Nat. Phys. Intermediate circuit measurements demonstrate quantum computing advantages

The ability to make measurements in the middle of a quantum circuit is a powerful resource - one that underpins a wide range of applications from remote state preparation to quantum error correction.

 

In an article published Aug. 3 in Nature Physics, a team of researchers from the National Institute of Standards and Technology (NIST), the University of Maryland, and the University of California, Berkeley, used IonQ's quantum computers to apply intermediate-circuit measurements to a special task: demonstrating the advantages of quantum computing.

 

 

"Interactive cryptographic proofs of quantumness using mid-circuit measurements."

 

The goal of such a demonstration is to allow a quantum device to perform a computational task that would not be feasible for a classical device with comparable resources. The distinguishing feature of the experimental team's approach, compared to existing demonstrations, is that the classical verification process is efficient both in terms of asymptotic complexity and in practice; and, this approach can be applied to a range of interactive quantum protocols.

 

To date, experimental quantum computation has largely operated in a non-interactive mode: i.e., classical data is extracted from the computation only at the last step. While this has led to many exciting advances, in practice it is clear that the interactivity enabled by intermediate circuit measurements performed on quantum devices is critical to the operation of useful quantum computers.

 

For example, in quantum error correction, projective intermediate circuit measurements are used to transform a range of possible errors into a specific discrete set of correctable errors, as demonstrated in a recent experiment. Certain quantum machine learning algorithms also use middle-circuit measurements to introduce fundamental nonlinearities; recent research has shown that interaction is much more than that: it has become an indispensable tool for verifying the behavior of untrusted quantum devices, and even for testing the fundamentals of quantum mechanics itself.

 

Interactive proofs have now been shown to verify many practical quantum tasks, including random number generation, remote quantum state preparation, and delegating computation to untrusted quantum servers. Perhaps the most immediate application of interactive protocols is "cryptographic proof of quantumness," which allows a quantum device to convincingly prove its nonclassical behavior to a polynomial-time classical verifier by performing a task that assumes computationally intractable for classical machines, but effective for checking.

 

In general, the simplest proof of quantumness is the Bell test (which does not rely on the computational difficulty assumption). It uses entanglement to produce correlations that are impossible to reproduce by classical methods in the absence of communication. While the simplicity of the Bell test is appealing, avoiding communication loopholes requires the use of multiple quantum devices at considerable distances apart. Demonstrating the quantum nature of a "black box" quantum device that hides its inner workings from the verifier can rely on the difference between classical and quantum computing power; in other words, the device is required to demonstrate its quantum computational superiority.

 

Unlike recent sampling-based tests of quantum computational dominance, in cryptographic proofs of quantumness, the verification step must also be efficient. While in principle any algorithm that shows quantum speed and has an efficient verifiable output could be used for this purpose, most such experiments are currently not feasible because the circuitry required is too large to run successfully on current quantum computers. Notably, it has been shown that interactive proofs provide a way to reduce the experimental cost (in terms of quantum bits and gate depth) of such tests while maintaining efficient verification and classical difficulty.

 

In practice, the experimental realization of interactivity is extremely challenging. It requires the ability to independently measure a subset of quantum bits in the middle of a quantum circuit and to continue the coherent evolution after the measurement. Unfortunately, the measurement of a target quantum bit usually interferes with neighboring quantum bits, thus degrading the quality of the computation after the midway measurement. One solution is to spatially isolate the target quantum bit by shuttling, which has some commonality among atomic quantum computing platforms. Although experimental progress in coherent quantum bit shuttling is daunting from a quantum control perspective, it opens the door not only to interactivity but also to unique information processing architectures.

 

 

Schematic of an interactive quantum verification protocol. The goal of the verifier is to test the "quantumness" of the prover by exchanging classical information. At the beginning of the protocol, the verifier sends an instance of TCF to the prover. By applying this function to a superposition of all possible inputs and projectively measuring the result, the prover commits to a particular quantum state |x0⟩+|x1⟩ . The subsequent challenge issued by the verifier specifies how that state can be measured and can effectively verify the commitment of the prover.The LWE protocol requires two rounds of interactions, while the factorization protocol requires an additional round (green box).

 

In this work, the experimental team implemented two complementary interacting quantum sex cryptographic proof protocols, using circuits with up to 145 gates, on a captured ion quantum computer with up to 11 quantum bits.

