arXiv subjects

Ben W. Reichardt

Publications and source records attributed to Ben W. Reichardt.

At least 19 recordsLinked to original sources

arXiv2026

Fire and ice: Partially fault-tolerant quantum computing with selective state filtering

We develop an error-corrected quantum computation scheme based on concatenating the five-qubit Laflamme code onto the four-qubit Iceberg code. The approach skates a thin line: it is explicitly not fault tolerant, risking higher logical error rates, and it relies on selective filtering to prepare encoded states for error correction, risking significant overhead. Yet, at realistic simulated noise rates, the scheme is reliable and resource efficient. It forges a practical path toward scalable quantum computation.

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arXiv2025

A Topologically Fault-Tolerant Quantum Computer with Four Dimensional Geometric Codes

Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional self-correcting quantum memory, and present codes targeted to both near-term and utility-scale quantum computers. We identify a full set of logical Clifford operations and with it design a universal fault-tolerant quantum architecture. Our design achieves single-shot error correction, significant reductions in required qubits, and low-depth logical operations. In turn, our proposed architecture relaxes the requirements for achieving fault tolerance and offers an efficient path for realization in several near-term quantum hardware implementations. Our [[96,6,8]] 4D Hadamard lattice code has low weight-6 stabilizers and depth-8 syndrome extraction circuits, a high pseudo-threshold of $\sim 0.01$, and a logical error rate of $\sim 10^{-6}$ per logical qubit per round of error correction at $10^{-3}$ physical error rate under a standard circuit-level noise model. A Clifford-complete logical gate set is presented, including a constructive and efficient method for Clifford gate synthesis.

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arXiv2025

Fault-tolerant quantum computation with a neutral atom processor

Quantum computing experiments are transitioning from running on physical qubits to using encoded, logical qubits. Fault-tolerant computation can identify and correct errors, and has the potential to enable the dramatically reduced logical error rates required for valuable algorithms. However, it requires flexible control of high-fidelity operations performed on large numbers of qubits. We demonstrate fault-tolerant quantum computation on a quantum processor with 256 qubits, each an individual neutral Ytterbium atom. The operations are designed so that key error sources convert to atom loss, which can be detected by imaging. Full connectivity is enabled by atom movement. We demonstrate the entanglement of 24 logical qubits encoded into 48 atoms, at once catching errors and correcting for, on average 1.8, lost atoms. We also implement the Bernstein-Vazirani algorithm with up to 28 logical qubits encoded into 112 atoms, showing better-than-physical error rates. In both cases, "erasure conversion," changing errors into a form that can be detected independently from qubit state, improves circuit performance. These results begin to clear a path for achieving scientific quantum advantage with a programmable neutral atom quantum processor.

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arXiv2024

Demonstration of quantum computation and error correction with a tesseract code

A critical milestone for quantum computers is to demonstrate fault-tolerant computation that outperforms computation on physical qubits. The tesseract subsystem color code protects four logical qubits in 16 physical qubits, to distance four. Using the tesseract code on Quantinuum's trapped-ion quantum computers, we prepare high-fidelity encoded graph states on up to 12 logical qubits, beneficially combining for the first time fault-tolerant error correction and computation. We also protect encoded states through up to five rounds of error correction. Using performant quantum software and hardware together allows moderate-depth logical quantum circuits to have an order of magnitude less error than the equivalent unencoded circuits.

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arXiv2023

Majorana qubit codes that also correct odd-weight errors

The tetron architecture is a promising candidate for topological quantum computation. Each tetron Majorana island has four Majorana zero modes, and possible measurements are constrained to span zero or two Majoranas per tetron. Such measurements are known to be sufficient for correcting so-called "bosonic errors," which affect an even number of Majoranas per tetron. We demonstrate that such measurements are also sufficient for correcting "fermionic errors," which affect an odd number of Majoranas per tetron. In contrast, previous proposals for "fermionic error correction" on tetrons introduce more experimental challenges. We show that "fermionic codes" can be derived from traditional "bosonic codes" by inclusion of tetrons in the stabilizer group.

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arXiv2023

Fault-tolerant syndrome extraction and cat state preparation with fewer qubits

We reduce the extra qubits needed for two fault-tolerant quantum computing protocols: error correction, specifically syndrome bit measurement, and cat state preparation. For distance-three fault-tolerant syndrome extraction, we show an exponential reduction in qubit overhead over the previous best protocol. For a weight-$w$ stabilizer, we demonstrate that stabilizer measurement tolerating one fault needs at most $\lceil \log_2 w \rceil + 1$ ancilla qubits. If qubits reset quickly, four ancillas suffice. We also study the preparation of entangled cat states, and prove that the overhead for distance-three fault tolerance is logarithmic in the cat state size. These results apply both to near-term experiments with a few qubits, and to the general study of the asymptotic resource requirements of syndrome measurement and state preparation. With $a$ flag qubits, previous methods use $O(a)$ flag patterns to identify faults. In order to use the same flag qubits more efficiently, we show how to use nearly all $2^a$ possible flag patterns, by constructing maximal-length paths through the $a$-dimensional hypercube.

