities have been benchmarked at a 500% (5x) increase and the annealing expansion has been benchmarked at up to a 2,000% (20x) increase.

QAmplify maximizes end-user investment in current QPUs by allowing quantum users to transform from science experiments to solving real-world problems without waiting for the quantum hardware industry to catch up. For example, in terms of real-world applications, this means that an IBM quantum computer with QAmplify could solve a problem with over 600 variables, versus the current limit of 127 variables. A D-Wave annealing computer with QAmplify could solve an optimization with over 4,000 variables, versus the current limit of 200 for a dense matrix problem set.

Story continues

It is central to QCIs mission to deliver practical and sustainable value to the quantum computing industry, said William McGann, Chief Operating and Technology Officer of QCI. QCIs innovative software solutions deliver expansive compute capabilities for todays state-of-the-art QPU systems and offer great future scalability as those technologies continually advance. The use of our QAmplify algorithm in the 2021 BMW Group Quantum Computing Challenge for vehicle sensor optimization provided proof of performance by expanding the effective capability of the annealer by 20-fold, to 2,888 qubits.

To learn more about QCI and how Qatalyst can deliver results for your business today, visit http://www.quantumcomputinginc.com.

About Quantum Computing Inc.Quantum Computing Inc. (QCI) (NASDAQ: QUBT) is a full-spectrum quantum software and hardware company on a mission to accelerate the value of quantum computing for real-world business solutions. The company recently announced its intent to acquire QPhoton, a quantum photonics innovation company that has developed a series of quantum photonic systems (QPS). The combination of QCIs flagship ready-to-run software product, Qatalyst, with QPhotons QPS, sets QCI on a path to delivering a broadly accessible and affordable full-stack quantum solution that can be used by non-quantum experts, anywhere, for real-world industry applications. QCIs expert team in finance, computing, security, mathematics and physics has over a century of experience with complex technologies; from leading edge supercomputing, to massively parallel programming, to the security that protects nations. Connect with QCI on LinkedIn and @QciQuantum on Twitter. For more information about QCI, visit http://www.quantumcomputinginc.com.

Important Cautions Regarding Forward-Looking StatementsThis press release contains forward-looking statements as defined within Section 27A of the Securities Act of 1933, as amended, and Section 21E of the Securities Exchange Act of 1934, as amended. By their nature, forward-looking statements and forecasts involve risks and uncertainties because they relate to events and depend on circumstances that will occur in the near future. Those statements include statements regarding the intent, belief or current expectations of Quantum Computing Inc. (the Company), and members of its management as well as the assumptions on which such statements are based. Prospective investors are cautioned that any such forward-looking statements are not guarantees of future performance and involve risks and uncertainties, and that actual results may differ materially from those contemplated by such forward-looking statements.

Statements in this press release that are not descriptions of historical facts are forward-looking statements relating to future events, and as such all forward-looking statements are made pursuant to the Securities Litigation Reform Act of 1995. Statements may contain certain forward-looking statements pertaining to future anticipated or projected plans, performance and developments, as well as other statements relating to future operations and results. Any statements in this press release that are not statements of historical fact may be considered to be forward-looking statements. Words such as "may," "will," "expect," "believe," "anticipate," "estimate," "intends," "goal," "objective," "seek," "attempt," aim to, or variations of these or similar words, identify forward-looking statements. Such statements include statements regarding the Companys ability to consummate its planned acquisition of QPhoton, the anticipated benefits of such acquisition, and the Companys ability to successfully develop, market and sell its products. Factors that could cause actual results to differ materially from those in the forward-looking statements contained in this press release include, but are not limited to, the parties potential inability to consummate the proposed transaction, including as a result of a failure to satisfy closing conditions to the proposed transactions; risks that QPhoton will not be integrated successfully; failure to realize anticipated benefits of the combined operations; potential litigation relating to the proposed transaction and disruptions from the proposed transaction that could harm the Companys or QPhotons business; ability to retain key personnel; the potential impact of announcement or consummation of the proposed transaction on relationships with third parties, including customers, employees and competitors; conditions in the capital markets; and those risks described in Item 1A in the Companys Annual Report on Form 10-K for the year ended December 31, 2021, which is expressly incorporated herein by reference, and other factors as may periodically be described in the Companys filings with the SEC. The Company undertakes no obligation to update or revise forward-looking statements to reflect changed conditions.

Qatalyst is the trademark of Quantum Computing Inc. All other trademarks are the property of their respective owners.

Company Contact:Robert Liscouski, CEOQuantum Computing, Inc.+1 (703) 436-2161Email Contact

Investor Relations Contact:Ron Both or Grant StudeCMA Investor Relations+1 (949) 432-7566Email Contact

Media Relations Contact:Seth MenackerFusion Public Relations+1 (201) 638-7561qci@fusionpr.com

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Quantum Computing Inc. Unveils Software Breakthrough That Amplifies Quantum Computer Processing Power By Up to 20x - Yahoo Finance