 

 

Intermediate circuit measurements. a-c, Schematic diagram of the intermediate circuit measurement scheme. a, Initially, the ions are closely spaced in a one-dimensional chain above the surface well. Coherent gates are achieved by a combination of individual addressing beams (purple) and global beams (not shown). b, By adjusting the electrodes of the surface trap, scientists can adjust the potential to split the ion chain deterministically into two or three separate segments, depending on the scheme. c, Once the segments are far enough apart, measurements are made without interfering with the coherence of the remaining ions (blue beams) individual segments. d, Fluorescence image of an example shuttle protocol for 15 ion chains. Initially, the average spacing between the ions is about 4 μm. at the end of the splitting process, the distance between the two segments is about 550 μm. the image shows a splitting distance of about 140 μm, at which point the two subchains reach the edge of the detection beam.

 

The interaction between the verifier and the prover is realized by experiments in which intermediate circuit measurements are performed on some of the quantum bits.

 

The first protocol, which involves two rounds of interaction, is based on the Learning by Error (LWE) problem, which enables particularly simple measurement schemes. The second protocol does not require this special property and is therefore suitable for more general cryptographic functions; here, functions from the Rabin cryptosystem (which is a modification of RSA) are used. By using additional interaction wheels, the encrypted information is condensed into the state of a single quantum bit.

 

This makes it possible to realize a quantum proof of encryption: a proof that is as hard to spoof as a classical factorization, but whose asymptotic scaling of the relevant circuits is much simpler than Shore's algorithm.

 

Then, to realize an interactive cryptographic proof of quantumness, the experimental team designed quantum circuits for LWE and factorization protocols. For the experiment, the team implemented these two interactive protocols using a captured-ion quantum computer with a base chain length of 15 ions. Each 171Yb+ ion has one quantum bit encoded in a pair of hyperfine stages. The quantum circuit was realized by successive applications of local single- and double-quantum-bit gates, using separate optical addressing: to achieve fast, continuous double-quantum-bit interactions, the team placed the ions in a single, closely spaced linear chain.

 

In the demonstration, the quantum bits play the role of "verifier", while the classical system plays the role of "controller". In this way, the experimental team was able to compile the verifier's decisions into the classical controller before executing the quantum circuit.

 

As with the Bell test, even the classical controller can pass the verifier's challenge with finite probability. If the classical controller cannot find a "point" in the TCF (which is assumed to be the case for a sufficiently large problem), then this probability is bounded by an asymptotic "classical threshold" that the quantum verifier must exceed in order to prove their superiority.

 

In this experiment, the team performed multiple instances of the LWE protocol for different matrices A and noise vectors e; for each possible choice of the verifier, the experiment was repeated about 103 times to collect statistics. This resulted in the experimental probabilities pA and pB, which confirmed that the quantum verifier exceeded the asymptotic classical threshold in all cases.

 

 

Circuit and experimental results. a, Circuit diagram of the LWE protocol; d, Circuit diagram of the factorization protocol.

 

Indeed, demonstrating the advantages of quantum computing through interactive protocols faces two major experimental challenges: (1) integrating intermediate circuit measurements into arbitrary quantum circuits with high enough overall fidelity to pass the verifier's test, and (2) scaling the protocols to problems large enough that breaking the cryptographic assumptions is classically infeasible.

 

In this work, the experimental team overcame the first hurdle: successfully implementing two interactive cryptographic proofs of quantum sex with fidelity sufficient to pass the verifier's challenge. Regarding subsequent development, the team said, "We left the second challenge, how to scale up these protocols, for future work. We estimate that cryptographic proof of the advantages of quantum computing can be accomplished using about 1,600 quantum bits."

 

"There are many other interesting directions that may result from our work. The obvious next step is to apply the power of quantum interaction protocols to realize additional quantum advantages, such as certifiable random number generation, remote state preparation, and verification of arbitrary quantum computation, among other tasks."

 

"Finally, with the advent of some platform intermediate circuit measurement capabilities, one can explore new phenomena such as entangled phase transitions as well as demonstrating quantum error correction."

 

Reference link:

[1] https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.041058

[2]https://ionq.com/resources/publications

[3]https://paper.sciencenet.cn/htmlpaper/2023/8/20238523531174284114.shtm