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arXiv2021

Distance-four quantum codes with combined postselection and error correction

When storing encoded qubits, if single faults can be corrected and double faults postselected against, logical errors only occur due to at least three faults. At current noise rates, having to restart when two errors are detected prevents very long-term storage, but this should not be an issue for low-depth computations. We consider distance-four, efficient encodings of multiple qubits into a modified planar patch of the $16$-qubit surface code. We simulate postselected error correction for up to $12000$ rounds of parallel stabilizer measurements, and subsequently estimate the cumulative probability of logical error for up to twelve encoded qubits. Our results demonstrate a combination of low logical error rate and low physical overhead. For example, the distance-four surface code, using postselection, accumulates $25$ times less error than its distance-five counterpart. For $six$ encoded qubits, a distance-four code using $25$ qubits protects as well as the distance-five surface code using $246$ qubits. Hence distance-four codes, using postselection and in a planar geometry, are qubit-efficient candidates for fault-tolerant, moderate-depth computations.

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arXiv2020

Short Shor-style syndrome sequences

We optimize fault-tolerant quantum error correction to reduce the number of syndrome bit measurements. Speeding up error correction will also speed up an encoded quantum computation, and should reduce its effective error rate. We give both code-specific and general methods, using a variety of techniques and in a variety of settings. We design new quantum error-correcting codes specifically for efficient error correction, e.g., allowing single-shot error correction. For codes with multiple logical qubits, we give methods for combining error correction with partial logical measurements. There are tradeoffs in choosing a code and error-correction technique. While to date most work has concentrated on optimizing the syndrome-extraction procedure, we show that there are also substantial benefits to optimizing how the measured syndromes are chosen and used. As an example, we design single-shot measurement sequences for fault-tolerant quantum error correction with the 16-qubit extended Hamming code. Our scheme uses 10 syndrome bit measurements, compared to 40 measurements with the Shor scheme. We design single-shot logical measurements as well: any logical Z measurement can be made together with fault-tolerant error correction using only 11 measurements. For comparison, using the Shor scheme a basic implementation of such a non-destructive logical measurement uses 63 measurements. We also offer ten open problems, the solutions of which could lead to substantial improvements of fault-tolerant error correction.

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arXiv2020

Quantum dimension test using the uncertainty principle

We propose a test for certifying the dimension of a quantum system: store in it a random $n$-bit string, in either the computational or the Hadamard basis, and later check that the string can be mostly recovered. The protocol tolerates noise, and the verifier only needs to prepare one-qubit states. The analysis is based on uncertainty relations in the presence of quantum memory, due to Berta et al. (2010).

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arXiv2020

Beyond single-shot fault-tolerant quantum error correction

Extensive quantum error correction is necessary in order to perform a useful computation on a noisy quantum computer. Moreover, quantum error correction must be implemented based on imperfect parity check measurements that may return incorrect outcomes or inject additional faults into the qubits. To achieve fault-tolerant error correction, Shor proposed to repeat the sequence of parity check measurements until the same outcome is observed sufficiently many times. Then, one can use this information to perform error correction. A basic implementation of this fault tolerance strategy requires $Ω(r d^2)$ parity check measurements for a distance-d code defined by r parity checks. For some specific highly structured quantum codes, Bombin has shown that single-shot fault-tolerant quantum error correction is possible using only r measurements. In this work, we demonstrate that fault-tolerant quantum error correction can be achieved using $O(d \log(d))$ measurements for any code with distance $d \geq Ω(n^α)$ for some constant $α> 0$. Moreover, we prove the existence of a sub-single-shot fault-tolerant quantum error correction scheme using fewer than r measurements. In some cases, the number of parity check measurements required for fault-tolerant quantum error correction is exponentially smaller than the number of parity checks defining the code.

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arXiv2019

Flag fault-tolerant error correction for any stabilizer code

Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grows linearly with the code's maximum stabilizer generator weight. For some common distance-three codes, the recent "flag paradigm" uses just two extra qubits. Chamberland and Beverland (2018) provide a framework for flag error correction of arbitrary-distance codes. However, their construction requires conditions that only some code families are known to satisfy. We give a flag error-correction scheme that works for any stabilizer code, unconditionally. With fast qubit measurement and reset, it uses $d+1$ extra qubits for a distance-$d$ code.

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arXiv2018

Test for a large amount of entanglement, using few measurements

Bell-inequality violations establish that two systems share some quantum entanglement. We give a simple test to certify that two systems share an asymptotically large amount of entanglement, n EPR states. The test is efficient: unlike earlier tests that play many games, in sequence or in parallel, our test requires only one or two CHSH games. One system is directed to play a CHSH game on a random specified qubit i, and the other is told to play games on qubits {i,j}, without knowing which index is i. The test is robust: a success probability within delta of optimal guarantees distance O(n^{5/2} sqrt{delta}) from n EPR states. However, the test does not tolerate constant delta; it breaks down for delta = Omega~(1/sqrt{n}). We give an adversarial strategy that succeeds within delta of the optimum probability using only O~(delta^{-2}) EPR states.

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arXiv2018

Fault-tolerant quantum error correction for Steane's seven-qubit color code with few or no extra qubits

Steane's seven-qubit quantum code is a natural choice for fault-tolerance experiments because it is small and just two extra qubits are enough to correct errors. However, the two-qubit error-correction technique, known as "flagged" syndrome extraction, works slowly, measuring only one syndrome at a time. This is a disadvantage in experiments with high qubit rest error rates. We extend the technique to extract multiple syndromes at once, without needing more qubits. Qubits for different syndromes can flag errors in each other. This gives equally fast and more qubit-efficient alternatives to Steane's error-correction method, and also conforms to planar geometry constraints. We further show that Steane's code and some others can be error-corrected with no extra qubits, provided there are at least two code blocks. The rough idea is that two seven-qubit codewords can be temporarily joined into a twelve-qubit code, freeing two qubits for flagged syndrome measurement.

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arXiv2017

Test to separate quantum theory from non-signaling theories

A Bell test separates quantum mechanics from a classical, local realist theory of physics. However, a Bell test cannot separate quantum physics from all classical theories. Classical devices supplemented with non-signaling correlations, e.g., the Popescu-Rohrlich "nonlocal box," can pass a Bell test with probability at least as high as any quantum devices can. After all, quantum entanglement does not allow for signaling faster than the speed of light, so in a sense is a weaker special case of non-signaling correlations. It could be that underneath quantum mechanics is a deeper non-signaling theory. We present a test to separate quantum theory from powerful non-signaling theories. The test extends the CHSH game to involve three space-like separated devices. Quantum devices sharing a three-qubit GHZ state can pass the test with probability 5.1% higher than classical devices sharing arbitrary non-signaling correlations between pairs. More generally, we give a test that k space-like separated quantum devices can pass with higher probability than classical devices sharing arbitrary (k-1)-local non-signaling correlations.

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arXiv2017

Fault-tolerant quantum computation with few qubits

Reliable qubits are difficult to engineer, but standard fault-tolerance schemes use seven or more physical qubits to encode each logical qubit, with still more qubits required for error correction. The large overhead makes it hard to experiment with fault-tolerance schemes with multiple encoded qubits. The 15-qubit Hamming code protects seven encoded qubits to distance three. We give fault-tolerant procedures for applying arbitrary Clifford operations on these encoded qubits, using only two extra qubits, 17 total. In particular, individual encoded qubits within the code block can be targeted. Fault-tolerant universal computation is possible with four extra qubits, 19 total. The procedures could enable testing more sophisticated protected circuits in small-scale quantum devices. Our main technique is to use gadgets to protect gates against correlated faults. We also take advantage of special code symmetries, and use pieceable fault tolerance.

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arXiv2017

Quantum error correction with only two extra qubits

Noise rates in quantum computing experiments have dropped dramatically, but reliable qubits remain precious. Fault-tolerance schemes with minimal qubit overhead are therefore essential. We introduce fault-tolerant error-correction procedures that use only two ancilla qubits. The procedures are based on adding "flags" to catch the faults that can lead to correlated errors on the data. They work for various distance-three codes. In particular, our scheme allows one to test the [[5,1,3]] code, the smallest error-correcting code, using only seven qubits total. Our techniques also apply to the [[7,1,3]] and [[15,7,3]] Hamming codes, thus allowing to protect seven encoded qubits on a device with only 17 physical qubits.

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arXiv2017

Overlapping qubits

An ideal system of $n$ qubits has $2^n$ dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can "overlap," in the sense that an operation on one qubit slightly affects the others. We show that allowing for slight overlaps, $n$ qubits can fit in just polynomially many dimensions. (Defined in a natural way, all pairwise overlaps can be $\leq ε$ in $n^{O(1/ε^2)}$ dimensions.) Thus, even before considering issues like noise, a real system of $n$ qubits might inherently lack any potential for exponential power. On the other hand, we also provide an efficient test to certify exponential dimensionality. Unfortunately, the test is sensitive to noise. It is important to devise more robust tests on the arrangements of qubits in quantum devices.

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arXiv2013

Universal fault-tolerant quantum computation with only transversal gates and error correction

Transversal implementations of encoded unitary gates are highly desirable for fault-tolerant quantum computation. Though transversal gates alone cannot be computationally universal, they can be combined with specially distilled resource states in order to achieve universality. We show that "triorthogonal" stabilizer codes, introduced for state distillation by Bravyi and Haah [Phys. Rev. A 86 052329 (2012)], admit transversal implementation of the controlled-controlled-Z gate. We then construct a universal set of fault-tolerant gates without state distillation by using only transversal controlled-controlled-Z, transversal Hadamard, and fault-tolerant error correction. We also adapt the distillation procedure of Bravyi and Haah to Toffoli gates, improving on existing Toffoli distillation schemes.

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